Cultivable Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣀⣀⣀⡹⠀⠀⢀⠄⠒⠉⠐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⢲⠀⠀⠐⠀⡁⠀⡨⠸
⠀⠀⠀⠀⠀⡀⠔⠉⠑⠄⡀⠀⠀⣠⠀⠢⡀⠀⠈⠢⠄⡤⠐⢤⠂⠀⠀⠀⠀⠀⠀⠀⠒⠺⠀⠀⠀⠸⢀⠀⠀⠴⠈⢒⠂⠁⠄⠀⢀⠒⠒
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡅⠀⢈⠀⠀⠀⠈⡂⠀⠀⡎⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠀⢸
⠀⠀⠀⠀⠀⠠⣀⠀⢀⡠⠆⠀⢢⣀⠀⠀⣀⠇⠀⠀⢄⡀⠀⢀⡨⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⣠⠀⠀⠃⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠓⡏⢀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠈⡒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣔⠉⠉⠉⠉⠀⠀⠸⠀⠸
⠀⠀⠀⠀⠀⠒⠒⠓⠑⠁⡇⠐⠒⠒⠛⠓⠒⡒⣒⡒⢒⣒⣛⣒⢒⡂⠀⠀⠀⠀⠈⢁⡈⠉⠈⠀⠉⠈⠉⠉⠉⠉⠉⡇⠙⠁⠁⠉⠁⠉⡈
⠀⠀⠀⠀⠀⠀⠀⡠⢌⠢⠣⠦⡀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⣉⣉⣉⣉⣉⣁⠠⠊
⠀⠀⠀⠀⠀⠠⢊⢤⠀⢷⠃⣤⡈⠄⠀⠀⠉⠉⠉⠉⠉⣑⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠃⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢛⢁⣸⡀⣈⣀⣇⡈⣛⠀⠀⠀⠀⡐⠁⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠂⢄⠀⠈⢂⠀⠐
⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠢⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠜⠀⠀⢠⠒⠈⠀⠑⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠃⠀⠀⡔⠒⠁⠈⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠠⠤⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠒⠠⢄⠀⣀⡀⠠⠤⠄⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠈⠢⠀⠈⠁⠲⡆⠄⡀⠀⢀⣀⡀⠤⠤⠄⡤
⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⣀⠤⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠱⡀⡀⢤⠜⠒⠉⠁⡰⠉⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠤⠄⢤⠠⠬⠄⠁⠀⠀⢠⠊⠀⠀⢀⠜⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢏⠑⢎⠀⠖⠈⠕⠀⠀⠙⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠇⠀⠃⡠⠁⠀⠀⢠⠂⠀⠀⠀⠜
⠀⠀⠀⠀⠠⡔⠚⠓⡞⠉⣖⠛⠒⢢⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠁⠄⢘⠢⡀⠘⠔⠆⠠⢀⡀⢠⠃⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠈⡝⠁⡼⠚⣄⠙⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠄⠂⢄⠑⡄⢀⠀⠀⡠⠀⢼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠓⠁⠰⣠⠀⠑⠂⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠦⠀⠜⢠⠇⠀⠀⢌⠰⣉⠆⡃⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠐⠁⠀⠀⠀⠀⠀⠑⠂⠀⠐⠁⠀⠀⠀⠈⠒⠀⠒⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⣾⣿⣿⣿⣦⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⣶⣿⣶⣶⣶⣿⣿⡏⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣽⡦
⠀⠀⠀⣿⣿⣿⣿⣧⣾⣿⣯⣭⣭⣿⣿⣶⡄⠀⠀⠀⠀⢠⡴⠾⠿⠛⣿⣛⡟⡻⣿⠿⠖⢦⡀⠀⠀⠀⠀⠀⣸⣅⣀⣤⣄⣀⣠⠜⢃⣈⣿⣏⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⡄⠀⠀⠈⠁⠀⢀⣀⠀⠉⣩⣇⠈⢛⡀⠀⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠉⢹⣿⣿⠉⠀⠀⠀⠀⠀⠘⢽⡤⢀⠙⡟⢀⠠⠹⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣄⡢⠀⠀⠙⡟⠀⠀⢤⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠈⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠍⠃⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡄
⠀⠀⠀⢀⡀⠀⢺⠏⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⢶⠻⡼⣣⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡁⠐⣠⡤⣶
⠀⠀⠈⣭⠃⠀⣀⣤⣤⣤⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣭⠃⢴⡦⢱⣿⣯⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠙⠖⠋⠀⠹⠆
⠀⠀⠀⢸⠀⣸⣏⣻⣟⣙⣿⡆⢳⡷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⡵⡄⣠⣜⢮⡉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⣠⣾⡃
⠀⠀⠀⢸⠀⠉⣿⣿⣿⣿⡉⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⡗⣿⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣧⡀⣿⣸⡁⠤⣄⣀
⠀⠀⠀⠸⠆⠀⣸⣿⣿⣿⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣼⡷⠘⠛⢀⡀⠀⠉
⠀⠀⠀⠐⡆⠀⣿⣿⣿⣿⡇⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢶⣿⢾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⢷⣶⣤⡄⣶⣶⣿⡇
⠀⠀⠀⠀⡇⠀⢿⣿⠘⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡸⢎⢈⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡀⠸⣿⡿⠋
⠀⠀⠀⣴⣷⡆⣸⡏⠀⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣁⣈⣻⣅⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠻⠦⣁⣠⣴⡶⢤⡄
⠀⠀⠀⢿⣿⡗⣿⠇⠀⣿⡇⢯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠹⣄⠜⠉⡓⣌⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠈⠛⠋⠁⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠾⠂⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⡴⠛⢦⡀⡇⡝⢌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⠀⠀⠳⡾⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⢛⣿⣽⣫⣟⣿⣿⣢
⠀⠀⠀⠀⠀⠀⢐⣋⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢻⡏⠓⠹⠵⠶⠯⠾⠼⡧⠦
⠀⠀⣠⠀⢀⠰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡁⠠⠠⠠⡤⠤⠀⢜⡁
⠀⣀⢰⣾⣿⣷⣿⣯⣷⣮⣿⣾⣶⡆⢀⡀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⢀⣴⣾⣿⣶⣿⣿⡛⣥⣤⡀⠀⠀⠀⠀⠤⠤⠜⢸⡇⠀⠀⣠⣥⡀⠀⢸⡇
⢾⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣇⣨⠆⠀⠀⠀⠀⠀⠈⠙⠦⣔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠤⢿⣿⣧⣦⢼⡇
⠀⠀⢹⡿⡯⣿⢽⣿⣯⣿⢿⣯⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⢿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣬⣙⡶⣴⡆⣴⡴⣦⠾⣉⡄
⠀⠀⠘⣿⣿⣻⣻⣟⣟⣿⣻⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⣙⠿⣏⣵⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⣛⢿⠗⠿⢟⡿⣟⣯⡄
⠀⠀⠀⠻⠿⠿⠿⡿⡿⡿⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠞⠁⠀⢾⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣘⢻⣿⢿⣿⡗⢿⠟⠿⣋⡁
⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⠀⠀⠀⠀⠈⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⣶⡶⣶⠶⡿⠟⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡙⢿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⣿⣌⢿⣶⠤⠀⣀⣀⣠⡄⣠⣶⣶⣶⣶⣶⠟⣡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠨⣷⡹⣿⣿⣿⣿⣿⣧⡹⣿⡿⠿⡛⢩⣤⣶⣾⣿⣿⡿⣫⣾⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⡿⣿⢿⣿⣿⣷⣤⢶⡟⣴⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⢋⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⢰⣶⣶⣶⡆⣶⣶⣶⠰⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⡟⣵
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣇⢿⣿⡆⡟⣴⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⣿⣿⢏⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠸⠿⠿⠿⠇⢻⣿⣿⣿⡘⣿⡇⣼⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⢏⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢋⡴⢟⣋⣭⣝⡛⢷⣝⢿⣿⡇⣬⣤⣭⣭⣝⣛⠿⢏⣾⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢏⣼⣿⢟⣛⡻⢿⣷⡙⣿⣿⡇⣿⣼⣼⣧⡿⠿⢿⡜⣿⣿⣿⣿⣿⠏⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣿⢱⣿⣿⣿⡎⣿⣷⢙⣛⣣⣿⣿⡟⣱⡾⠿⢷⣦⢻⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡸⣿⣦⡻⠿⢟⣱⣿⠏⠾⠿⠿⠿⠿⠱⣿⡰⣿⠇⣿⡇⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⡌⠻⠿⢿⠿⠟⢫⣾⣿⣿⣿⣿⣿⣷⠙⠿⣶⠾⠋⣼⣿⡿⠃⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢠⡶⠂
⠀⠀⠀⠀⠀⢴⣾⣾⣿⣤⣶⣶⣿⣔⢷⡀⠀⠀⠀⠀⣶⣟⣧⡘⠂⠀⠀⣀⣤⣤⣤⣤
⠀⠀⢀⠀⠀⠺⣻⠻⠛⡾⠏⢿⣾⣿⡟⣯⣵⠷⣦⣼⣿⣿⢈⣁⣀⠀⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⣼⡿⢦⠆⢘⣷⣾⣖⢲⣶⣤⣷⣿⣯⢙⣯⣒⣽⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣰⣶⢦⠀⠀⠀⠀⠀⠀⠠⡇
⠀⣂⣗⡆⠲⣏⠹⠿⣿⣾⣿⣾⣏⠉⢻⡃⢉⠹⡯⡀⢸⣿⣿⣧⣼⣿⣯⣷⣿⣿⠱⡬⢿⣿⡟⠘⠷⠤⠀⠀⠀⠄⠘⠁⣶
⠀⠙⢺⣷⣟⢳⡖⢰⣿⣿⣿⣷⢺⡷⣾⣿⣮⣧⣃⣳⣿⣯⠉⣉⣘⣛⡉⠉⠉⠉⠀⠁⢼⠿⢿⣶⣀⠀⠀⠰⣦⡟⠀⢸⣿
⠀⢀⠀⠈⠟⢀⣿⣻⣿⣿⣿⣷⣌⡅⠙⠿⣿⡧⣝⣿⣾⠿⣾⣿⣿⣿⣷⡴⠶⣶⣦⣿⣿⣶⣤⡏⠀⣬⠉⡔⠺⡷
⠀⢸⣶⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣄⣼⣯⣿⣿⣿⡇⣾⣿⣿⣿⣿⣝⢿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⡅⠄⠀⠀⠀⠀⠀⠀⠔⠭⠀⠦
⠀⠉⠉⠁⠉⠉⠻⠻⠎⠿⣿⣿⣿⣿⣿⣿⣛⠛⠿⣿⡿⠿⠿⢿⣿⣿⣿⣺⣶⣾⣿⠋⠉⠉⠉⠝⠉⠻⣿⣏⣹⣿⣿⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢻⣿⣁⣏⣀⣉⣙⣿⣹⣇⣭⣤⣤⣶⣽⣿⣿⣿⣿⢤⣤⡤⠦⠤⠄⠀⠀⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠷
⠀⠀⠀⠀⠀⠳⣴⣿⣷⣤⣯⣄⠈⠛⠛⢻⣿⣿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠷⠦⠀⠐⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠋⠙⠛⠛⠃⠄⠀⠀⠘⠻⠍⣙⡛⠁⠉⠉⠀⠉⠉⠉⠁⠉⠚⠛⠛⠀⠠⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⡄⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣶⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣎⢻⡷⠦⢀⣀⣠⣤⡴⣠⣶⣶⣿⣿⣿⡿⢋⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡘⣿⣿⣿⣿⣿⣿⣎⢿⣿⠿⢟⠋⣩⣶⣾⣿⣿⣿⡿⢋⣾⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣿⣿⠿⢛⣠⣴⡾⢋⣾⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣫⣵⣾⣿⣿⡟⣱⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⣿⣿⢏⣼⣿⣿⣿⣿⣿⡟⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣝⢿⣼⢋⣭⡄⣿⣿⠏⣼⣿⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⠏⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡻⢈⣇⠚⣛⣵⣿⢏⣾⣿⣿⠟⠻⣿⡟⣴⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣝⢿⣿⢋⣭⡄⣿⣿⠟⢿⡇⣾⡇⣹⣶⠟⣻⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡛⢈⣇⠛⣛⣴⣿⢡⣿⠌⣧⣛⣵⠿⠴⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⠏⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣍⢻⣿⢋⣵⡆⣿⡜⢋⣼⣿⣿⡐⢶⣷⡮⢻⣿⣿⢇⣾⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣛⣈⣇⣛⣋⣴⣿⣿⣏⢴⣶⣦⡝⣶⣶⣶⣿⣿⡏⣼⣿⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⢛⣿⡋⣵⣶⣍⠳⣮⣥⣶⣿⣿⣿⣿⡿⣰⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠘⠛⠛⠛⠈⠉⠉⠘⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠋⠘⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠒⠂⠀⠀⠀⠀⠉⠁
⠀⠉⠁⠈⠈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢔⡆⢭⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉



⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠂⡀⢒⠀⢂⡀⠀⣀⡐⢀⡀⠐⠀⠂⠀⢀⡀⠀⠀⠂⢀⡀⠀⢐⠀⠈⣀⣀⡀⣀⡀⢀⢈⣂⣠⣀⡀⢠⣌
⣃⡀⢈⣛⣚⡈⢛⣃⠀⠘⠛⣁⣚⣛⡊⠘⣏⣙⡛⡀⠉⢋⣀⣙⣃⣉⢙⣃⡀⠛⢢⣈⣻⡒⠂⣛⣀⣙⠁⠡⠛⠁⠀⢹⡉⢬⠙⠃⡬⠯⠅⢹⣯⢍⠉
⠆⠀⠀⠦⠌⠁⠀⢩⡅⠀⠀⠹⢷⡌⠀⠀⠉⠽⢥⡅⠀⡀⠹⣭⠁⠀⠈⠭⠥⠀⠀⠶⠧⠈⠀⠹⠆⠀⣀⠰⠗⠀⠀⣘⠟⠂⠀⠈⡛⠃⠀⠀⡛⠂
⠀⢀⣽⠖⠀⠀⠀⠲⠷⠄⠀⠀⠀⣦⡀⠀⠀⠸⠲⠶⠄⠀⠀⡠⢶⡄⠀⠀⠾⠷⠦⠀⠀⠼⣦⠀⠀⠀⠛⠳⠀⠀⠈⠿⠳⢀⠀⠘⠛⠃⠀⣀⠛⠁
⣤⡆⠀⠀⠀⠀⢠⣌⡁⠀⠀⠀⠀⣤⣷⣦⡀⠀⠀⢠⣶⠶⣄⠀⠀⢀⣴⣦⣤⡄⠀⠀⠀⣶⣼⣄⠀⠀⢈⣅⣀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠰⣿⣶⣦
⡉⠙⣡⠆⠲⠄⠈⣩⣉⠡⢤⠋⠀⠠⠉⢀⣁⠀⠀⠀⢘⣀⠐⠒⣀⡐⠧⠀⢀⡄⠀⡀⠀⠉⣉⠃⣤⠀⠉⠍⢩⠄⠀⢀⠉⣉⣉⡃⠤⠀⠤⠀⠀⢰⡀
⣿⣿⣿⣾⣷⣤⣦⣾⣿⣷⣦⣿⣼⣷⣾⣿⣿⣿⣷⣶⣾⣿⣧⣥⣿⣷⣶⣷⣴⣿⣾⣿⣦⣤⣿⣿⣷⣾⣾⣿⣿⣶⣶⣿⣷⣾⣯⣽⣿⣶⣶⣾⣴⣾⣿
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⡿
⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⣿⠉⠉⠉⠉⠛⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⣿⠀⠀⠀⢀⡀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⣿⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⢹⡄⠀⠀⠈⠉⠳⢦⣄⠀⠀⠙⣧⠀⠀⠀⠀⠀⢿⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠉⠳⣄⠀⢸⡆⠀⠀⠀⠀⣸⠷⢤⣤⣤⣤⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠈⢷⣸⡇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣠⣿⡇⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠛⠛⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠛⠛⠛⠀⠀⠀⣶⣿⡷⣶⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⡇⠀⠈⢁⡙⠿⠟⡈⠉⠀⣀
⠀⠀⠀⠀⠀⣾⣿⣿⡦⠀⢠⣴⣿⣦⡄⠀⠀⣴⣿⣧⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠉⠀⠰⠀⠉⠀⢸⣿⠁
⠀⠀⠀⠀⠘⠿⣿⡿⠟⠀⠸⢿⣿⡿⠇⠀⠐⢿⣿⡿⠇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣀⣴⣶⣾⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠂⠀⠀⣭⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣷⡄⢾⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣻⢿⡟⢻⡿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣷⠀⠀⠀⠐⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣯⣿⠿⡿⢿⢿⣿⣽⣿⣿⢯⣿⡿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠀⠀⢠⣤⣾⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⣴⣾⣿⣶⡄
⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣶⣤⡤⣤⣄⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣠⣤⣤⣶⣶⣶⣶⣶⠀⠀⠀⠀⣻⣿⣿⣾⣿⣿⡷⣳⣦⣤⣤⣴⣶⣶⣶⣾⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣛⣿⡟⣻⡟⣾⣿⣿⣻⣿⣿⣟⣿⣿⣿⡃
⠀⠀⠀⠀⢸⣿⣿⣍⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⡟⣽⣿⣿⢯⣿⣿⡿⣽⡇
⠀⠀⠀⠀⢈⣿⠷⣏⠿⣹⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣷⣧⣿⣾⣿⣯⣿⣿⣿⣻⣿⣿⡿⣽⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣾⡿⣿⣹⣿⣿⣿⣾⣮⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠿⠿⠿⠒⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠀⠀⠷⠙⠿⠞⠳⠾⠷⠷⠛⠿⠛⠿⠛⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠉⢲⠀⠀⠀⢀⢤⠔⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⣄⠀⠀⠤⠀⡃⠀⢑⠌⠄⠄
⠀⠀⠀⠀⠀⠀⢀⡔⠒⢄⠀⠀⠉⠉⠉⡩⢍⠀⠀⠀⢅⡀⢀⣀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠤⡇⠀⠀⠀⢼⠀⠀⠀⣀⠑⠤⠭⠊⣀⠀⠀⡠⠤⠄
⠀⠀⠀⠀⠀⢜⠉⠀⠀⠀⠙⠄⠀⡴⠊⠀⠀⠑⢆⠀⠀⢠⠊⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⡅⠀⡇⠀⠀⠀⠈⠃⠀⠀⠁⠀⠐⠀⠀⠈⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⢢⠀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⡇⠀⡇
⠀⠀⠀⠀⠀⠈⠑⢦⣠⠔⠉⠀⠀⠙⠲⣄⡠⠒⠁⠀⠀⠈⠒⢄⣠⠖⠊⠀⠀⠀⠀⠀⠠⠚⠁⠀⠃⠀⠀⠀⠀⠈⠢⡀⢀⠤⠾⠤⠤⠄⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⢀⣀⣸⣸⢠⢦⠀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣸⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⣀⢀⡀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠠⠆⢠⠁⢀⡀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⡴⠊⢎⢋⠜⠑⢄⠀⠀⠸⣄⣈⣁⣀⣀⣈⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠤⠤⠤⠤⠤⠤⠐⠁
⠀⠀⠀⠀⠀⢠⣊⠴⡆⠈⡿⠀⡶⢌⣆⠀⠀⠀⠀⠀⢀⠠⠠⠕⠀⠀⠐⠂⠀⠀⠀⠀⠀⠂⠀⠀⠣⣀⠀⠈⠀⠀⠑⠒⢄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢘⡡⠄⠧⠠⠧⠤⠇⠤⢝⡀⠀⠀⠀⢸⠁⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⢄⠀⠀⢣⠀⠈⠁
⠀⠀⠀⠀⠀⠧⠠⠠⠠⠤⠠⠤⠠⠤⠤⠕⠀⠀⠀⠈⠢⠄⠠⠠⠄⠤⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠂⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⣀⣀⣀⡸⠀⠀⢀⠔⠒⠉⠉⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣀⣀⣀⣈⠇⠀⠀⢠⠔⠊⠉⠑⠂⡄
⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠠⠠⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡉⠉⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠸⠠⠂⠀⠀⠀⣀⠤⠝⠒⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠑⡄⠀⠀⢈⣣⠭⠖⠒⢒⠟⠉⠉⠁⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠊⠀⠀⠀⠀⠀⠀⢀⣃⣀⣀⣀⣘⣒⠊⠋⠀⠀⠀⡰⠋⠀⠀⢀⠔⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢠⠤⣀⡎⢱⣀⠤⣄⠀⠀⢤⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⡇⠀⢹⠀⢠⠀⢀⠞⠀⠀⠀⣠⠋⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⣘⣄⡈⣧⣼⢁⣴⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⣇⠀⠀⣇⢸⠀⠎⠀⠀⠀⡰⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠫⠄⣠⠼⣄⣨⠧⣄⠠⠝⠀⠀⠀⠀⠀⠀⠂⠘⠐⠁⠀⠀⠀⠀⠀⠀⠀⠰⡫⠖⠒⠒⠬⡓⠀⠘⠉⡁⡒⠂⢄⠰⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢰⢁⡰⡇⢹⢆⡈⡆⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠁⠑⡄⢱⠄⠜⠀⢠⠖⣀⠲⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⡜⠀⠉⠀⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠘⢄⠑⠠⠒⢁⡼⠠⠀⠠⢆⠨⠤⠇⡼⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⣸⣿⡇⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢀⠀⠀⠀⢀⡀⠀⢻⣧⠀⣿⡇⠀⣠⡶⠁
⠀⠀⠀⠀⠐⢦⣤⡘⣿⣷⠀⣿⣿⠃⣠⣶⣿⠏⠀⠀⠀⠀⠰⣦⡀⠀⣿⣿⠀⣴⡏⠀⢀⠀⠀⠹⣶⣄⠻⣇⣿⢃⣼⢟⣥⡴⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⡇⣿⡟⣼⡿⢛⣁⣀⡀⠀⠀⠀⠀⢻⣷⡄⢿⡿⢸⡿⣡⣴⠃⠀⠀⢀⣈⠛⠷⠝⢘⢜⣿⣿⣭⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣽⣼⣕⣽⡾⠿⠋⠁⠀⠀⠀⠐⢦⣤⡙⢿⣸⣇⣟⣷⠟⠁⠀⠀⠀⠉⣩⣽⠿⣶⠛⣴⠿⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠐⠚⠛⣻⠞⠋⠿⡓⠶⢄⡀⠀⠀⠀⠀⠀⠀⢬⣭⣷⡫⢬⡯⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣿⠀⣸⠀⠀⠀⣠⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⢤⡀⠀⣿⡇⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢾⢸⠀⠀⣠⠀⠀⢄⡀⢻⣷⠀⣿⠇⣿⠀⣴⡾⠁⠀⠀⠀⠀⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠈⢿⣆⣿⢣⣾⠏
⠀⠀⠀⠠⣤⣤⡀⠸⡸⢀⢎⠇⠀⠀⠀⠙⠷⣝⢧⢹⠰⣣⠾⠋⠀⠀⠀⣦⣤⣀⢻⣿⣿⡿⢀⣠⣤⡖⠀⠀⠙⠲⣿⣿⣿⡥⠖
⠀⠀⠀⠀⠈⠑⠢⠅⢀⣄⠁⠠⠀⠀⠀⠠⠶⠦⣫⠷⠆⡑⠒⠒⠒⠂⠀⠘⢿⣿⣿⣿⣿⣷⣿⣿⠿⠁⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠈⠁⠀⠀⠀⠀⠐⠾⠿⠿⣻⣿⠿⠿⠷⠦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⣷⡀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⢀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⣿⡇⣰⣿⠟⣁⣤⣶⠖⠂⠀⠘⣶⣤⡀⠀⣿⣿⡇⢀⣠⣴⡖⠁⠀⠀⠀⠙⢯⡒⠤⡀⠀⣇⠀⡇⠀⡰⠋⣰⠃
⠀⠀⠀⠀⠒⢶⣼⣧⣟⣷⡾⠟⠋⠁⠀⠀⠀⠀⠘⢿⣿⣆⢿⡿⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠱⢄⠘⠄⢻⢀⠇⠜⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠚⠙⣿⡛⠶⠶⠦⠤⠀⠀⠀⠀⠤⢤⣬⣿⣾⣷⣿⣥⣶⠶⠄⠀⠀⠀⠀⠀⢀⣀⠀⢑⠂⢈⡌⡰⠊⠁⣤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠈⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢈⠽⠉⠳⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠉⠀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢢⠀⠘⣦⠀⠀⣶⣮⣿⣿⣷⣯⣭⣉⣩⣽⣿⣷⣦⣭⣭⣽⣿⣯⡽⢉⠉⢢⠀⠀⠀⠂⠁⠀⠀⠀⠈⡐⠄
⠀⠀⠀⠀⡀⠀⣄⠀⢱⣄⠀⢳⡀⠘⣷⡀⢿⣾⣿⣽⣿⣿⡟⢋⣉⣉⡉⢉⣉⣉⡛⢻⣿⣿⣿⣼⣷⠟⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠳⡀⠸⣦⠀⢻⣦⠈⢳⡄⠘⣷⡀⠙⠻⢿⣿⣿⡄⠈⠛⠹⡇⠈⠙⠋⠁⢸⣿⡿⠿⠛⠁⡰⠁⠀⠀⠀⢠⠖⣛⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢧⡄⠹⣧⠀⢺⢧⠀⢿⣄⢹⢳⠀⠀⠀⠙⢼⣧⠀⣀⣶⣦⣤⣂⣀⠀⣼⡽⠁⠀⠀⡐⠁⠀⠀⠀⡰⠁⣼⣿⠅⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠈⢿⣆⠸⣧⡀⠉⢷⣈⠟⣻⡟⠀⠀⠀⠀⠀⣿⡈⠉⢛⣿⣟⠋⠉⢀⣿⠀⠀⠀⠀⠙⠢⣄⢠⠎⢄⣼⣿⠃⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢻⡣⢼⠳⡶⠃⢩⣾⠋⠀⠀⠀⠀⠀⣠⣿⣷⣦⣤⣤⣤⣄⣶⣿⣯⡀⠀⠀⠀⠀⠀⠀⡏⣸⠞⣹⢃⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠛⠛⢿⡿⢧⢀⡤⢤⣤⢴⢻⣇⠙⠿⠿⣿⡿⠿⠛⢀⣿⢻⣤⡴⠠⣄⠀⡔⢤⡿⠋⠉⠂⢄⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠷⠛⠋⢳⣾⣷⡸⣆⣛⠷⣄⠀⠀⠀⢀⡴⢟⣃⡟⣼⣷⣷⠋⠙⠛⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠖⠀⠠⣤⡀⢿⣿⣷⠉⠉⠙⠛⠳⣄⡴⠛⠚⠉⠉⣹⣿⣿⠇⢠⠶⠂⠀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠙⡇⢸⣿⣛⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⣽⣿⡻⢀⠀⠀⠀⠀⠨⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡂⠀⠀⠀⠀⢿⠀⣯⣭⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣿⣇⣾⠀⠀⠀⠀⠐⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⣶⣀⣀⠀⢝⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠷⠖⠲⣶⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠐⠋⠩⠥⣾⠶⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⠀⠈⣉⣉⣉⣙⣿⣋⠉⠉⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣾⣟⡁⢀⣈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣴⡿⠟⠋⠉⠉⠙⠛⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⣝⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣀⣀⣬⣿⣿⣦⣄⡀⠀⠠⢤⣀⣀⣀⣀⡀⠀⠀⠀⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣤⣭⣭⣉⣉⣉⣉⣉⣩⣭⣭⣾⣿⣿⣿⣿⣷⣶⣦⣬⣭⣿⣖⣒⣀⣀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⣴⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠁⠈⠉⢁⣘⣿⣿⣿⡟⠛⠀⠀⠀⠀⢀⡀⢀⣾⡿⠛⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⣿⣿⣦⠀⠀⢻⣿⣿⣿⣿⡇⢸⡀⠀⣠⣤⠘⠓⢸⣿⣶⣿⡶⠆⠁⡀
⠀⠀⠀⠀⡠⠐⠀⠈⠀⠀⠀⠀⢀⡀⠀⣀⡀⢀⣿⣿⣿⣿⣄⣀⣀⣿⣿⣿⣿⣧⣾⣄⠀⠙⣿⣷⣤⣤⣿⣿⣷⣶⣶⣗⣀⠄
⠀⠀⢰⣏⠀⣾⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣈⣻⣿⣿⣿⡟⣿⣥⣶⣿⣿⣿⣿⣿⣥⣤⣀⣿⣿⢰⠀⣿⣿⣯⣯⠰⢀⣴⣲⠖⡃
⠀⠸⠿⠯⣭⠄⠶⢷⡨⠉⠀⠀⠀⠀⠉⠉⠀⠉⢙⡛⠛⠛⠋⡛⡛⠋⠉⠙⠋⠉⠙⠋⠛⢛⠉⡉⠀⠀⠉⠉⠙⢃⠀⠁⠀⠀⠀⠠⠀⣀
⠀⠀⠀⢀⣂⡀⢁⣀⠀⠠⣀⢀⢠⣠⠄⡁⣄⡀⡡⣀⣄⠤⠀⠀⠀⠀⢠⠀⢀⠀⠀⡈⡀⠄⠄⢀⠀⠀⠀⠠⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⡈
⠀⠀⠘⡧⣥⠙⢠⠶⠁⢹⣇⡛⡒⣍⣳⡇⢠⣰⡗⢁⡺⣔⡧⠀⢰⠉⠋⢃⠛⣀⠇⢀⣴⢏⠉⡻⠰⢏⡔⢩⣬⣧⣘⡀⠁⢐⡄⢷⡃⢂⣀
⠀⠀⠠⣿⢸⢡⣞⠞⢠⡈⢻⡄⣰⣍⡏⢸⠊⢹⡇⠪⡽⢙⡿⣶⡆⠙⢰⢢⠟⠟⢠⠟⢙⣶⣋⡁⠜⣿⣌⡹⠄⢰⡴⣄⢠⢼⠁⢻⠿⠉⡉
⠀⠀⠐⣿⢸⡷⣻⠨⣄⣽⢿⡀⣷⣌⡷⠲⡗⢸⣧⣸⡵⠌⣃⢤⣹⡣⡆⣼⢖⠃⢰⡖⠁⠹⢘⢹⣇⣉⣮⠁⢈⡑⣚⣉⠙⣀⢠⡼⠳⢒
⠀⠀⠤⣯⣸⡇⣻⢰⡇⠀⣿⠂⠻⢮⣧⣈⣟⢼⡅⣽⣟⠈⡗⣘⢩⡅⠜⣩⣻⡇⢸⡇⠾⢧⣄⢨⣿⣡⢯⡿⠸⡷⣩⣯⡵⠈⠟⠶⠃⡤
⠀⠀⠠⠿⢤⣀⣹⡈⣁⠃⣿⠐⠶⢓⡷⠼⠇⢠⡇⣺⣁⣘⣇⠐⢱⣍⡎⠉⢹⡃⢜⡃⠶⡫⠅⢼⣯⠘⢡⣿⣸⡟⣩⣟⡛⢘⡟⠸⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠚⠓⠦⠤⢤⣧⣤⣄⣘⡇⠈⠁⢸⣟⠀⠉⠛⢘⡱⠈⠥⠀⢸⣟⠀⣀⣷⣸⡏⣰⠏⠋⢸⡟⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠓⠶⠦⠤⢼⣅⡀⣀⠀⠰⡿⠀⠀⠁⢸⡏⠁⠑⠒⢺⠇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠓⠲⠰⠦⠬⠧⣀⡀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡄⣿⢸⣸⢀⣀⡇⢀⢸⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⡆⠀⣸⣼⣿⣷⠀⠀⠠⣀⣸⣇⣿⣰⡀⠀⣸⣿⡿⠻⣿⣿⠿⠷⣻⣿⣿⣘⢿⡄
⠀⠀⠀⠀⠀⢀⣆⣼⣿⣿⣇⡄⢸⣿⣿⠻⠀⠀⠀⡿⢿⣿⣿⡿⢀⣀⡀⣸⠁⠀⠘⣯⠼⣷⣏⣿⢗⣯⡘⣧
⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⢳⠇⠀⢿⡏⠀⣞⣄⣤⠀⠘⣿⡏⠀⠀⠭⠉⣧⠀⠂⠄⢉⣿⠉⣦⣷⢾⡽⢏⡁
⠀⠀⣼⣿⣿⣿⡿⠿⠟⠻⠟⠀⠀⣸⠀⡀⢻⣽⠇⣀⠠⠻⠿⠦⢶⣦⡏⠀⢀⣠⣄⣀⡟⣾⣿⠇⢸⡿⠴
⠀⠐⠛⠉⢡⠀⠀⠀⠴⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠃⠉⠄⠠⠟⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠘⠛⠓⠆⠈⢉⠴⢳⡦⠘⣲⣄⡀⠀⣄⠀⠀⠀⠀⠀⣤⣀⡀⠀⣤⠀⠲⢦
⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠀⠐⠲⠶⠴⠌⠒⠚⠃⠀⠷⠒⠚⠃
⠀⠀⠀⠐⠚⠻⢷⣶⣦⣼⣆⡄⢸⣆⢠⢠⣦⣠⠀⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣶⣿⣿⣿⣷⡿⠾⣯⣷⣿⠀⠀⢠⣀⠀⢠⣷⣦⢀⣷⠀⠀⠀⣆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠟⣿⡟⠿⠿⢿⡄⢘⢸⢿⣿⣿⣿⣿⢈⣹⡇⠀⢰⢼⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠀⠁⠀⠀⣭⣭⠭⣿⢿⡥⣤⣶⠁⠸⢟⣯⣉⣡⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠁⠛⠛⠉⠛⠛⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠇⠛⢷⠾⠶⢠⣶⣤⣶⣿⣿⣷⡀⠀⠘⠋⠛⠛⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠮⡹⢿⣿⣿⠿⢟⠛⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠓⠲⢤⣃⡒⡈⠹⣧⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⣀
⠀⠀⠀⢰⠀⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⡐⠀⠄⠀⠀⠀⠀⠀⢀⠀⡎⠈⢠⠀⢀⠀⡀⠀⠀⠀⠀⢀⣀⡀⠐⣄⠄⠒⠢⠓⠉
⠀⠀⠀⢀⠀⠄⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠶⠁⠀⠀⠀⠀⠀⠀⠘⠁⢤⠊⢈⣁⣀⣀⡠⣤⢄⣤⣤⠤⠄
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠐⠄⠈⠀⢀⠠⣄⠢⠆⠛⠓⢋⠁⠀⡉⠀⡀⠐⡨⢀⠁⠉⡐⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⣔⠀⠈⠀⠀⠙⠂⠰⠈⢠⣀⠶⢤⢂⠠⠀⡀⠐⡀⠄⡀⠐⠁⡀⠀⡠⠂
⠀⠀⠀⠀⠀⢠⠎⠐⠅⠀⠀⠀⠀⠀⠀⠀⠬⠃⡀⣠⠀⠀⠀⠀⠀⠀⠀⣌⠀⢀⡃⠲⠄⢄⢈⠠⠈⢀⠄⠈⡀⠈
⠀⠀⠀⠀⠠⠃⠀⠀⠸⡄⠀⠀⠀⠀⠠⠠⠒⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠉⠙⠙⠀⠀⠀⠀⠘⠂⠒⠄⠠⢎⣀⡐⠀⠄
⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⢀⠀⠀⠀⠀⠁⠀⠁⠉⠉⠀⠂⠀⠀⠀⠁⠀⠀⠐⠈⢄⠂⠤⢉⠚⠠⡖⠠⠉⠂⡈⢑⠢
⠀⠀⠀⠀⢠⡀⠀⠄⢸⠂⠈⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡴⢡⠜⠀⣉⡐⠢⠄⣀⠈⠅⡒⠑⢄⠒⠄⡐
⠀⠀⠀⠀⠈⠀⠀⠀⣠⠄⠒⡹⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⢀⠔⠪⡔⠢⢌⡁⠐⠄⡙⢄⠀⠤⠈⠑⠤⠑⠀⢕⡢
⠀⠀⠀⢀⢠⠆⠂⢁⠤⠒⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠈⠙⠍⠑⠤⠁⡂⠡⠑⠢⢄⠁⠬⠕⠒⠠⡉⠠⠈⠐⠠⠂
⠀⠀⠀⠀⣀⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⣠⢋⡠⠋⢀⠱⠀⣁⠂⠤⢁⠤⠈⠒⢈⠓⠄⡀⠠⣈⠀⠤⡈⠁⠀⡁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⢊⢁⠛⠠⡈⠢⢁⠂⠀⡁⠢⡀⠑⠈⠑⠢⡉⠂⢈⡢⢀⠀⠐⠨⡢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠘⠤⠉⠢⡀⠠⠄⠑⠢⠈⠀⠈⠒⠀⠀⠀⠂⠁⡀⠈⠂⠁⠢⠀⠈⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⣀⣤⣖⣰⣤⢤⠤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠲⣄⠀⣷⢸⡇⢰⣶⣶⣿⣶⣶⣆⣀
⠀⠀⠀⠛⠛⠛⠛⠿⠴⠿⢿⣿⣿⣿⣶⣦⣄⠀⠀⠀⢠⣤⡀⢰⣾⣿⣷⣶⣤⠀⠀⠀⠀⢀⣾⢸⣏⣷⢘⠀⢸⣾⡗⣼⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣷⡀⠀⡂⢀⣴⡶⣶⣤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣜⣓⢄⠀⣿⣿⢛⣉⣉⣠⣹⡁⣿⣿⣋⣲⣹⣧⣥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣂⢃⠈⢿⣿⣿⣯⣿⡉⠀⠀⠀⠉⠙⠛⠛⠻⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⠹⣿⣿⣍⢦⣼⣿⣿⣿⠿⢟⠛⠶⠦⣄⣄⣀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢈⠀⣿⣿⣷⢸⣿⣿⣿⣿⣶⣾⣿⣷⣶⣤⣄⡁⠘⠻⠟⠂⢀⣃⡄⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠀⣽⣿⣟⣼⣿⣿⣿⣿⣿⡿⣃⡿⣿⣿⣿⣿⣷⡄⠀⢸⣿⢽⣿⣿⠿⣷⣌⡆
⠀⠀⠠⠄⠀⣀⠀⠀⠀⠀⢿⣿⣿⣧⣠⣿⣿⣿⣻⣿⠀⠿⠿⠿⢇⣿⣿⣿⡒⠬⣿⣻⣷⡀⣹⣿⣻⣿⢇⠑⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠒⠦⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦⠘⣿⣛⡃⣛⣉⡴⢿⣦⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⡏⡀⣿⣿⣧⣿⠻⡿⠿⠛⠁⠀⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣿⠇⠀⣿⢛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢼⣿⣷⠾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢀⠸⡀⠀⠸⠘⡀⣀⢤⠀⠀⠀⠀⠀⠀⠀⢠⣝⡾⢷⣫⣤⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠈⠁⠀⠀⣴⣑⣁⠈⠀⠈⢣⣄⠙⡄⠀⢘⡿⣷⡾⢿⡛⠯⠝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡀⠀⢠⠀⡈⡄⢰⢀⣀⣄⢺⣷⢷⡆⠁⠠⠐⡀⡂⡏⠀⠉⠉⠉⠉⠋⣿⡟⢻⠀⠀⠈⢹⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠰⢃⢀⡠⠐⠉⠀⠀⠀⢀⠤⠿⠚⠂⠑⡃⣚⣿⡠⢄⡅⠀⠀⠀⠀⠀⠀⣿⡧⢸⠀⠀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡶⠤⠀⠀⠀⠠⠄⠀⠀⣀⣀⢀⡤⠖⠉⠀⠀⠉⠑⠫⢧⣤⡀⠀⠀⠠⣻⡅⢸⠀⠀⠀⠚⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⢐⠀⠀⡎⠠⠂⢀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣶⠀⠀⠀⠀⠀⠀⠀⣤⣽⡷⡤⠀⠀⢹⡇⢸⠀⠨⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠂⡋⠠⠁⠀⠐⠀⠀⠀⠀⠐⠂⡰⠁⠛⠻⠀⣾⢒⠶⡲⢦⠀⠿⠿⠙⣽⡀⠀⣸⣇⢸⠀⠀⢠⠒⠟⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢠⣆⣀⣈⠁⠊⣁⣀⣀⣀⡀⣰⠃⠀⠀⠈⠀⢸⣯⣶⣡⣾⠀⠐⠖⠂⠙⣿⣿⣿⣿⣿⣷⣃⣾⣷⠾⣷⣷⢦⡀
⠀⠀⠀⠀⠐⠀⠀⢀⡠⢒⠘⠊⠉⠉⠭⢙⣳⣧⣍⠀⠀⠈⠉⠻⠀⢰⠖⠒⢿⢳⣶⣴⠖⣾⡗⠒⡂⠑⠒⡛⠋⣛⡛⣛⠛⠓⢈⣕⡺⣿⣿⣞⢧
⠀⠀⠄⠀⠀⠀⠀⠀⣛⠙⠙⠚⠓⠺⢶⠋⠁⠀⢹⢀⠀⠀⠀⠀⠀⢸⠁⠆⢸⣿⢹⡿⣛⢽⠉⡞⢹⠀⠀⡏⠉⣿⡏⣹⠉⠉⠉⠉⠁⠻⢯⡁⠣⡀
⠀⠀⠀⠴⠤⣤⣤⣴⣟⣰⠀⡀⠀⠀⠰⠀⠉⠁⢸⣸⣤⣄⠴⠴⠀⣸⣦⣀⠾⠿⠾⠧⢥⣼⣶⣀⣲⣀⣺⣷⣴⣿⡷⠿⠿⠶⠶⠶⠗⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠀⠁⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠔⠈⠀⣙⢑⠄⠳⠆⠸⠦⠄⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠄
⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣇⣀⢀⣭⡥⠤⠤⠤⠶⠾⠶⠄⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣤⣼⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣦⣹⣿⡛⠉⠉⠉⡐⠲⠢⢈⡴⣷⠤⡄⠀⠀⠀⠀⠀⠈⠿⠗⠖⠒⠒⠒⠂⠒⠲⠄⠚⠋⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠋⣡⢽⡲⢄⢀⠐⠈⠂⠑⠌⠳⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠯⣐⠬⣕⡒⠤⠭⢭⣀⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠪⠍⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠈⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⠀⠀⣾⠀⢠⣿⣿⡆⠀⠀⢀⣀⣀⣀⣀⣤⣤⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠀⠀⡴⣄⣥⣹⡇⠀⠀⠀⠀⢷⢀⡘⣿⡿⠛⠛⠚⠩⠭⠁⠁⣥⣄⡀⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠰⢞⢋⢋⢫⢫⠋⠫⠛⠻⠻⠶⠟⠛⡋⠁⠀⠀⠀⠀⠸⣌⡩⠟⢃⣰⠦⢄⠀⠀⠐⠙⠬⠳⢌⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠬⢄⠒⡒⠂⠑⠁⡠⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠙⢆⣰⠯⣒⠭⣒⠨⠥⢐⣂⣐⠒⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠀⠠⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣌⣉⡒⠉⠁⣒⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣤⣤⣤⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠒⠒⠀⠀⠰⠆⠀⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠰⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣎⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢊⠀⠀⠈⡄⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠘⢄⠀⠄⠀⠠⠄⠀⡀⠀⠀⠀⠀⢀⡄⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠃⠀⠀⠈⠁⠀⠀⢨⠗⢄⠘⠁⢠⡄⠀⡆⠀⠀⠰⢣⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⠈⠤⠀⠀⠀⠂⠀⢀⠴⠳⠀⠀⠀⢱⢀⡄⠀⢈⠈⢱⡌⡆⠀⠖⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⡀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⠀⠀⠀⠋⠴⠀⢀⡄⠀⢨⠀⠀⠀⠉⠀⠁⠀⠀⠀⢰⠁⡇⠂⠀⠀⠠⠀⢰⠆⠴⠀⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⡌⠀⠃⠀⠀⠀⠀⢠⠇⡀⠀⠀⠈⠁⠀⢸⠅⠀⠀⠀⠀⠀⠀⡀⠀⠘⠰⠿⣇⠀⠉⠈⠀⢨⣀⠀⠀⠛⠆⠁⠀⡁
⠀⠀⠀⠀⢠⠃⣆⠀⠀⠀⠀⢀⡇⣀⠀⠀⠘⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡏⢠⠄⢨⠀⣸⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠈⣢⣀⠀⠁⠀⠀⡾⠠⠀⠀⠀⠋⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠗⠂⠀⠂⠀⠁⠀⠀⠘⠀⡀
⢀⠀⠀⠢⣴⠉⠉⠛⠻⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⡜⠢⠀⠀⠀⠀⠀⠀⠴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠒⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠈⠁⠒⠀⠤⠤⠤⠄⠀⠀⠀⠀⢱⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠈⠁⠀⠛⠁⠴⠂⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠰⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠐⠂⠁
⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣈⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⢊⣉⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢷⣾⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡚⠛⠛⠛⠛⣳⣶⣿⣿⣿⣿⣿⠿⢟⣛⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣄⣀⣬⣭⣭⣤⣶⣾⣿⣿⣿⠀⠀⠀⢀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢷⣤⣿⣄⣈⣧⣀⣀⣧⡀⢳⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠢⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⡿⣿⠿⠿⠿⠿⠿⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢨⣭⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⢸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⢾⡿⣄⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣾⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⠷⠶⣶⣤⣀⠀⠀⢀⣴⣾⣿⣿⡙⣿⣿⣆⠃⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⣠⡟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⢷⣶⣦⣄⡈⢙⣿⣶⣿⣿⠿⠏⠉⢳⠘⣿⣿⣆⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣏⠉⠉⠀⠀⠀⠘⣇⢹⣿⣿⡀⠀⣄⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡏⢸⣿⣄
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⣿⣿⣿⣿⠇⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠅⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⡇⢩⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢈⣿⣿⣿⢰⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⢁⣀⡀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢀⣠⣿⡇⠀⠀⠀⠀⢀⠀⣼⣿⣿⡄⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠃⣿⠹⣿⣿⣿⣿⣿⣿⣿⡄
⢠⣶⣋⣁⣻⣿⣆⠀⠀⣄⠈⣷⣾⣿⣯⡀⠀⠀⠸⣿⣿⣿⣿⡏⠉⢸⠟⣿⢿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⢸⡿⣄⠋⠿⣿⣿⣿⣿⣿⣿⡄
⠉⠉⠉⠉⠉⠙⢿⣧⡀⠸⣧⡘⣿⣿⣿⠁⠀⠀⠀⣿⣿⡟⣿⡇⠀⠀⠘⠁⡾⢻⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⠁⠈⠳⣤⠉⣻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⡇⠈⢿⠀⠀⠀⠀⠀⠟⢩⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡟⠀⠀⣼⠏⠠⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡟⠛⠛⠶⣿⣿⡇⠀⠈⠂⠀⠀⠀⠀⠀⠘⠁⡿⣿⣆⠻⣿⣿⣿⣿⣽⣿⣿⣿⣿⡏⢸⠇⠀⣰⠏⢠⣜⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢋⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⠀⢰⣏⢀⣲⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⠏⢠⣟⡻⣿⣿⣿⣿⣿⣿⢠⣧⣴⣿⣿⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣿⡉⠓⠈⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⢀⡀⠈⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣄⢸⣿⡿⣼⠃⣿⣿⣿⣿⣿⡿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⢸⣿⠀⣿⠧⠉⠓⠀⠀⠀⠀⠀⠀⢀⣼⠋⣿⣿⣿⣿⣿⣿⠟⢁⡿⢸⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⢆⣄⢸⠀⢸⣿⣦⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡾⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠁⠈⢷⣄⣶⡦⠀⣀⡤⠞⠋⠁⠠⣤⣭⣿⣿⣿⣿⣿⣿⣿⣯⡥⠶⠟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣸⠃⢸⣿⠁⠀⠀⠶⠶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠿⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⣠⣿⣃⣀⣐⣒⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⣶⣶⣾⣿⣿⣦
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣁⣀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⢄⢄⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠑⢕⣄⢀⣦⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠔⠆
⠀⠀⠀⠀⠀⢀⣽⣿⡟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⡠⡻⠟⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⣤⣕⣠⡭
⠀⠀⠀⢀⠈⠀⠀⠀⠸⣿⡅⢀⠀⠀⠀⠠⠒⢽⣿⣷⣈⣹⠉⠉⢠⠀⠀⠀⠀⣠⢄
⠀⠀⠀⢀⠀⣴⢒⡒⢲⣿⡇⠁⠀⠈⠉⠀⡀⠃⠈⠙⠁⠈⣱⢦⣯⢠⠀⠀⢠⠁⠁⠈
⠀⠀⠀⠀⠂⠀⠀⠑⠉⠛⠋⠈⢉⠁⠀⠈⠁⠳⢚⠳⠄⠠⠔⠋⠭⢉⠉⠙⠛⠲⠒⠤⠄⢦⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠆⠀⠀⠀⠠⠀⠀⠀⠀⠉⠂⠀⠀⠀⠥

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⡶⢖⢲⠛⠛⠋⢉⡍⢍⡝⡻⠛⡳⠒⣶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡚⠫⣍⠳⢌⠢⡙⢌⠀⠇⠀⡇⠸⠀⠜⠔⣡⡞⠡⢊⡡⠖⣋⠤⠞⢉⠹⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠲⢌⡑⡂⠍⡒⠅⠢⣈⣤⣬⣄⣡⠞⠛⠲⠞⠉⠉⠳⠴⠶⣭⣴⠶⡶⣄⠒⣩⡷⣤⠉⡓⣦⣀
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠳⡄⠁⠀⣴⣾⣿⣿⣿⣿⣿⡴⢶⢶⠶⣶⠖⣶⡶⠒⢿⠾⠶⢷⣿⣰⡿⠧⣿⡟⠉⠁⠈⠳⢦⡀
⠀⠀⠀⣠⠞⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠶⣾⣿⣿⣿⣿⣿⣿⡿⠶⠶⡶⣶⢶⡾⠁⠀⠀⠀⢱⡄⢸⣿⢹⡇⠈⣿⡇⠀⠀⠀⢀⣠⠿⢦⡀
⠀⠀⡼⠃⠀⠀⠀⠁⠀⠀⢄⣠⣤⠞⠁⠀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣈⣓⣙⣙⣈⣻⠇⠀⠀⠀⠀⠀⣧⢸⣿⢸⡇⢰⣿⡇⠀⠀⠀⠈⢡⠀⢈⣷⡄
⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣟⣏⣙⣁⣛⣘⣃⣸⣤⣤⣤⣀⣀⣠⣯⣸⣿⣼⣅⣈⣿⣇⣀⣀⣀⣀⠀⠀⠈⠀⠻⡄
⣸⣷⣶⣶⣶⣦⣤⣤⣀⣀⣀⣠⣤⠤⠤⠶⠶⣟⣛⣿⡿⠿⡟⢛⣛⣯⠿⠟⠛⣋⣭⡤⠶⢚⣫⡭⠖⠋⠁⣠⡴⠛⠉⢀⣩⠟⠉⡽⠉⣟⠛⣟⠲⣶⢿
⣿⠢⠬⢭⣅⣉⢉⣙⠛⠻⠻⡿⣿⣶⣦⡶⠟⢉⣁⣀⣤⠾⠛⠉⠁⣀⣤⠶⠛⠋⢁⣤⠞⠋⠁⠄⣠⡴⢛⠁⠀⢀⡴⠋⠀⠀⡾⢁⢰⣗⢀⣹⣄⣈⣻
⣏⠑⠮⣄⡠⡉⠙⠓⢦⣴⣠⣠⣴⢛⡩⢀⣤⣞⡋⠉⠉⣀⣤⣶⣻⣥⣤⣤⣤⣞⠋⠀⠀⠀⣠⡾⠋⠀⢁⡀⢠⡟⣁⣤⠶⠟⣩⠉⠉⠉⢉⣉⣁⡤⢾
⢻⢳⢤⣤⣉⣳⣷⣿⣛⣫⣯⣥⣬⣩⣿⣿⣟⣉⣹⣻⣿⣽⣽⣭⣭⡁⠹⠛⠟⢻⢧⣀⣠⡾⠋⠀⠀⠀⡚⣵⠿⠭⠕⠒⠉⠀⠀⠀⠀⠠⢝⣛⣓⣟⣿
⠈⢿⣭⣼⣻⣿⣿⡿⣿⠷⣿⣷⣾⣷⣿⣿⣿⣿⡻⣿⣿⣿⠿⣿⣯⣟⡿⣷⢶⣤⣈⣻⣿⡟⣽⢳⣠⢄⣼⣟⣿⣟⣷⣖⣶⣦⣀⣤⣤⣀⣀⡈⠉⣨⠏
⠀⠈⢷⠦⣠⡠⠍⢿⣟⣷⣾⣅⣇⢉⢻⣷⡿⡻⣿⢤⢿⡿⣶⣿⣻⣿⣿⣿⣯⣽⡟⣛⣮⣏⡙⠾⢯⣿⣿⣽⢧⡿⣿⢻⣭⡟⣽⣛⢷⢶⡭⠽⣽⠏
⠀⠀⠀⠳⣄⠹⣯⠭⠇⡹⢤⢿⠿⣿⣦⣻⣶⣻⣫⢿⣷⣟⡻⣯⣿⣟⣯⣟⠿⡽⣷⢿⣆⡿⣓⣾⢧⣸⡟⣛⣧⠹⡷⣟⣲⡧⠯⣝⡟⣼⣭⡿⠁
⠀⠀⠀⠀⠈⠳⢿⡅⣢⢍⡛⣿⡁⣹⣿⡇⣿⣿⣟⣏⢿⣾⣷⣛⣟⣳⣝⣯⣾⡟⣫⣻⣞⢿⣭⢿⣦⣯⣿⣧⣞⣷⢛⡟⢾⣓⢦⣈⣳⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⣐⢢⣟⡙⣿⣿⣿⣿⣼⣿⣭⡑⢿⣚⣿⣴⣿⡷⢿⢯⣿⣫⣿⣿⡛⣾⡷⣾⣩⣿⣝⣿⣟⣿⣟⣽⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣥⣼⣿⣿⣿⡟⡷⢮⣉⠟⣾⡿⡻⣼⣗⡿⢳⣿⣿⣮⣽⣛⣷⣿⣿⣯⣴⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠿⢶⣟⣚⣇⣿⣯⣍⣽⣷⣿⣿⣿⣿⣭⣭⠾⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠋⡄
⠀⠀⠀⠀⠀⠀⢠⡿⠀⢀⣀⣀⣀⣽⣄⡀
⠀⠀⠀⠀⠀⢀⡼⠿⠟⠛⠛⠉⠉⠉⠙⠛⣻⣥⡶⠦⠀⠀⠀⢀⣀⣀⣤⣤⣤
⠀⠀⠀⣠⡶⠋⠀⣀⣀⣀⡠⣤⣴⡖⢺⣿⣿⣧⢤⠀⠶⠚⠛⠉⠉⠁⠀⠀⢸
⠀⠀⠘⠛⠛⠉⢩⠏⠘⠛⠀⠈⡟⣷⠞⠁⢸⠀⣎⡄⠀⠀⠀⢀⣠⡄⠀⠀⢸
⠀⠀⠀⠀⠀⢠⣯⠤⢦⣀⡀⢰⣿⡿⢤⣤⢾⡄⢻⡄⣀⠴⠚⠋⢹⠃⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⣾⡿⢳⣄⠀⠈⡇⠀⠙⢦⣀⣀⣀⡟⠀⠀⢠⠃⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢲⣴⡟⠁⠈⣿⠣⡴⠞⠀⠀⠀⠀⠉⣹⣿⣿⣶⣾⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠸⣇⠀⠲⣦⡀⠀⠀⡰⠋⢑⠞⠉⠁⠀⠀⠀⠀⠙⢿⣧⡔⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢻⣦⡼⠁⠀⡏⠀⠀⠀⠀⠀⠀⢀⣤⣾⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⣿⡁⠀⠀⣇⠀⠀⠀⠀⣠⣾⣿⠷⣫⠑⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢹⢇⣿⠶⣿⣿⣶⣴⣾⣿⡫⠕⡡⣐⡵⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢸⢸⣡⡶⡟⢝⢝⡿⢿⣭⢖⠔⣊⠤⢚⣽⣷⡀
⠀⣠⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡟⢸⡻⡌⣌⢇⠡⣻⣶⣿⣷⡫⣷⢯⣣⢿⡻⣧
⠀⠙⡟⠳⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⣿⠝⣎⢂⣦⣷⡿⠟⠉⠘⢿⣕⢿⣷⠱⣒⣽⣇
⠀⠀⢧⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⢿⠧⡇⣿⣮⣶⠿⠛⠉⠀⠀⠀⠀⠈⢻⣯⢾⣿⡻⣝⣿⡄
⠀⠀⠈⠉⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡹⡀⡟⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢻⣾⣷⡽⣧
⠀⠀⣦⡀⠈⣇⠀⠀⣀⣼⠀⠀⠀⠀⠀⢻⣗⡝⣽⣿⢷⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣛⡭⢔⣿⡆
⠀⠀⠘⢏⢳⢸⡄⢀⡍⢙⡖⠀⠀⠀⠀⠀⠹⣮⣪⢿⢸⠟⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣾⡛⠽⠧⠀⣀
⠀⠀⠀⣼⠈⣦⣧⢾⠀⣯⠀⠀⠀⠀⠀⠀⠀⣬⠇⣸⢸⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣠⣴⣶⣿⠿⡃
⠀⢳⡲⡈⣇⣹⣻⡼⡰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠦⡇⡎⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠋⠉⠀⣿⣿
⠀⢠⣷⣉⢫⣹⡟⡗⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠾⣄⠧⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠳⣆⠀⢀⣠⢄⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠘⢤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣽⠞⠛⠉⠉⣩⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣀⣤⣿⣃
⠀⠀⠀⠀⠀⠀⢛⣷⠀⡀⢠⠀⢀⠀⠀⣀⣐⣊⣼⣟⡀⢀⣀⣀⡀⠀⣼⠁⣠⡞⣠⠟⠀⠀⠀⠀⢀⣠⠿⠂⠶⠖⠠⢶⡟
⣀⣀⣀⣴⠛⠦⡼⠿⠜⢳⠿⣤⣯⠀⣸⣿⣿⣿⣿⣿⣿⣟⣁⠈⠉⣉⣉⡴⠛⠫⠿⢾⣥⣀⣰⣛⣉⣁⣀⣀⣠⣄⣠⣼⣥⣾⣥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠻⣷⣦⡄⠀⠀⠀⠀⠀⠘⠻⣷⠂⡸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⣐⣒⣸⣿⣶⣶⣶⠀⢀⣠⣴⡴⠿⠷⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡟⠿⣟⠛⢶⣄⡀⠀⠀⢀⣴⣾⣿⡿⠛⣛⣉⠉⣥⢽⣿⠟⠀⠈⠋⢩⠀⣾⡆⣿⡀
⠀⠀⠀⠀⠀⢀⣠⣿⠿⠿⣿⠓⢾⣦⣈⡌⠙⣶⣄⠸⣿⣿⡏⠻⠀⠀⠁⠀⢣⠈⡏⠀⠀⠀⠀⡼⠀⠙⠁⢸⣇
⠀⠀⠀⠀⠀⣾⣿⠿⣿⠓⢶⣦⣌⣅⠙⡿⣦⣦⢹⡇⠈⠉⠙⢲⡄⠀⠢⠍⠹⢀⠇⠀⠀⠀⣀⣇⠀⣶⠉⣻⣇⡀
⠀⠀⠀⠀⣼⣿⢣⣄⠀⠣⢄⣇⠉⠿⢷⣷⣸⣟⠻⣿⣶⣄⢀⢠⡟⠢⣄⣀⣀⣼⠀⠀⠀⠠⠠⠤⠶⠶⠭⠭⠭⠉⠁
⠀⠀⠀⠀⣽⣿⣛⠳⢶⣶⣊⣉⡁⠾⢨⣯⣙⢿⣿⣮⣙⢿⣿⣎⠓⠦⢤⣉⠛⡿⠻⣷⡶⠦⣤⡀⠉⠉⠉⠉⠐
⠀⠀⠀⠀⣿⡿⢿⣯⣀⡠⠛⠛⢻⣾⣟⡻⢿⣷⣬⡻⢿⣷⣝⢿⣷⣄⠑⠊⠙⠁⠀⢿⣧⡄⠀⠙⢷⡀
⠀⠀⠀⢰⣿⣿⣶⠒⠋⢻⠿⢿⣥⣴⠿⣿⣶⣍⡻⣿⣶⣝⢿⣷⣌⢮⣳⣄⠀⢀⣀⣸⣿⡇⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠈⠉⠙⠛⠻⢦⣤⣖⣉⣽⣿⣾⠟⢩⢻⣮⣝⢿⣷⣝⢿⣷⣝⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡙⠁⡀⠀⠈⣿⣿⣷⣝⢿⣷⣝⢿⣯⡻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣶⣬⣤⣴⣿⣷⣝⢿⣷⣝⣿⣷⡻⣿⣞⢿⣿⣿⣿⣿⣷⣂⣈⠙⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠛⠛⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣮⣿⣷⣿⠿⠛⠋⠉⠀⠈⠻⣆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⣰⣿⡏⣿⣿⣿⣿⣷⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⡽⠟⠀⢸⣿⣿⣿⡍⠀⠠⡀⠀⢠⣴⣶⣶⣶⣶⣶⣶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣤⢤⣶⣿⣿⣿⣿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⢟⣽⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠷⠜⠟⠱⠿⠛⠋⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣄⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⣰⠉⢳⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠁⠤⠉⠠⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐
⠀⠀⠀⠺⠰⠉⠆⠀⠀⠀⠀⠀⣶⣏⣳⡖⠀⠀⠀⠀⠀⢀⣘⣁⠀⠀⠀⠀⠀⠀⠹⠺⠈⠁⠀⠀⠀⠀⠀⢨⡀⠗⣈⠂
⠀⠀⠀⠐⠿⠗⠃⠀⠀⠀⠀⠀⠁⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠺⠏⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢘⣏⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡉⣯⠩⠀⠀⠀⠀⠀⠀⡑⣇⣿⡋⠀⠀⠀⠀⠀⣾⠃⢷⡄⠀⠀⠀⠀⠀⢸⠦⠿⠀⠀⠀⠀⠀⠀⠠⠛⡈⠓⠆
⠀⠀⠀⢓⣿⡀⠂⠀⠀⠀⠀⠨⠃⣇⡿⢡⠀⠀⠀⠀⠀⢻⠀⣾⠃⠀⠀⠀⠀⠀⡅⠀⠀⣏⠀⠀⠀⠀⠀⢐⠀⠁⠘⡂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⢸⣁⡿⠀⠀⠀⠀⠀⠀⠹⣀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠴⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠰⣤⣤⡔⠢⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡀⠀⠀⠀⠀⠐⢀⡊⣒⠀⠀⠀⠀⠀⠀⠀⡤⢢⠄
⠀⠀⠀⢐⢠⢰⠂⠀⠀⠀⠀⠀⡜⠀⠂⠀⠀⠀⠀⢀⢀⡻⠻⡟⡀⠀⠀⠀⠀⠀⠈⠀⠃⠔⠀⠀⠀⠀⠀⢀⣄⣀⡀
⠀⠀⠈⢹⡸⢀⠁⠀⠀⠀⠀⠐⠢⢝⢡⠃⠀⠀⠀⠀⠀⢿⡘⣿⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠘⢖⣲⠗
⠀⠀⠀⢻⣒⣚⡗⠂⠀⠀⠀⠀⢶⣌⣰⠦⠀⠀⠀⢀⠁⠪⡄⠼⠉⠀⠀⠀⠀⠀⠀⢇⡼⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⢀⠁⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⣄⡄⠀⠀⠀⠀⠀⠀⠀⢨⣡
⠀⠀⠐⡘⠁⠋⠪⠀⠀⠀⠀⠀⢈⠇⣺⠀⠀⠀⠀⠀⠀⠒⠐⠀⠠⠀⠀⠀⠀⠀⠼⠃⠷⠀⠀⠀⠀⠀⠀⠀⠚⠳
⠀⠘⠒⠄⠀⠀⠔⠀⠀⠀⠀⠀⣰⠐⡰⠀⠀⠀⠀⠀⠬⠀⠀⠈⠤⠀⠀⠀⠀⠈⢦⣛⣠⠆⠀⠀⠀⠀⠀⠀⠂⠘⠂
⠀⠈⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢤⠔⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠚⠘⠆⠀⠀⠀⠀⠀⠀⠐⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⣶⣤⡴⡇⠀⠀⠀⠀⠀⠘⢡⠛⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡆⣖⠀⠀⠀⠀⠀⠠⠌⠀⠀⠠⠄
⠀⠀⠠⠄⣿⠅⠃⠀⠀⠀⠀⠀⢂⠸⠀⡂⠀⠀⠀⠄⠀⡌⠈⣄⠀⠀⠀⠀⠀⠀⣠⡞⠤⠀⠀⠀⠀⠀⠀⢴⡄⠀⣼
⠀⠀⠀⠶⠊⠛⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠑⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⣀⣀⠀⡀
⠀⠀⢠⣤⣤⣤⣦⣤⡤⢶⠆⠀⠀⢩⣥⣭⢄⣈⠀⠀⠀⠀⠀⠺⠀⢉⡉⠹⣦⠀⠀⠉⠙⠻⣿⣿⣶⡀
⠀⣠⣿⣿⣿⣿⣿⣿⣄⡞⢡⡀⠀⠈⠙⢿⣾⣿⣦⣄⠀⠀⠀⠀⠀⠈⠁⠸⠤⠂⠀⠀⢳⣌⠉⠉⠙⢿⡄
⠀⣿⣿⣿⣿⡿⣿⠿⡟⠃⣀⣠⠠⠀⠀⠀⠈⠟⠋⠀⠀⠀⢀⣤⣶⣿⣷⣄⣼⣧⡿⠂⠉⢁⠀⠀⠀⠘⠁
⠀⢿⣿⢿⣿⣻⢻⠿⣿⠿⣿⡧⠌⠷⠤⠀⠄⠤⠂⠀⠤⠀⠀⢙⣿⣿⣾⣿⣿⣿⣧⣶⣾⣿⣿⣿⣿⣿⡇
⠀⣾⣿⣧⣮⣭⢠⣰⣿⣦⣴⢃⣀⣉⠋⢽⣶⡄⠈⠁⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⣹⢿⣿⠇
⠀⠻⣿⣿⣿⣿⡶⣿⣿⣿⡇⢸⣿⣿⣶⣾⣷⠄⡀⣝⣿⡿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐
⠀⠐⣿⡿⠾⠿⣷⣿⣿⣿⣧⣠⣭⣭⣡⣬⣽⣷⣩⣿⣟⡀⣿⣶⣶⣶⣤⡼⠛⢻⣧⣸⣿⣿⣿⣿⠏
⠀⠀⢤⠀⡀⢀⠀⣿⡏⡽⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⡛⠳⡤⠜⠛⠿⣿⣿⣿⣿⠃
⠀⠀⠀⠚⢿⣿⣅⣸⣇⠉⢿⡿⢿⣿⣿⣿⣿⡏⣦⠻⠿⠿⠟⠿⠙⠿⢯⣙⡶⠶⠟⡓⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠺⠷⠦⣘⣻⠿⣿⠿⠿⠗⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣥⣤⣉⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣤⣿⣶⣆⢠⡀⠻⣿⣶⣶⠆⢀⡄⣴⣿⣽⣿⣿⣟⠀⢀⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⢿⣿⣿⣿⡩⣅⠸⡿⢊⡴⣤⣦⡁⢾⠇⣡⠌⣿⣿⣿⣞⣿⣿⢯⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠚⠛⠿⠿⠷⠎⠳⠀⣸⣏⠻⣿⣇⠀⡞⠱⠞⠻⠻⠛⠛⠛⠉⠈⠀⢆⡀
⠀⠀⠀⡀⠀⣠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡇⢀⣼⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠲⡦⠅⠂⢄
⠀⠀⠐⠀⠀⡘⣧⣕⡠⠀⠀⠀⢀⠀⠠⠄⠀⠀⠸⣿⣾⣿⣿⣿⡇⠀⠂⠠⠄⠀⣀⠀⠀⠀⠄⣊⣶⣄⣠⣰⡌
⠀⠀⡄⠀⢸⣿⣯⣿⣿⣶⣦⡄⠀⠠⡴⣓⢤⣦⠤⢿⠏⠿⣿⡿⠤⣰⡦⠘⢦⡄⡀⢀⣠⣶⣾⣿⣿⣿⣿⠟⠃⠆
⠀⠀⢄⠀⠼⣿⣛⣿⣿⡿⢟⣁⣀⠪⣵⢿⠇⡼⢶⣥⣴⣶⣾⣯⡴⢧⠘⣿⡦⠑⣀⣬⣙⠉⢿⣻⣿⣿⡤⠀⡀
⠀⠀⠀⠙⠂⠈⠛⢋⣥⣶⠿⠛⠉⠑⠢⠉⣐⠃⣼⣁⣠⣶⣶⣿⣅⠀⣃⠉⠀⠀⠉⠛⠿⣿⣦⡈⠉⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⡌⠉⠁⠀⠀⠀⠀⠀⠀⡟⣴⢹⣥⣤⣴⣾⣿⡍⣤⢻⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡠⠏⡄⣿⡀⢧⣀⣬⣿⡦⠰⣷⠀⠹⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡃⢟⣮⡌⠻⢿⢟⣡⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡈⠛⠷⠞⠛⠋⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⡠⠚⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠒⢠
⠀⠀⠀⠘⠢⠐⣄⠀⠀⠀⠴⠢⡄⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣀⡀⢠⣤⠀⠀⣀⠀⠀⣀⣤⣄
⢰⣤⣤⠴⠶⠤⠾⠶⠾⠀⠀⠀⠒⠂⠛⠓⠰⠿⠧⠴⠷⠾⠦⠤⠤⠴⠆⠀⣤⠤⢤⡄⠁⠀⠀⢰⣋⣁⡀⠉⡿⠔⠢⡄⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠋⠙⠁⠛⠋⠁⠠⠾⠿⠿⠿⠶⠤⠤⠤⠧⠄⠘⠛
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠉⠀⠀⠠⣴⣞⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⡀
⠄⡀⠀⡀⢠⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⡉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠁⠁⠁⠈⠉⠉⠁⠉
⡆⣄⡷⠀⡼⣄⠀⢀⡀⠀⣸⠡⢛⣀⣧⣻⣽⣇⣀⣀⣀⣀⣀⠀⣀⣀⣴⡷⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡆⠏⡟⢡⣟⣾⣾⢀⣇⣆⣟⠰⠮⡉⠁⣀⠀⠀⠀⠂⠀⠀⠀⢠⡇⠀⠘⣻⢿⣯⡆⠆⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⠘⠀⡄
⠟⢰⣰⡧⣩⡎⠙⠞⠒⠈⠀⢀⡠⠔⠈⠀⠀⠀⢀⠐⢀⡠⣤⡚⠀⠀⠈⠻⢿⣷⢣⢸⡌⠆⢠⠀⢹⠀⡅⢀⠀⢀⠀⠰⢀
⣟⣸⡿⠛⠊⠁⠀⢀⣠⡴⠚⢉⠀⠄⠀⠀⠀⠄⠁⢀⠞⡤⠺⠁⠀⠀⠀⢀⣤⣶⢟⡋⢿⢀⢈⡄⡄⣀⢣⡈⠀⣸⠃⠀⣾⠈⡀
⠁⠀⠀⠀⢀⡤⠴⠋⢁⡀⠢⠀⠀⡠⣂⠄⠀⠀⡰⠋⠘⡽⠀⠈⢠⠀⠀⠀⢈⡿⣸⡅⣻⣈⡌⢰⡟⢋⠀⡇⠁⠇⠀⠂⢸⢸⣷
⢀⣠⠴⠚⠁⠀⢀⡸⠁⠀⠀⣐⣄⠣⠀⠀⠀⡜⢡⢠⣼⠃⠀⠀⣾⠀⠀⠀⢈⣸⣛⣛⣋⢿⣃⡘⣧⠄⠀⣷⢠⠀⡼⠀⡖⢨⡾
⠉⠀⠀⣠⣶⠙⠋⠀⢀⢠⣳⠹⠌⠀⠀⢠⠌⠄⣠⡻⠇⠀⠀⠐⠇⠀⠀⠀⠩⠑⠛⠋⢉⢴⡇⣧⢸⣧⠀⠁⡿⢡⣻⠀⡿⡘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡄
⠀⠀⠀⢠⣖⠀⠀⠀⢸⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠀⠉⠀⠀⠀⠀⠁


⡐⠢⣁⠺⢔⡒⠤⣀⠀⠀⢂⠤⢀⠀⠀⠀⡀
⠙⢦⡈⠒⢄⡈⠑⠦⣌⠁⠢⢌⣐⠂⠭⢑⠚⠬⣄⣒⠤⢤⣀⡀
⣄⠀⠙⢤⡀⠉⠦⣀⠈⠓⢦⣄⡈⠛⠶⣤⡉⠑⠢⠄⣉⡑⠢⠭⣍⣓⠦⢤⣄⡀
⠸⣦⡀⠈⠻⣄⠀⠈⠳⣄⠀⠈⠛⢶⣀⠀⠉⠛⠶⣀⡈⠉⠳⠦⣄⣈⠙⠲⠤⣍⡉⠛⠲⢤⣄⡀
⠀⠘⣏⠀⠀⠘⢧⡀⠀⠈⢳⡀⠀⠀⠙⠷⣤⠀⠀⠈⠙⠷⣦⣀⠀⠉⠳⢦⣄⠀⠉⠓⠦⣄⡈⠉⠓⠦⣤⣀
⡆⠀⠹⣧⠀⠀⠈⢻⡄⠀⠀⠙⢶⡀⠀⠀⠈⠻⣦⣄⠀⠀⠈⠙⠶⣤⣀⠀⠈⠛⠦⣤⡀⠈⠙⠳⣤⣀⡀⠉⠛⠦⣤
⣷⣤⣤⣽⣧⣤⣤⣤⣿⣦⣤⣤⣤⣶⣦⣤⣤⣤⣬⣿⣦⣤⣤⣤⣤⣬⣿⣷⣤⣤⣤⣬⣽⣷⣶⣤⣤⣭⣿⣷⣦⣤⣬
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡈⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⠁⠨⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡑⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠠⠔⠒⠉⠉⠉⠉⠁⠐⠠⢌⡀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠐⠤⣄⢀⠀⢀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠑⠠⠤⣤⣄⣀⣀⡀⠒⠦⠁⠀⠈⠂⢀⠹⣧⣾⢷⣾⣷⣤⣤⣄⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣷⣤⡶⢶⣄⣀⣘⠢⣴⣀⣀⣿⣿⣿⣿⣿⡍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣇⣤⣿⣿⣿⣿⣿⡛⡿⠿⠿⣰⣿⣿⣷⣸⣿⠟⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⡘⢶⣶⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠈⢿⣿⣷⣴⣿⣿⣿⠿⣷⣾⠛⠿⢻⡟⡟⢡⡈⢿⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⣷⣦⣤⠀⠙⢿⣟⣵⣿⠏⠀⣾⣿⠀⠀⠈⠃⠁⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠈⠻⣿⣿⡿⣷⣿⡿⠁⢀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠹⣦⠔⠆⠀⠀⢀⠔⠀⠀⣀⣴⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣴⣩⣿⣿⡏⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠉⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⣿⣿⠏⣿⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⡿⠊⣡⢂⠀⡀⠀⡠⠔⠊⠈⠁⠀⠀⠉⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⠀⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠿⠇⠸⢧⣾⣪⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢠⠔⠀⠀⠀⠀⠀⢻⣾⡇⠔⠊⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣻⣿⡍⠃⠀⠀⢀⠈⠀⣰⣿⣿⠿⠿⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠃⡠⠀⠀⣈⣴⣾⣿⣏⠙⠓⠂⠀⠠⠀⠀⠀⠉⠐⠒⠄⠀⠡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣝⣿⣿⣿⠟⠿⢿⣮⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⡀⠈⠁⡾⢫⢯⠏⠸⣿⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠀⠯⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢄⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⣎⣷⠀⠀⠀⠀⠀⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡧⠊⠀⠀⠀⠀⠀⠻⡅

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣤⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⡿⡇
⠀⠀⠀⢰⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡶⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣴⣇
⠀⠀⠀⠀⠙⣿⣿⣿⣽⣿⣶⣤⣀⢀⠰⠃⠘⠆⠀⢀⣤⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢻⣙⣻⣿⣿⣿⣿⣿⣷⡇⠡⠄⠸⣾⣿⣿⣿⣿⣿⣟⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠉⣵⣿⣿⣿⡽⣛⢵⡂⠙⠋⢐⡪⣝⢯⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠷⠀⠀⡀⢀⣰⡄⠀⣸⢿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢰⢹⣿⣾⣿⣿⡏⣆⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠂⠁⣠⣴⣿⠿⠋⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠶⠭⠭⠷⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⣵⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠸⢿⠿⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢢⢂
⠀⠀⠀⠈⠖⡼⢀⣃⡤⢠⡄⣀⠀⢄⡘⠃⠘⠃⣀⠀⢀⠠⡄⢰⣔⣇⢧⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢳⡧⠀⡄
⠀⠀⠀⠀⠘⡍⣑⡒⠽⡶⠳⢺⢧⣦⡍⠁⠈⢉⣴⡤⣟⠺⢳⡮⠔⡚⡉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠮⢷⠢⠌
⠀⠀⠀⠀⠀⠀⠨⠦⠎⠑⠘⠋⢋⣹⡄⠀⠀⢠⣏⠙⠋⠋⠚⠹⠴⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣮⡯⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⣴⣤⣤⣤⣶⣦⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⡀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣛⡻⠿⠿⠿⢛⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠀⢠⣀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢩⣙⣛⣛⣋⡭⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢻⣛⣩⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡛⠋⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠞⠶⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⠂⡀⠀⢀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡿⠘⡇⠘⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢰⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣾⡏⢀⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣸⣿⣿⣿⣿⣿⣧⠋⠀⠘⢶⡄⣟⣘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⣿⣿⣿⣿⣿⡀⠀⠀⠁⠞⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⢀⡀
⠀⠀⠀⠀⣀⠀⠀⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠂⠀⠂⠀⠀⠔⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠛⠻⠟⢿⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠐⠁⠀⠀⠀⠀⠀⡀⠀⠈⣀⣠⣤⠤⡤⠀⠐⠀⠲⠛⢻⣿⣿⣿⣾⣿⠷⠶⠶⢦⡀⠠⠶⢖⠉⣀⡟⠁
⠀⠀⠀⠁⠢⢄⡋⠀⠀⠀⠀⠀⠀⠀⢉⡽⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀⢰⡆⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡟⢻⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣇⠘⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢹⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠘⣿⣿⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⣿⣿⣿⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠘⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⡇⠀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⠇⠀⣹⠿⢿⣙⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⣦⣶⣶⣶⣶⣶⣶⣦⣶⠾⠿⠿⠛⠁⠀⣠⣤⣶⣿⣿⣾⡿⠃⣠⠾⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢋⣴⣿⣿⣿⢿⠟⠛⠁⢉⣁⡀⣀⣀⣀⣀⣤⣤⠝⠛⠟⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠐⠋⠈⠉⠁⠁⣠⠄⣠⣾⣿⢿⡿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠘⠡⠞⠱⠋⠁⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠈⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⠊⡀⠐⠒⠀⠘⠓⠂⣀⡀⠀⢬⡇⠀⠀⠀⠀⢠⠀⢰⡏⠁⢀⢰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠉⠀⠆⠴⠀⠀⠀⣤⣦⢼⡇⠀⠀⠀⠀⢼⠀⢸⣟⠓⠈⢾⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⢀⠀⠀⢸⡇⣼⣼⡆⠀⢸⣇
⠀⠀⠀⠃⡇⢸⡀⡄⢀⣆⣸⠀⠀⠀⠀⢺⣧⡀⠀⠀⠀⠀⠂⠀⠀⠘⢿⢿⣿⡐⠂⠈⠀⠀⢸⢢⣿⣿⣷⠀⢸⡟⠁
⠀⠀⠀⠀⢰⠸⠛⠃⣾⡿⢿⠆⠀⠀⡷⢸⠇⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⢠⠈⠻⠀⠈⠀⠀⢸⣈⣿⣿⣿⣶⢸⡷⠀⢠
⠀⢀⠀⠀⣸⣄⠀⠀⠻⣷⣿⠆⠀⠒⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣸⣷⢀⣿⣷⢶
⠀⣿⢃⢆⠀⠙⠀⠀⣀⠛⠛⠂⠀⣀⠄⠀⢀⣀⡀⢰⠀⠀⠠⡆⠀⠀⠀⣿⡗⠛⠃⠙⠒⠒⠒⠶⢾⣷⣶⣿⣿⣿⠆⢁⠀⣀
⠀⠉⠹⠟⣭⣴⡀⢈⣻⣦⣀⣀⡐⠋⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢃⣠⣤⣄⠀⠀⡀⠐⠚⠿⠿⠿⠋⠁⠈⣉⣥⣶
⠀⠀⠀⠀⠈⠉⠁⠈⠉⠛⢿⢆⢈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠁⠈⠁⠀⠀⠠⠶⡄⠀⣈⣄⢀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣤⣄⠈⠁⢠⣴⣶⣄⠀⠀⠀⠀⠀⣰⣲⣀⡀⠀⠀⠀⠙⠈⣛⣟⣓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⢛⣛⠁⠀⠈⠉⠁⢧⡀⠀⠀⠀⠀⠻⠟⠋⢩⣍⠀⠀⠀⠀⠈⠛⠹⣿⣷⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣡⠀⠀⠀⢠⡆⠀⣻⣿⡆⠀⠀⠀⠉⠙⣿⣶⣄⡀⠀⠀⠀⠀⠙⢯⣭⣼⣦⠀⠀⠀⠀⠀⠉⣰⡶
⠀⠀⠀⠀⠀⢀⠀⣪⣶⠏⠀⠀⠀⣠⣿⠇⠐⣿⣿⣇⠀⠀⠀⠀⠀⡤⠻⣿⣿⣄⠀⠀⠀⠀⠀⠋⠉⢷⣼⣶⣦⡀⠀⠀⠀⠺
⠀⠀⢀⠤⣒⣵⣾⠟⠁⠀⠀⢀⣞⣿⣟⠀⠀⢸⣿⡞⠇⠀⠀⠀⠀⠀⠀⣤⣿⣿⣷⡄⠀⠀⠀⠀⠀⠸⠿⡟⢋⡑⠄
⠀⠀⢠⡾⠟⠋⠀⠀⠀⠠⠀⠜⣿⣿⡏⠀⢐⣾⣿⡧⢃⠀⠀⠀⠀⠀⠀⡻⡿⢿⡿⠿⠀⠀⠀⠀⠀⠀⠈⠟⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⢴⣟⣿⠁⠀⢸⣾⣿⡟⣈⠀⠀⠀⠀⠀⠀⢧⣿⣟⢰⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠇⠹⠺⠃⠀⢦⠙⠇⢻⡴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣂⣂⣂⣀⣀⣐⠒⠒⠒⢒⠒⠒⠂⣀⣐⠐⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⣄⣀⣐⣂⣒⣂⣀⣐⣒⣒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⣤⠤⢶⠶⣶⣶⠾⠿⠒⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⢛⣂⣶⣾⣽⢋⠙⣿⣻⣿⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣻⠫⢛⢛⢛⣛⣛⠛⣉⠛⠋⣩⣿⣿⣯⣙⡛⠛⡙⠉⡛⢛⡛⠛⢋⣙⠻⣛⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⣛⣯⣯⠯⠿⣿⣞⡿⠯⠀⠀⠭⣿⣿⠿⣤⡉⠳⢾⣶⣌⡳⣮⣝⠳⢾⣍⡓⠶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣷⠶⢟⣛⣿⣿⡾⣞⣿⣷⠃⣶⠀⠑⣠⣿⣿⣿⡶⡇⢿⣷⣮⠛⢿⣶⣭⣙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣥⡶⣿⠿⣫⣿⣿⣿⣿⣿⡋⣸⢣⠊⢹⡟⢯⢻⣿⣷⡏⣯⣿⣿⣿⣄⠛⢿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣋⣵⣾⣿⣿⣿⣿⢿⡏⠙⢠⣿⡏⢠⡿⠋⠀⢻⣏⡉⠤⢝⣿⣷⡹⣿⣷⢷⣞⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠟⢹⡿⡏⠦⡸⣟⣼⣿⡇⣾⡇⢀⣧⠰⣿⣟⣇⡚⣿⣿⣧⠩⢻⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣠⡎⡛⣑⡁⣞⣿⣿⣿⣿⠀⣿⢳⣾⣿⡀⣿⣿⣷⡍⣽⣿⣿⣧⠀⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⡿⠧⢭⣬⣷⣿⣿⣿⡿⢻⣤⣿⣿⣿⣿⣿⣿⣿⣿⢧⣳⣿⣿⣿⡆⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠭⢛⡦⡬⣾⣷⣿⣿⠟⠁⢷⣿⣿⣿⣿⣿⡟⣿⣿⣿⣻⣦⣽⢿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠐⠙⠛⠝⠻⠋⠀⠀⠀⠉⠀⠀⠁⠁⠁⠀⠙⠿⠟⠛⠘⠛⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⣀⠀⠈⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢞⣥⠞⠉⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢻⡄⠀⠀⢀⡟⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠙⠶⠶⠛⠀⡏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢳⡀⠀⠀⠀⠀⠃⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠀⢣⠀⠀⡀⢠⣦⠀⠀⡖⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣼⡇⡠⢷⢂⡍⠉⠓⠛⢾⠤⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⡼⠉⣿⠀⠀⠁⠀⠀⠀⠀⠸⢦⠀⠀⠈⢣
⠀⠀⠀⠀⠀⢀⣾⠃⠀⢲⡆⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠙⠢⣄⣸⢀⣀⡀⠀⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⡴⠛⠉⠈⣍⡳⡄⠀⠀⢸⠀⠀⠈⢷⡀⠀⣠⢾⣀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣾⣀⣠⡤⢜⡶⠳⠀⠀⠀⢸⠀⠀⠀⠈⢷⡞⠻⡄⠀⢠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠛⡶⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡸⢻⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡇⢸⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⡇⢸⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡾⠀⢸⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡇⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⢱⡇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡎⠀⢸⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠃⠀⠀⣽⠋⠉⠉⠁⠈⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢠⡄⠀⢀⠀⠀⠀⠻⠖⠚⠛⠛⠒⠒⠋⠀⢀⡴⢇⣤⢤⡤⢴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⡠⠀⠉

⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⡷⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢾⣿⣿⣿⣯⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣿⣿⣿⡀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣉⡀⠀⠀⣿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃⠀⠀⣀⣠⣾⣿⣿⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣦⣀⠀⠀⠀⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣀⣰⣿⣿⡿⣋⠹⡏⣼⢹⣿⡄⠀⠀⠀⠀⣰⡿⣿⣮⡿⠩⣿⣿⣿⣧⣀⣀⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣻⣿⣿⣟⠁⡁⢙⡀⠄⠠⠎⠞⠛⢦⣾⣆⣼⢋⣇⡱⠀⠀⢰⡋⢈⠙⣿⣿⣿⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣯⣿⣿⠄⠓⠸⠧⠀⠀⠂⣆⡄⠈⣿⣿⣰⣄⡏⡃⡀⠀⠞⠁⠄⠰⠿⣿⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⠲⣶⣾⣶⡷⡖⠒⢦⣿⣟⡻⢿⣶⣶⣶⣻⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣟⠻⢿⣷⣿⢿⡇⢑⠍⣉⠀⣿⡏⠐⣻⣿⠉⣹⠿⣷⣾⣿⢿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡉⢶⣊⠁⠉⠒⠀⡍⠀⠀⠀⢽⡇⠀⠀⢷⣧⠐⠊⠉⠙⣻⣾⣸⣳⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢷⣟⠲⠍⣀⠖⠀⣤⢀⠀⠀⠀⠸⠃⠀⠀⢀⡆⣤⠑⢟⣈⡹⢟⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⢿⣿⣶⢾⣥⢴⣆⠤⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⢿⣬⣶⣶⣯⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠏⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⣤⣤⣴⡄⢀⡀⠀⠀⣀⣀⠀⠀⢠⣤⣿⣧⣤⣤⠀⡀⠀⣤⣤⣴⣾⣷⣄⣤⣤⣴⠦⣠⣾⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣶⣤⢖⣤⣤⣡⣸⣾
⠛⢻⢻⢛⠛⠃⡛⠛⠓⢛⠛⠻⠛⠛⠛⠛⠛⠃⠉⠁⠀⠈⠀⠈⠉⠙⠉⠉⠛⡿⠟⠛⠛⠉⠉⠀⠀⢰⠆⠀⠀⠀⠸⡭⠿⣿⣿⠾⣿⣿⣿⠿⣿
⢠⠁⠀⡀⠀⠢⠈⠀⢈⠀⠀⠐⠂⠀⠀⠀⠄⠀⠀⠀⠒⠂⢀⡀⠈⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠲⢤⡀⠉⠒⠤⣀⠒⠤
⡘⢰⠀⡧⠘⡀⠀⢄⠀⠑⠄⡀⠀⠢⠈⠁⠢⢀⠀⠢⢄⠀⠀⢀⠀⠂⠀⠤⠄⠀⣀⠤⠂⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠐⠦⢀⠙⠲⠤⣀⠙⠲
⠁⢼⠀⢰⠀⢠⠀⠀⢂⠀⠀⠙⢦⡀⠀⠁⠀⡀⠙⠢⡀⠙⠢⣀⠁⠦⣀⠀⠈⠉⠀⠀⠚⠀⠀⠐⠂⠀⠠⠔⠒⠈⣀⡠⠤⠂⢀⠁⠲⣄⠈⠑⢤
⠀⣼⠀⢸⡄⠀⠇⠀⠀⠳⡄⠀⠀⠹⠄⠀⠀⠈⠢⠄⠈⠲⠄⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⠐⠖⠆⠀⠠⢠⠒⠈⠁⢄⠈⠙⢦⡀
⠀⠸⠀⠀⠧⠀⠘⠀⠀⠀⠡⠬⠍⠀⠀⠀⡀⠤⠈⠀⠀⢀⡐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠶⠆⠀⠀⡤⠤⠀⠳⠀⡀⠃
⠠⠀⠐⠀⠀⠂⠀⣀⠀⠠⡄⠀⠢⠀⠒⠀⠁⠀⠀⡀⠀⠀⠉⢀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠒⠀⠀⠠⠤⠀⠀⠲⠒⢀⠉⢀⠤
⢶⠀⠘⠀⠉⠁⠀⠀⡀⠀⠠⠤⠄⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠀⠐⢀⣤⠄⠀⠈⠁⣀⡤
⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⣀⡄⠀⠀⢀⣠⠄⠀⠀⠈⠀⠰
⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⡀⠀⠈⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣀⠀⠀⠀⠀⣠⡴⠆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⡠
⠀⠀⠀⠀⠉⠙⠒⠤⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠊⠁⠀⠀⣀⠀⠀⠈
⢾⣶⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠰⠓⢤⠄⡀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠉⠉⠉
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠉⠁
⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠚⠂⠀⠀⠀⠀⠀⠰⠗⠂⠂⠒⠀⠀⠀⠀⠚⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⢤⡤⠤⠖⠂

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⣟⣀⣀⡀⠄
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠶⠶⢦⡀⠀⢰
⠀⠀⠀⠈⠛⠿⠟⢿⡏⠹⠁⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣷⣄⣈⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡠⠔⢺⡙⢧⣴⡇⢙⡦⡀⠰⢊⡩⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣦⣤⣄⢰⣀
⠀⠀⠀⢠⡎⠀⠀⠈⠙⠲⣿⠟⡉⡀⠙⢲⡎⠀⠀⠈⠀⠀⠀⡀⠤⠀⠀⢀⠜⢡⠤⠈⢻⣿⣿⣿⣿⣄⠀⠀⠀⢄⣀
⠀⠀⠀⢸⣇⠀⠱⣦⣠⣶⠹⢄⣛⡤⠀⠺⠷⢤⡀⠀⣀⡀⠀⠀⠀⠀⠀⡀⢠⣤⠀⣤⠀⣬⠉⣭⣽⣛⠃
⠀⠀⠀⠘⣿⣄⡤⢿⣧⣿⣷⡿⣵⡛⠁⣀⣔⡿⣿⣿⣿⠀⠀⠀⠀⡀⠀⢀⣈⣉⣀⣉⣀⣿⣶⣿⣿⣿⣿⣦⣀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⢻⣿⣾⠟⠓⢦⡀⠀⠈⠁⠈⠉⠹⠛⢛⡏⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢿⣿⣷⣦⣀⡉⠓⠶⠚⠓⢛⣷⣰⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣤⣴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣾⠿⠾⣫⠀⠀⢠⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣿⡋⠀⠀⢠⡾⠀⢀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣾⡇⠀⣸
⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠟⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣠⠞⣁⣤⠶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣵⡞⠉⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣿⠀⠀⠀⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⢿⡄⠀⠀⠀⢀⡗⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⣶⣤⡴⠟⠀⢸⠈⠱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢧⠀⠐⠀⠀⠀⠀⡄⠀⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠈⣇⠀⠀⠀⠀⠀⡇⠀⠇⠀⣀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⢠⠀⠘⣆⣀⠠⣤⣤⣟⣁⡀⢸⠃⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⢠⣿⣆⡴⢻⣎⣤⠆⠀⠉⠉⠙⣿⠶⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢰⠏⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢦⣤⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠙⢦⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠉⢓⣾⡴⠖⠶⢤⡀⠀⠀⠀⠀⣀⠀⠀⠈⢷⡀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⡰⠋⠁⠀⢀⡲⢦⡼⠆⠀⠀⠀⣿⠀⠀⠀⠈⢷⡀⢀⣴⠛⠷⠶⠖⠋⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣼⣧⣄⣠⠶⠦⠽⠇⠛⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠷⠋⠘⣷⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠟⠓⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢰⡇⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⠁⣿⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⣬⠀⢹⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡟⠀⢸⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⣼⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢶⠀⡧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠇⠀⢸⡏⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠈⣷⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⡼⠀⠀⣾⡁⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠇⠀⠀⠙⣿⠖⠒⠒⠚⠀⠙⠒⢦⣄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢰⠀⠀⠀⠸⣧⣀⣤⠶⠶⣤⣤⣤⡤⠟⠀⠀⣀⡀⠀⡀⢀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠛⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠏⠙⠛⠋⠛⠉⠙⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣀⣀⡤⠂⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣭⣭⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣩⣯⣭⣭⣯⣽⣬⣭⣯⣍⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣷⣤⣤⣿⣾⣿⣧⣭⣭⣧⣬⣭⣽

⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡾⣇⠒⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⡄⡄⢠⢀⡀⡀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⡙⢳⣶⡿⢾⠷⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣼⣾⣧⣿⣾⣾⣧⣝⣯⢼⣤⣸
⠀⣴⣦⢺⣦⣀⢠⣤⣿⣦⣤⣬⣿⣿⢿⡿⣿⠱⣤⡠⠀⣤⠀⣄⡀⢠⣄⣰⣾⣿⣿⣿⡷⣿⡿⢸⣿⣿⠷⣿⡟⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣼⣿⣿⣿⣾⣻⣾⣺⣷⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣅⣿⣟⢻⣿⣿⡓⣿⡷⣿⣿
⢻⣿⣿⠟⡀⣀⣙⣿⣭⣭⣭⣽⢻⣿⡿⢿⣿⣿⠿⢿⣿⣿⢿⡿⡿⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢨⣴⣶⠿⠟⢛⣙⠿⠶⠀⠲⠾⠟⠋⠁⣚⢟⣠⢞⡵⠁⡇⢹⡙⢦⡑⠬⣓⠮⢽⣛⠯⠬⣝⣛⡛⠿⠿⢶⣿⣶⣾⣿
⠨⠶⣒⣫⠭⠀⣀⠠⠄⠀⠀⢀⣠⠶⣋⡵⠛⢠⡾⠀⢰⡗⠈⢳⡌⠻⣪⡈⠙⢦⣌⡙⠳⠶⣭⣙⡛⠛⢶⣾⣭⣭⣉
⢘⣩⡵⠒⠚⠉⠀⠀⣀⡤⠒⣩⡴⠞⠁⠀⣠⠟⠀⠀⡾⣶⠀⠘⣇⠀⢈⢿⡶⣄⠈⠙⣷⣦⣀⠙⠿⠴⣦⣄⣌⡙⠒
⠈⠁⠀⠀⢀⣠⡴⠚⢁⡴⢚⠍⠀⠀⣀⣾⠃⠀⠀⢸⡷⢻⠀⠀⢹⡅⢀⠀⠙⢻⣵⢤⣀⠈⠛⢿⣆⠀⡤⠽⠳⢦⣄
⠀⣀⣴⡾⠛⢉⣤⣾⠏⠈⠀⠀⢠⡴⣻⢧⡆⠀⠀⢼⠂⣻⢐⡀⠀⢻⣜⢧⡀⠀⠹⣦⡿⢤⡀⠀⠉⢛⣶⣶⡤⣔⣚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡥⠤⣄⣀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣒⠾⠭⢭⡭⠭⣍⣉⣑⠒⠭⣖⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⢼⢀⡴⠙⢆⠈⣍⢑⢲⠭⣗⣤⡀⠀⠀⠀⠀⠀⠀⡼⠁⣨⣷⠚⠙⣦
⠀⠀⠀⠀⡴⠋⠳⣎⠙⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢻⠃⠀⠀⠑⠪⠷⡿⣱⣀⣉⣻⠄⠀⠀⠀⠀⠀⡇⢠⠛⢉⡇⣨⠇
⠀⠀⠀⡖⠳⢤⣀⣈⣆⡀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⣘⣠⠀⣴⡻⡅⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⡠⠔⠋⢻⢳⡄
⠀⠀⠘⡦⠀⠀⠀⠀⣰⣷⣼⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣝⡩⢾⣅⡇⢸⠀⠀⠀⠀⠀⠀⠀⣺⣏⠀⣸⢶⡚⠋⠀⡽
⠀⠀⠀⣏⣄⢀⣀⣸⠁⣻⠉⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⡝⠀⠀⠈⣺⡇⡼⠤⣄⠀⠀⠀⢀⣞⠀⢸⢷⣡⣠⣷⣀⠖⠋
⠀⠀⠀⠀⠈⠹⡄⠀⡼⣇⠉⣟⣿⡞⠣⡄⠀⠀⢀⢴⠋⠀⠚⢤⣸⡄⠀⣰⣣⠷⠇⠀⠀⠉⠢⢄⡞⠌⣠⢃⣸⠈⢰⠃
⠀⠀⠀⠀⠀⠀⠳⢴⡁⢱⡄⣿⢸⡀⠐⣳⣀⠔⠁⠈⡇⠀⠀⠻⣄⢹⡉⡏⣨⠗⠀⠀⠀⠀⢀⡌⢈⠼⡇⢦⣿⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠙⠻⡄⠷⡀⠈⣟⢦⠀⠀⢹⠀⣀⠀⠈⢳⣿⡷⢁⣀⣀⣀⢸⡀⣼⠔⠁⠀⡇⡼⡹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠃⣿⣄⢸⣄⣳⢀⡼⡀⠒⠻⠿⠀⣥⡄⠐⠛⠛⠋⢸⠉⠓⠤⣀⠀⠿⢳⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣯⠈⢻⣦⠜⠉⠀⢹⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠉⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠻⣦⡀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣤⠾⠛⠉⠉⠈⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠈⢿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠙⢿⡄⠀⢸⡇⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠷⠿⠷⣤⣀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠉⢳⣤⣴⡶⠶⠺⣿⣷⣤⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣿⣿⣿⡏⠉⢻⣿⣿⡟⠛⢿⣿⣛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠋⠀⠁⠀⠀⠀⠀⣸⣿⣿⠃⠀⢸⣿⣿⣿⠇⠀⣾⣿⣿⡇⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢠⣿⣿⣿⡟⠀⢀⣿⣿⣿⠇⠀⣾⣿⣿⠃⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠻⣿⠃⠀⣠⣿⣿⣿⡟⠀⠀⣼⣿⣿⡿⠀⢰⣿⣿⡟⠀⢸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣿⠟⠀⠀⣼⣿⣿⡿⠁⢀⣿⣿⣿⠃⢀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡃⠀⣠⣾⣿⣿⡿⠁⢀⣾⣿⣿⠃⢠⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣟⣀⣠⣿⣿⣿⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢁⣤⣶⣷⣿⣷⣶
⣿⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⡆⠀⣄⣘⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⣀⡇⢸⠿⣿⠀⠀⠀⠈⠳⣦⣄⣀⣀⣤⣶⣶⣶⣶⣴⣶⣦⣶⣾⣿⣿⣿⣿⢿⣿⢿⣿⠀⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣷⣀⣀⢸⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣧⣼⣿⣬⡟⡃⠈⡿
⠿⢻⡿⣿⣿⢿⡟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡛⠛⠁⠸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡧⠏⣻⣿⣿⣷⣿⣶⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠙⠋⠙⠁⠉⠙⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠛⠛⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⡋⠛⠹⡿⠋⠇⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡇⠀⠀⠀⠈⠀⢘⠩⢻⣏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠉


⠃⠀⡄⠀⢀⠀⣠⢀⡄⠠⠀⠀⠀⢠
⢀⡹⠁⠀⠘⣟⣿⢘⡀⣠⡅⣰⣴⡀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢺⡯⣿⠸⠳⠧⢸⣉⠉⠇⠀⣦⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠜⠃⠛⠁⠀⠀⠘⡋⠀⠀⠃⠡⠀⢰⠀⣰⢿⡁⠰⡇⢰⠄⣠⠄⢠⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠗⢸⠃⡀⠀⣿⣤⣿⠀⢀⡀⡄⠀⠀⠀⠀⠀⠠⣣⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠋⢻⡟⠌⠘⠃⠀⡀⠸⢃⠀⣏⢠⡟⠀⠀⢸⣿⢠⠀⣠⣰⠇⠀⡆⠈⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⢱⠀⠀⠀⠸⠀⣀⣤⠀⠀⠠⢀⠀⠀⠀⢀⣜⣦⣿⣞⣥⣄⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⡀⠀⠀⠀⠐⡂⠀⠀⡠⠻⡃⠈⠀⠐⢓⣄⠑⣄⠀⠐⣿⢿⣶⢿⡿⠿⣛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡂⠀⢢⠀⡄⢀⠀⠀⣾⣯⣤⠀⡀⢀⠠⠨⠀⡏⠉⠛⠒⠒⠛⠟⣿⣿⠻⠀⠀⠁⠛⣿⠂⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡆⠀⠀⠅⠕⠂⢀⡐⠞⠋⠀⠀⠉⢉⣉⡿⠷⠘⠠⠂⢶⡶⣉⣀⡇⠀⠀⠀⠀⠀⠀⣿⣇⢸⠀⠀⠀⠰⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢅⠉⢀⣀⢀⣀⠀⠀⠁⠀⠀⢀⣠⠤⠊⠁⠉⠃⠪⢕⣂⣄⠀⠀⠀⢀⢹⣇⢸⡂⠀⠀⠰⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠀⠈⢠⢃⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⣱⣭⣅⠀⠀⠀⠀⠀⠀⠀⣈⣻⣧⡀⠀⠀⢻⡇⢸⡇⠀⠀⣠⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢲⣥⠠⠃⡐⠀⠐⠍⠀⠀⠀⠀⠤⠀⣴⠛⠿⡿⠀⣧⠤⣤⢤⡄⢠⣿⣿⢣⣣⠀⠀⢸⣿⢸⠄⠀⡁⠤⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⡈⠠⠀⠖⢠⠒⠀⠀⠀⠀⠀⣸⠃⠀⠀⠐⠀⣷⠞⣄⢃⣧⠀⠠⠄⠄⠻⣷⢶⢽⣿⣼⣦⡤⣸⣧⣤⣿⣵⣤⡀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⡠⠐⠧⠒⠛⢛⠒⠶⣴⣒⠛⠛⠛⠓⠒⡇⠀⣀⡀⢠⣤⣭⣯⣫⣭⣽⡄⡤⡄⢶⠤⡷⠤⠾⣿⢿⠿⠯⣉⢻⢤⣿⣿⠧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢶⠦⢤⠤⣤⣤⡴⠞⠉⠻⡇⠀⠀⠀⠀⡇⠀⡿⢡⠀⣯⡾⢿⣻⡴⣻⠓⡴⢶⠐⠐⡷⠲⣲⡶⢲⡒⠒⠚⠛⠓⢽⣟⠛⠲⡁
⠀⠀⠀⢀⣠⣀⣀⣀⣼⢸⠀⢠⠀⠀⠀⡃⠠⠒⠀⡇⡇⢀⠀⣀⡃⠀⣇⠈⠁⣿⣇⣺⡇⣎⢸⣀⠁⣼⠀⣠⣧⢀⣽⣷⣼⡦⣄⣀⣤⣼⣠⣬⣷⠤⠴⠄
⠀⠀⠀⠈⠉⠉⠉⠙⠛⠾⠶⠶⠤⢤⣤⠄⠠⠠⠴⠓⠛⠛⠋⠉⠉⠉⠉⠙⠋⠁⠉⠉⠉⠉⠋⠉⠒⠛⠒⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐




⠀⠀⠀⠀⠀⣀⡠⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢐⠒⠂⠉⠂⠀⠀⠉⠀⠀⠀⣀⣀⣤⣤⡤⠤⠄⠤⠤⠄⠄
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣤⣀⣠⣶⣤⣀⣀⡀⠀⠀⠀⠀⢒⣀⠀⣀⣠⣶⣶⣶⣄⣤⣽⣤⣖⣂⣐⣚⣍⣉⣉⣉⣴⣶⣶⣦⣶⣦⣤⣤⣀
⠀⠀⠀⠞⠿⠿⠛⠛⠛⠛⠛⠛⠛⣛⡛⠉⠛⠙⡉⠉⠽⠛⠛⠛⠍⠛⠋⠉⠛⢉⣉⠉⠹⠛⠋⠉⠉⠉⡉⠙⠉⠉⠩⠉⠉⢉⠩⠂⢋⠨⠸⠏⠉
⠀⠀⠀⠀⠋⠈⠀⠈⠀⠀⡀⠀⢀⡤⠀⠄⠄⠀⠀⠀⠀⠀⠀⢀⡁⢠⠀⠀⠀⠠⠐⠀⠀⡉⡈⢀⠀⠤⠦⣂⠀⢤⡀⠠⠁⠀⣀⡰⢯⠁
⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⠁⠀⠀⣀⠀⠀⢤⠄⠀⣄⠀⠀⠀⠉⢀⡀⠠⡁⠠⠔⠀⠄⠀⠈⢁⡀⣠⠄⠰⠄⠂⠀⠀⢠⡀⠲⡟
⠀⠀⠀⠀⠀⣰⡄⠀⡀⠮⠀⠀⠄⠉⠁⠀⢀⡀⠀⣤⡄⠀⠲⠀⠈⠁⠀⠁⢀⡀⠀⢴⠆⠀⠛⠠⠘⠀⠀⠀⣀⣄⠈⢷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢾⠀⠀⠸⠇⠀⠈⠀⠀⢀⡀⠀⣴⠀⠈⠻⠁⠀⠰⠂⠀⠀⠀⢀⣀⠀⢐⣯⡍⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠄⠀⠀⠀⠀⠀⢀⡀⠄⠐⢾⠂⠀⠸⠀⠒⠁⠀⠀⠀⠀⠀⠀⠐⠂⡦⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠁⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢠⣄⠴⣶⢲⡆⢤⣴⣤⠄⣰⢲⡶⢂⣤⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠻⣧⣄⠀⠹⠀⣽⡇⠰⠉⠀⣠⣾⠋⠀⠀⠀⠀⢠⣾⠏⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢻⣿⡄⠁⠏⢀⠁⣰⡿⠉⠀⠀⠀⠀⠀⠀⢊⣽⣿⣯⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠈⡿⠞⠀⠈⠻⣏⠀⠀⠀⠀⠀⣴⣶⣶⡽⢻⡿⡿⢻⣹⣾⣶⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⣤⣄⡘⢿⣿⠇⠀⢇⠃⠀⣿⣿⠋⣀⣴⡄⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡠⠀⠀⢠⠤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢧⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡶⢶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢶⣦⠆⡀
⠀⠀⠀⠀⠀⠀⢀⣀⡾⣏⡙⣃⢈⡄⠀⠀⠤⠄⢀⠀⠀⡀⢠⣶⡄⢀⡀⠀⠀⡠⠤⠀⠀⠀⢈⣠⣼⣧⣄⡃
⠀⠀⠀⠀⠀⠀⣨⣭⣿⣿⣟⣯⡭⡄⠀⠀⠀⠀⠀⠈⣓⢉⣿⣿⣿⡉⢉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣿⣿⣋⣀⡀
⠀⠀⠀⠀⠀⢀⠃⣾⣿⣿⣿⡇⢇⠰⠀⠀⠈⠙⠱⠋⠁⠞⠈⣿⠉⠣⠀⠙⠟⠛⠁⠀⠀⠎⠀⣿⣿⣿⣿⠁⠰⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣇⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⣿⣿⡷⠦
⠀⠀⠀⠀⠀⢸⠁⣿⣿⣿⣿⡟⢸⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⠇⠹⣷⣿⣍⣠⠊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠈⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣷⣆
⠀⠀⠀⠀⠀⠀⢠⣤⣤⡌⣿⣿⣿⣿⣿⣿⣇⣠⣴⣤⡀⢤⣾⡿⣿⠟⣫⠟⣫⠝⢋⡵⠛⣩⠴⢛⡭⢟⡫⠟⡃
⠀⠀⠀⠀⠀⠀⢠⠖⣠⠎⣛⡿⢿⣿⠿⣻⠋⣩⠟⢩⠟⢳⠖⢶⡥⢬⣁⡚⠡⠞⢉⡴⣋⣥⣞⡡⠖⠉⠐⢋
⠀⠀⠀⠀⠀⠀⠀⢚⣵⠦⠥⣾⣾⣧⡘⠁⠔⠁⠴⣁⠴⠁⣠⠞⢠⠞⢁⠜⠉⣓⣠⠾⠿⣿⠛⠛⠻⣏⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⡭⠭⣩⣿⡪⠝⠓⠈⣙⣳⣶⣤⣀⠛⠁⢚⡥⢤⡒⠛⢯⡀⠙⢦⣄⠈⠻⣦⣀⠈⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡯⠖⠁⠀⣠⠖⣿⢾⣏⡙⠲⠬⣍⣓⠒⠦⠤⠭⣄⣀⣙⣂⣀⠙⠓⠂⠈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⠛⠷⣤⣀⠉⠛⠶⣤⣈⣉⠛⠓⠲⠶⠶⠤⢤⣤⣤⣤⣬⣤⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡙⠳⢦⣄⡙⠻⢶⣤⣀⡈⠉⠛⠛⠶⠶⢦⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠉⠛⠷⣦⣄⣉⠛⠛⠶⠦⣤⣄⣀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠤⠄⠀⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠢⡤⠤⡤⠤⣠⣀⣀⡀⣸⣴⣿⢹⣷⣼⠄⣀⡀⣠⡠⠤⡠⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠘⣦⣽⣿⣿⣻⣭⡍⡏⠈⡏⢩⢙⡹⠻⠙⣣⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠀⢀⣠⠄⠀⠰⠁
⠀⢂⡛⣯⠛⠘⠫⠝⣿⡛⠅⠣⠀⠓⠘⣛⣚⠠⠛⠈⠋⡏⣻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢠⠀⢀⠀⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠉⠈⠂⠀⠈⠁⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⣀⠠⣤⠀⠀⠀⣤⢄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢰⠁⠀⠀⠀⠉⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠀⠂⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⠢⠀⠀⠠⠊⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠄⢀⠀⠀⠀⠐⠂⠀⠉⠀⠁⠂⠺⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢀⡤⠀⢄⡀⠸
⠀⠀⠂⢬⠓⠉⠀⠄⠐⢒⡏⠈⠈⠀⢟⠒⠀⠀⠀⠑⢫⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠻⠈⠀⠠⠟⢃⡀
⠀⠀⠀⠀⢣⡖⠢⡍⠙⡻⢃⠀⠀⠀⠚⢛⠁⡥⠒⣦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠃⣀⠘⠄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠈⣰⡇⠀⠀⠀⢳⡈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡀⠀⠀⠀⣸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⢣⡀⠀⢀⠃⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠠⠀⠀⠀⠀⠀⢄⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠇⠀⠀⠀⠀⠀⠰⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢠⢠⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠤⠀⠀⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠆⠉⡞⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠓⠀⢃⣠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠣⡀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⢈⠀⠀⠀⠉⠀⠉⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠁⠀⠎⠁⢱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠒⠀⠐⢤⠊⠁⠀⠉⠓⠴⡀⠀⠒⣁⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⢴⡃⠀⠀⠀⢘⡆⠌⢀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠆⠀⠀⠀⠀⠀⢆⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠜⠁⢂⠘⡀⠀⠀⠀⠘⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⢲⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡤⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⢀⠠⠁⠀⠐

⡿⣏⠉⠉⠉⠙⡏⠉⠉⠉⢻⠋⠉⠉⠉⡟⠉⠉⠉⢉⡟⠉⠉⠉⠉⢉⡟⠉⠉⠉⠉⠉⠉⢉⡽⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙
⡇⠸⣆⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⢸⠇⠀⠀⢀⡾⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⠴⡁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄
⡇⠀⢹⡆⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⡼⠁⠀⠀⢀⡼⠁⠀⠀⠀⠀⣠⠞⠁⠰⠖⠨⠅⠀⠀⠀⠤⣈⡉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⢻⡄⠀⠀⣷⠀⠀⣼⠀⠀⢸⡇⠀⠀⣼⠃⠀⠀⣠⠟⠀⠀⠀⢀⣠⠞⠁⠀⠀⠠⣤⠀⠒⠀⠀⠄⡀⠐⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠈
⣿⣄⠀⠀⢿⡄⠀⢹⡆⠀⣿⡄⠀⣾⠁⠀⣼⠇⠀⢀⡼⠋⠀⠀⢀⡴⠟⠁⠀⢀⠀⢎⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠁
⡇⠙⣧⡀⠈⢿⡀⠸⣷⠀⣿⡇⢰⡟⠀⣸⠏⠀⣠⡟⠁⠀⣠⡴⠋⠀⠀⠀⠀⢹⠑⠛⢹⡯⠁⠀⠀⢀⣀⡤⠶⠚⠉
⣧⡀⠈⢿⣄⠘⣷⡀⢿⡄⣿⡇⣼⠇⣰⠟⠘⠛⢋⣀⣠⣾⠋⠀⠀⠀⠀⠀⢀⣸⣄⢠⢈⠉⣤⡴⠚⠋⠁
⡏⠻⣶⣄⠹⣧⡘⣷⠸⠇⠻⠃⠿⢰⣿⣶⡶⠛⢸⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣼⣤⠷⠾⡦⢹⠁⠀⣀⣤⣀
⣿⣦⣄⡙⢷⠜⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣎⠈⣿⡗⢹⠍⢿⣿⢿⣿⣿⣿⣿⡷⠀⣰⣖⣁⣠⣮⣩⣿⣝⢷⡀
⣧⣤⣙⡻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁⠀⣿⡷⣿⣿⣾⢫⢦⣤⣹⣷⠆⡇⢠⣿⠏⠋⢰⢺⣷⣿⣿⣯⣷⡤⠤⠤⠤⠴⠖⠐⠒
⣯⣬⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⢻⣧⠟⣻⣿⣼⡆⣙⣛⢳⡇⣿⣿⣎⣴⠀⠈⣿⣿⠿⢿⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢀
⣯⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⡀⠀⢍⣤⣴⠿⠃⢰⣿⠷⣛⣶⣿⣿⣿⣿⣿⣿⡟⠻⣀⡌⣿⣿⠠⢸⣿⢇⣀⣀⡀⠀⠀⠀⢀⢀⡴⠁⠀⠀⠀⠀⠈
⣯⣭⣤⡆⠀⠀⠀⠀⠀⠀⠀⢸⡏⣬⣇⣈⡀⠸⣷⣀⠀⢀⣿⠸⣍⠼⣿⣿⣿⡿⠛⠛⠁⣦⠙⠇⠉⠟⢀⣼⡟⠈⠉⠉⢉⠛⢃⠊⠁⠀⠀⡴⠂⠀⠀⠄
⣟⣉⣴⡾⢂⡀⠀⠀⠀⠀⠀⠈⡗⣕⠃⠀⠀⠈⠀⠀⠀⠀⡍⡗⢢⣟⠉⢏⣿⠃⠀⠀⠐⠿⣦⠀⢰⡆⣸⣏⠀⠀⡀⠐⠃⠀⠀⠀⠐⠰⠋⠁
⡟⠋⠁⠘⠛⠁⠀⠀⠀⠀⠀⠒⠶⠒⠲⠶⠒⠒⠖⠲⠶⠶⠤⡴⠿⠿⣽⢾⠿⠤⠤⠶⢶⡴⢾⣦⡿⣄⢉⣌⢀⣤⠤⣤⣄⣤⣄⣰⣲⡖⣶⢶⡶⣶
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣬⣥⣤⣬⣤⣤⣤⣤⣤
⣿⣿⡿⡻⠿⠛⠿⠿⡿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠠⡤⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⣀⠀⠀⠢⠄⠤
⢀⡀⣀⣀⠀⠀⢀⣀⣈⣤⠤⠤⠤⠬⠉⠢⠤⠴⠶⠶⠶⠤⠤⠤⠤⠤⠽⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⣤⠬⠝⠛⠛⠋⠉
⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠀⠀⠀⠐⠒⠀⠐⠂⢁⠂⠀⠂⠐⠂⢤⠤⠤
⠀⠀⠀⢠⡄⠀⡂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣠⣤⠿⠔⠰⠤⠐⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠤⠀⠄⢠⣄⡀⢀⣠⠴⠰⠒⠂⠀⠙⠛⠉⠙⠢⠀⠀⠀⠀⠀⠙⠩⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⡤⠴⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠛⠷⠶⠶⠆⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⠒⠒⠓⠒⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣴⣷⡆⢠⣾⣿⣧⠀⠀⠀⠀⢀⠀⠥⠦⠐⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠋⠀⠀⡿⢿⣿⡧⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠠⠄⠀⠀⠀⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⠀⠉⠹⣷⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠁⢸⣿⠀⠉⣀⣀⠀⢀⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣄⠀⢀⣀⡈⠁⢸⣿⠀⠉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢷⣆⢀⣶⠟⢻⡿⠀⣾⣯⣤⣤⣄⣤⣤⣤⣤⣤⣤⣄⣤⣬⣿⠂⠸⣿⠛⢷⣆⢀⣶⠟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣶⠿⠻⢷⣾⣛⣁⠀⠈⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⣉⠉⠉⠀⢀⣙⣿⣶⠿⠸⢷⣾⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⢷⣆⢀⣾⠟⣻⣿⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠹⣿⡛⢷⣆⢀⣶⠟⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⡶⠿⠹⠷⣾⣟⣁⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⢀⣙⣿⡶⠿⠹⠷⣾⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⢿⣆⢠⣾⠟⡻⠋⣠⣴⠶⠿⢦⡈⠙⠻⠿⠿⠛⠋⣠⠾⠷⣶⣤⡈⠻⡛⢿⣦⢀⣾⠟⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠹⠷⠾⢁⣾⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢿⡄⠹⠶⠟⠙⠷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⢸⡏⠀⠀⣀⣀⣼⣧⣀⣀⣀⣀⣀⣠⣿⣄⣀⡀⠀⠘⣿⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣶⡄⢸⡇⠀⠀⣿⡏⢹⡏⠉⠉⠉⠉⠉⠉⣿⠉⣿⡇⠀⠀⣿⠀⣴⣾⣿⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣴⣾⡇⢸⡇⠀⠀⣿⡇⢈⡁⠀⠀⠀⠀⠀⠀⣉⠀⣿⡇⠀⠀⣿⠀⣿⣶⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣟⣉⣈⡀⢸⣧⣀⠀⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⣿⡇⢀⣠⣿⠀⣈⣈⣹⣿⣧⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉







⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠦⠤⢤⣠⣶⡿⠷⢤⡷⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡋⣁⡀⠀⢀⠀⠀⢻⣦⣾⣧⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠶⣒⣒⠛⢛⣋⡉⠭⢨⣟⢲⣿⡟⣿⡞⠋⠙⣷⠼⣿⣿⠟⣿⣦⠟⠉⠛⠛⠒⠶⠶⠶⠴⠖⢤⣄
⠀⠀⠀⠀⢀⡤⠒⡡⠊⠉⢑⠀⠠⡔⠀⠈⠁⠀⠛⠉⢀⣤⡾⠉⠾⣿⡿⣿⣶⣾⣿⣿⣷⠈⠿⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⣠⣴⠞⢉⡞⣰⣇⠈⣿⣧⣙⢿⡿⣿⣿⡋⠀⠀⠘⡇
⠀⠀⠀⠀⠁⠀⠄⠀⠀⣀⣀⣀⣀⣠⠴⠺⢿⡿⠃⢠⣾⠅⢿⣿⣶⡍⠛⠿⣿⡞⠲⡏⠀⠀⣾⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡹⢿⣿⣄⠈⠣⠴⠛⢿⣦⠘⣿⣿⣏⣀⣀⣼⣷⠚⠉⣀⠞⠙⠛⢭⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣡⡀⠘⢿⣿⡀⠀⠀⢀⣼⡿⠷⢟⣿⢟⣟⠟⡼⣿⡷⠊⠁⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⢀⣠⠿⡭⠭⣯⡈⢿⣿⣷⡀⠙⢿⣦⠀⠘⣿⣀⡰⠋⢡⣾⣧⣾⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠋⠁⠀⠀⣬⣿⣿⡌⠻⣿⣷⡀⠘⣿⣿⡶⠋⢘⢷⣴⠟⠁⠽⠁⣿⠻⣟⡒⢢⣄⡀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡿⣿⣄⠙⣿⣿⣦⣘⡿⠅⠀⠉⠛⢳⣄⡔⠰⣺⠇⠀⠈⠻⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⣌⢿⣷⣌⣿⣿⣿⠀⠀⠀⢀⡔⢣⠋⠀⢠⡏⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠃⠉⠉⠉⣠⡏⠀⠠⠖⠉⢀⠄⠁⠶⡞⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⠀⠤⠐⠁⠊⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠈⣀⠖⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠦⣠⠾⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠀⠀⢀⠀⡀⠀⣠⣿⣄⠀⢀⠀⠀⠀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠻⣄⠈⢲⣷⣶⠿⠿⠿⣿⣿⡶⠁⣠⠶⠁⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠂⠉⠉⠁⠉⢉⣛⣿⣿⣶⣤⣄⣀⡈⢓⣿⣿⣿⣧⣰⣤⣿⣿⣿⣛⣁⣤⡴⠶⠟⠻⠿⠍⣉⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠁⣀⣤⣎⣁⣈⣹⣿⠟⠙⢻⣿⣿⡿⣿⣿⡿⠋⠻⠍⠲⣤⣤⣤⠷⠦⢄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠉⠀⠀⡤⢻⠛⠀⠀⠀⠀⢸⣿⣟⣛⣿⣿⣷⡀⠀⠀⠀⠈⢦⠉⠲⣄⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⣟⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠢⣀⠀⠀⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠖⠊⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡄⠈⠛⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠻⣿⣿⣿⡿⠛⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⠀⠀⠀⠞⠀⠂⠐⠀⢐⡮⠀⠤
⠀⠀⠀⡀⠐⢐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢈⢀⠃⠀⠀⠠⠔⢠⡄⡀⠀⠠⠘⠁
⠀⠀⣀⠱⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡄⠩⡀⠁⠀⠀⠀⣡⠴⠛⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠔⢀⠀⠀⠀⠀⢠⠀⠀⠠⠙⠼⠒⠒⠒⠀⠁
⠀⠰⣄⣀⡀⠰⠴⢄⡀⠀⠀⠒⠊⠀⠄⡄⣀⠁⡈⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⢀⡠
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⠄⠀⡀⠀⠀⠀⠁⢀⠠⠀⠐⠀⠤⠒⠋⠁⠈⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡀⣀⣿⠄⠀⠀⢠⡴⠻⡆⠿⣄⠀⠀⠀⠀⠠⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⣤⣤⣬⣿⠀⢠⣶⠎⠀⠀⠁⠀⠈⠇⠀⠀⠀⠀⢈⣷⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡯⠀⢰⣿⠀⡄⡄⡤⠀⡀⠛⠲⢤⣀⠐⠚⠉⢻⣯⠀⠀⠀⢀⣠⣄⠳⢶⠶⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣗⣀⣸⣿⡀⠀⢄⡇⠀⢁⣜⣿⠛⠃⡀⡤⠤⢼⣿⠀⠀⠐⢀⠘⠛⠛⠓⣦⣼⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠈⠀⠀⠂⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠈⠈⢉⠀⠁⠀⠈⠑⠋⠒⠐⠈⠉⠍⠉⠙⠒⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠄⠠⡀
⠀⠀⠀⠄⡈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⢀⣀⡀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⠔⡢⣀
⠀⠀⠀⢀⠀⠀⠀⠂⢈⠁⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠤⠦⠄⠬⢤⢠⠤⡄⠀⠀⢈⠠⢒⠁⡈⠑⠒⡤⠁
⠀⠀⠀⠴⠄⣀⣀⢄⣀⡰⠀⠀⠀⠀⠀⠀⠂⠀⠈⠖⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣂⣥⠂⠋⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣠⣧⣤⡀⠀⠀⠂⠂⠀⠀⠀⠠⡀⠀⠠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡠⠀⠐⠀⠐⠢⡀
⠀⠀⠀⠀⠆⠁⠀⠸⠉⠀⠀⠀⠈⡏⢀⣠⡇⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠘⡀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠢⠀⠀⡥⠀⡨⢀⠀⠀⠀⠠⢀⠙⠀⠂⠀⠆
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⡠⠞⠓⠒⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣤⡴⠋⠁
⠀⠀⠀⠀⠋⠰⡂⢴⠇⠀⠀⠀⢀⠀⢸⣅⠴⠳⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⢷⢀
⠀⠀⢀⣆⠾⢋⠕⠀⠀⠀⠀⠀⢞⣺⠄⢿⡄⠒⠀⠄⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠁⠀⠃⠃
⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠐⠞⠂⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠂
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀
⠀⠀⠀⠀⠀⡏⠀⠈⠃⠀⠀⠀⠀⠀⡀⠤⠤⠮⢀⠀⠴⠂⠀⠀⠀⡇⣾⣿⣿⣆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⣀⠀⠔⢚⠁⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠀⠀⠀⠃⠾⠇⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢐⡰⠒⠢⡔⠀⠀⠀⠀⢀⣼⡟⠉⠀⠀⠀⠀⠀⠀⠀⠆⣀⠀⠀⠤⣀
⠀⠀⠘⠒⠂⠐⠂⠈⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⢤⡀⢰⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⣀⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢂⣂⠴⠚⠁
⠀⠀⢧⠀⠈⢦⣧⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣹⣶⣿⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣯⠠⠈
⠀⠀⠀⠙⠲⢄⣳⡍⢇⣀⠀⠀⠀⠀⡤⣊⡵⢆⠜⣷⠶⣿⠦⡱⢮⣑⢤⠀⠀⠀⠀⢾⣿⢀⡍⡔⣇⣦⡀
⠀⠀⠀⢠⣾⣇⡮⠇⠘⠟⠀⠀⠀⠈⠉⠛⠚⠁⠀⢘⡿⠍⠀⠈⠓⠛⠉⠁⠀⠀⠀⠠⠂⠈⡀⠸⡙⢟⠇
⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠨⠁⠂⠄⠀⣰⣆⠀⠠⠐⠈⡅⠀⠀⠤⣄⣀⡀⣠⠶⣤⢀⣀⣀⠤⠤⡀⢀⠤⠤⠄⣀⢠⣶⣄⢀⠀⠤⠤⣄
⠀⠀⠹⠛⠓⢿⠷⠾⡿⠚⠛⠏⠀⠀⠀⠀⠀⠀⠀⣽⠒⣿⠀⠀⡀⠄⠀⠀⠈⠒⠶⡒⣨⢿⠿⢿⢭⡐⡲⠖⠊
⠀⠀⠀⠀⠀⠈⢽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠢⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠉⠳⣄⢰⣄⡠⠞⠁⠀⠀⠀⠀⠀⢀⣀⣀⢠⢢⢀⣀⣀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡱⡎⠀⣀⣀⣀
⠀⠀⠈⠓⠒⠂⣡⣈⠒⠒⠚⠁⠀⠀⠀⠀⣏⠀⢀⣨⠞⠉⠀⠀⡷⠀⠀⠀⠀⠘⠤⣄⢈⣁⡷⢞⣉⠀⣤⠔⠁
⠀⠀⠀⠀⠀⠘⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⡝⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣯⣵⠀⠉
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠐⠲⣕⣦⡔⣩⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠤⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡔⠉
⠀⠀⠀⠓⢒⣾⣿⣿⣶⡒⠚⠀⠀⠀⠀⠀⠀⣀⠴⣞⣙⣳⠤⡀⠀⠀⠀⠀⠀⠀⠂⠉⣩⣤⡼⣦⣬⣉⠁⠂
⠀⠀⠀⠚⠁⠐⣟⡿⠀⠉⠂⠀⠀⠀⠀⢀⠜⠁⡠⢧⠀⡼⣄⠈⢢⡀⠀⠀⠀⠀⠲⠟⠋⠐⣛⡛⠈⠛⠷⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠀⠉⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⢀⣠⣤⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠻⠁⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣀⢀⣀⡈⠁⠉⠀⠀⠀⠀⠀⠂⠄⠀⣰⡖⠛⠣⣸⣿⠟⢀⡴⢦⠀⠤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡞⣿⡏⢻⠇⠁⠀⣶⣶⣶⣤⣤⣀⣀⡀⠀⠀⢈⣤⣿⣵⣶⣿⣧⠀⠐⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢶⣆⢶⣮⠀⢀⣿⣿⡛⢻⣿⣿⠿⣍⡳⢤⣼⣯⣏⣽⣭⠽⢿⡄⣀⣶⡎⠀⠒⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠤⢀⣸⣛⣨⣏⢠⣭⠁⢸⣿⣿⣄⣸⣀⠠⠰⣿⣾⣿⡏⢁⣻⣿⣶⣷⡰⠛⣉⡄⠀⠀⠘⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠈⣿⠄⣿⠆⣿⠂⣸⣿⣿⣂⣻⣫⣶⡴⢿⣿⡜⣤⣼⡽⢿⣆⢉⡴⠟⠛⠁⡴⠀⠳⡄⢹⣿⣿⠀⢀⡀
⠀⠀⠀⣴⡦⣶⣗⢾⡀⢘⠀⠘⠁⠀⠀⠀⠀⠀⠰⡇⢠⡅⠀⠀⠉⠈⠉⠈⠉⠛⠭⠉⠃⠉⠀⠒⣀⠙⠋⣠⣴⡆⢰⡇⠀⠀⢧⠀⣿⣿⡄⠿⠽⠶⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣷⠀⠇⠀⠀⠀⡀⣄⠂⢴⣲⣶⣶⣝⢳⡄⠀⠙⢷⡾⠋⢁⡄⠘⡇⠀⠀⡟⢀⡿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣿⣇⣄⠀⠀⠀⠀⠘⢀⣿⠿⠛⠋⢹⣙⣫⣽⣿⠿⠿⣿⣏⢿⠂⢲⣤⣀⣴⠟⢁⠀⢳⣀⣰⠃⣸⠁⢀⣀⣀⣀⡠⠤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢺⣿⡇⠀⢸⣷⣾⠢⢤⣤⠴⠞⠛⢣⡤⣲⣿⡏⠀⣦⢹⣿⣾⣧⣤⣤⣉⣉⣴⠟⣤⠈⠻⠤⠞⠃⠀⣠⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣩⣿⣿⡶⣿⣿⣿⣶⣶⣶⣶⣿⣿⡗⣚⡽⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣉⣾⢏⣷⣄⣀⣀⣠⣴⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⢾⣿⢿⣿⣿⣿⡿⠟⠉⠉⠉⠙⠛⠱⣺⠿⣿⣭⣼⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠾⠯⠟⠋⠋⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢕⣯⠷⣫⣖⢋⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡼⠁
⠀⠀⢀⠴⠒⠛⠛⠒⠲⠤⣄⡀⠀⠀⠀⠀⢀⡼⠟⠉⠉⠻⢧⡀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠛⠒⠦⡀
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⣠⠏⠀⠀⠀⠀⠀⠀⠹⣄⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⣤⣤⣤⣤⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⠟⠛⠛⠻⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠙⠒⠦⠤⠤⠤⣴⡶⠶⠛⠋⠉⢠⣿⣶⣶⣶⣶⣿⡄⠉⠙⠛⠶⢶⣤⠤⠤⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⣠⠋⠉⠉⠉⠉⠉⠉⠛⣄⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣴⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣦⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠖⠋⠈⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠃⠙⠲⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⣀⠀⡀⠀⠀⡀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣤⣤⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⣸⣠⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠷⠶⣿⣿⣿⣵⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣶⣍⡑⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⣿⡿⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⠋⠇⢸⣿⠌⠻⣝⣝⠉⠒⡄⣀⡀⢀⣠⣤⣬⣵⠀⠀⠀⠀⠀⣻⣻⠃⠁
⠀⠰⠖⠂⠀⠀⠒⠲⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣋⡙⠿⢠⣿⣯⣿⠶⠆⣀⣴⣼⣴⣄⣀⠠⠤⠤⠶⣶⣶⡆
⠀⠀⠶⠶⠶⠶⢦⣠⣤⣄⡍⠿⠿⢝⣻⣟⣻⣿⣿⢸⣿⣃⢸⣿⣿⣿⣏⣽⣦⣶⣼⣿⡏⠉⠉⢹⣿⣄⣀⣤⣤⣿⣿⣛⣭⠁⠐⠒⠂⠐⠒⠒
⠀⢠⣤⣤⣤⣤⣤⣤⣬⣤⣖⣲⣿⣿⣿⠿⠿⠟⠛⠘⠛⠋⣻⣟⣛⠛⠋⠙⠛⠛⠘⠛⠃⠀⠀⠚⠿⠿⠿⠛⢿⣭⣷⣴⣾⣴⣶⣶⣤⣤⣠⣤⡀
⠀⠸⠿⠿⠟⠛⠛⠉⢉⡩⠁⢀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⢙⣿⣏⣤⣤⣰⡤⣴⣤⠴⣶⣤⣤⠦⢀⣀⣀⡀⣀⣛⣻⠿⠿⠿⡿⠿⠟⠻⠿⠿⠇
⠀⠀⣀⣿⣇⣤⣜⣅⣀⣦⣤⣏⠙⣿⣟⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣟⣱⡇⠢⣦⣿⣿⠃⣠⠈⢻⣿⣤⠈⠛⢛⣦⣤⣤⠂⠀⠀⠀⡀⢀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⣿⣶⣀⡀⠀⠀⡀⠀⠀⠈⠙⠿⣿⣿⣿⣷⢀⡟⡿⠿⣢⣿⡀⢸⣿⠿⣆⠀⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⡀
⠀⠠⣶⣾⣿⣽⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⡷⠗⠖⠺⡿⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣇⣹⢇⣿⣿⠗⣾⣶⣾⣿⡶⣶⣾⣿⣾⣶⣶⣶⣶⣿⣿⡄
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣨⣯⣗⣀⣐⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣻⣻⣛⣿⣿⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠔⡳⠀⠀⠱⠀⠀⠀⠀⠡⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⢣⠀⠀⠀⡘⠀⣀⣀⡠⠀⠀⢀⠂⠀⠠⠈⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠤⠄⡈⠀⠀⠀⠸⠆⠀⡁⠈⠑⠂⠠⠧⣠⡛⢢⣾⠛⠛⠋⠻⠛⢻⣻⣯⡎⠀⠀⠙⣼⣟⡛⠛⠛⠛⠛⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠈⠗⠂⢦⠘⠂⠀⠀⠀⠀⢀⡿⣶⢻⠁⠉⠈⠻⠶⣶⣶⠿⠟⠿⠛⠃⠀⠀⠀⠛⠻⠻⠿⣶⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣀⠃⡰⠐⠄⠀⠀⠀⠀⢸⡷⢁⠄⠀⠀⠂⠀⠰⢈⠟⠛⠒⠶⢴⡃⠀⠀⢸⢦⠴⢶⡓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣄⠀⢀⠀⠀⠀⠀⠀⠄⠠⡀⠠⠀⠀⡀⠀⣸⠗⠀⠀⠁⠀⠀⠁⠀⠀⡇⠀⢀⡠⠜⣣⠀⢀⡂⠀⠀⠀⠉⠑⢦
⠀⠀⠀⠀⢀⣀⣀⣤⡀⢀⠀⣤⣌⠋⠊⡿⠣⡄⠀⠉⠀⠘⠀⠀⠉⠑⡄⠈⠹⡿⢤⠀⠀⠄⠀⠀⢀⢢⠛⠀⠀⢈⠇⠘⢿⣇⣿⠟⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣠⣦⣭⣭⣽⣷⣞⣷⡟⢻⠟⠈⠀⠀⣄⠀⠡⠀⠇⠀⢆⠀⠐⠌⠀⠀⠈⠑⠐⢟⢠⡚⡈⠈⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣭⣍⣙⠻⠏⠀⠈⠿⠃⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⣔⢂⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢻⡿⠛⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠡⠘⡄⢀⠳⣦⠀⢀⢀⣀⣀⣠⣤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠳⡀⣥⠀⢉⠄⠀⠆⠁⢄⠉⡇⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠁⠀⠀⡀⠀⠓⠀⠀⢀⠈⠧⠘⡌⠻⡊⠄⠑⠆⠀⠸⠁⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⠲⠒⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠀⠂⢀⠀⠂⢤⠀⡅⠠⠡⠀⣠⡔⠂⠀⠚⢃⠀⣾⡷⡄⠁⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠠⠀⠀⠀⠀⠂⠓⠀⠀⠀⢀⣀⠤⠀⠂⠉⠉⠀⢀⠸⡁⡇⢰⢦⡄⠰⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢳⠀⠀⡀⠉⠐⠀⠤⡀⠀⠀⠀⠶⠆⡀⠄⠠⠀⠀⠂⠠⠀⠀⠀⠈⢇⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⡇⠠⠀⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠐⠐⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⢀⣠⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⡛⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠀⠄⠋⠲⠅⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠎⠰⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣟⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡄⢠⠀⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣟⣿⢧⢤⡤⢀⡓⣼⠀⡇⠀⣀⠀⠈⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⢀⣤⣦⣄
⠀⠀⠀⢠⣤⣿⣷⣏⠉⠉⠁⠈⢡⠘⡀⠇⠸⠿⢧⣤⣯⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠦⠴⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠓
⠀⠀⠀⠈⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣇⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣟⢛⣛⣠⢻⡤⣾⣀⣠⣤⠀⢠⡀⠀⠀⢸⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠤⣄⡨⢻⣦⣀⡻⣿⣿⣿⣩⣀⠀⠀⠈⠉⠛⠿⠷⣨⡄⠀⠸⣿
⠀⠠⣀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡶⡀⠲⢧⡁⢘⣧⣁⡨⣿⣿⣋⣰⣶⣤⣀⠀⠄⠀⠀⠀⠀⠀⠀⠛⢀⡀
⠀⠀⠈⠁⠙⠣⠴⢤⣤⣀⡀⣾⠟⠀⠀⢛⢧⠈⣼⣿⣧⣿⡇⣯⣉⠻⣿⣿⣿⣷⣶⣤⣀⡴⠒⠋⠉⣠⡅
⠀⠀⠀⠀⠀⠐⢠⣶⣿⣿⡆⣿⢸⡆⠀⣼⣕⠤⣿⣿⣯⣿⣷⣿⢿⣆⠬⠿⡿⣿⣏⠛⢿⣿⣿⣿⠉⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠹⡟⢀⠀⣿⣾⣷⣿⣷⡴⡔⣖⢧⣘⢿⣇⡀⡏⣿⣿⡆⠈⣿⣿⣯⠀⣿⣷⡶
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣆⠻⠎⣸⣿⣿⣿⣿⣿⣷⣾⣮⣷⠙⡓⠆⠉⢃⡸⢿⡇⡀⣽⣿⣿⠠⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⣷⣶⣹⣁⣼⣟⣿⣠⣭⣼⣿⣿⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⢻⣿⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⠉⠛⠉⠉⠀⠉⠻⣿⣿⣿⣿⣿⠀⠓⠘⣿⣿⣿⠉⠉⠀⠈⠻⠿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⣠⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠾⠿⠿⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣸⣯⣍⣭⣭⣩⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡆⠀⣀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⢀⣾⣇⡀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⢌⠡⡾⠁⠀⠀⠀⠀⣾⣾⣿⣠⡶⠷⣄⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⣸⢯⡉⠙⠀⡀⠀⠀⣼⣿⡿⠿⠿⣿⡁
⠀⠀⠀⠈⠉⠄⠀⠀⠀⠀⠘⠧⠟⠁⠈⠳⠶⠋⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠴⠃⠀⠙⠄⠀⠁⠀⠸⠟⠌⠀⠀⠠⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⢀⡄⢠⣀⣄⠀⠀⠀⠉⣜⣾⢉⢭⠉⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⢿⣿⣆⣀⣀⡀⠀⠀⠀⣶⣆
⠀⠀⢉⣿⣦⠘⣿⡿⠟⠀⠀⡆⡈⣹⣞⣁⣢⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣼⣿⣿⣿⢿⡳⠦⠀⠀⢿⣿⣧⣤⣾⡇
⠀⠀⣬⡙⠛⣾⣿⠁⠀⠀⠀⠈⢻⡆⣾⠟⠁⠀⠀⠀⠀⠀⠀⠁⡒⠒⠀⠀⠈⠀⠘⠀⠘⠂⠢⠀⠀⠀⠀⠹⠿⠋⠁
⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⣠⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢
⠀⠀⣠⣿⡟⠛⣿⣧⠀⠀⠀⢰⣧⣿⣼⣧⣷⠀⠀⠀⢀⠀⣴⣶⣿⣶⡄⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⣴⣶⣶⣿⣿⣿⡆
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⢰⡷⣿⢾⡷⣷⠄⠀⠀⠀⠑⢻⠛⣿⣏⡀⠀⠀⠀⣼⣶⡄⠀⠀⠀⠐⠛⠛⣿⡿⠛⢻⡇
⠀⠀⠘⠟⠛⠛⠛⠟⠀⠀⠀⠚⠳⠿⠾⠗⠿⠆⠀⠀⠀⠀⠀⠁⠀⠛⠃⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠃⠃⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣸⡷⠄⠀⠀⡄⠀⠀⢠⡶⠛⠿⡗⠰⠿⣧⡀⠀⠀⠀⠀⠀⠀⠑⢌⢢⡀⠀⢀⠀⣠⢔⡵⠊
⠀⠀⠀⠈⠉⠈⠉⣿⣧⠄⠀⠀⡀⢀⣠⠋⠀⠀⠀⠳⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠑⢽⣖⣸⣿⡕⠁
⠀⠀⢱⣶⣶⣶⣿⣿⡧⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣏⣱⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣃⡀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⠿⣦⣄⡀⠀⠀⣠⢞⠽⠉⠙⣿⣿⢏
⠀⠀⢸⣿⣿⣿⣿⣿⡁⠀⠀⠀⣿⢿⠇⠸⠇⠸⠁⡿⠈⠀⢾⠆⢠⡄⣤⡌⣭⣷⢒⠔⠁⠀⠀⠀⢸⣿⡗⠀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⠋⠁⠀⠀⣿⣸⡀⣀⣀⣸⣀⣿⣀⣀⣀⣀⣈⣃⣿⡇⠛⣃⢈⠀⣠⡦⠤⠤⣴⣿⣇⠈⠁
⠀⠀⠘⢿⣿⣿⡿⠿⠛⠛⠛⠫⠋⠉⠁⢀⡠⠐⠋⠁⠀⠀⡀⠊⣉⠛⠁⠀⠀⠀⠈⠠⠈⠁⠘⠤⠚⠿⠷⠶⠂⠐⠐⠂⠀⠀⠤⢤⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠀⠀⣀⠀⠀⠀⠀⠐⠀⡀⠀⠈⠀⠒⠀⡔⠂⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠈⡉⠉⠐⡒
⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡀⠀⠀⠀⠊⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠩⡄
⠀⠀⠀⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠐⠂


⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢰⠀⠀⣿⠀⢰⠇⠀⣰⠂⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠙⢦⠀⠹⡀⠀⠘⡇⠀⡏⠀⡼⠀⢠⠃⠀⢀⡞⠁⠀⠀⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠙⢦⡀⠳⡀⠘⠀⠀⠃⠀⠃⠀⠃⢀⠃⠀⡠⠋⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀⠉⠢⢄⠙⠦⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠔⠁⢀⠴⠊⠀⠀⠀⠀⣀⣤⠴⠾⣭⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠒⠲⣤⣀⡈⠁⠀⢠⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠤⠔⠚⠩⠋⢀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⠞⠙⢆⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠖⠂⠀⢼⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⣶⣲⣆⣾⣾⣿⣦⣼⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢼⣆⠀⠀⠀⠀⠐⢰⠑⢺⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣇⣀⣀⣀⣼⣿⣫⣿⣿⣿⣿⣿⣿⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣶⣶⣤⣄⣠⣯⡴⣯⠷⡶⢶⠗⡶⠲⡶⢦⡤⣤⣤⣦⣼⡀⢸⣯⣿⡽⠷⠿⣟⣛⣛⣿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡟⣿⢩⠇⣿⢁⡏⢠⡏⣼⢁⡇⣸⠁⡾⢠⠏⠴⠡⠞⣱⠯⢛⣫⠥⠖⣂⣩⡭⠤⠔⠒⣒⣒⣒⣒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣸⢰⡇⣸⠁⠾⠀⣋⣨⡤⢤⠲⡖⢦⠒⡺⠖⣉⠔⢊⡩⠔⣚⣩⠥⠒⢒⣉⣉⡭⠭⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⣉⣴⢲⡙⣏⠳⡜⢆⠳⠈⡠⢊⡠⢊⡠⠚⣩⠔⢋⣡⠴⠚⣋⡩⠤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠷⠘⡆⢱⡘⢠⠎⡠⢋⡴⢋⡴⢋⡤⠚⢉⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠉⠀⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⡰⠃
⠀⠀⠹⣿⣿⣦⣀⠀⠀⡰⢆⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠙⠻⣁⡐⠙⠆⠓⠈⣇⣀⣀⣼⣇⣀⣈⠧⠀⠠⠐⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⠀⢀⠀⠤⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⢠⣴⠖⠋⠉⠙⠄⠈⠀⡄⠀⠁⠒⠂⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠉⠁⠀⠀⠀⡀⣠⣀⠈⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⠀⠀⠀⣀⢤⡆⠀⠅⠂⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠽⠍⠙⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠂⠀⠀⠐⠂⢄⡀
⠀⠀⠀⣠⣴⣶⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠉⢓⡐⠒⠂⠀⠀⠈⠉⠻⣦
⠀⡴⣾⠿⠿⡶⡤⣄⠈⠀⣖⢲⡖⢲⣴⣤⣄⠀⠀⠀⢀⠀⠴⢶⠋⢻⡀⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⢀⣻⠄
⠀⠀⣙⠻⡱⣓⡗⠀⠘⢼⠃⣜⠣⡞⠥⠗⢽⣳⠄⠀⠀⠀⠀⠘⢷⠮⢶⣦⣤⣸⣷⣤⣶⣷⣶⣶⡶⠿⠛
⠀⠀⠈⠋⠀⠈⠈⠱⠤⢥⠔⢤⠞⣥⠖⠀⠲⠟⠁⠀⠀⠀⠀⠀⠘⠀⣀⡿⠙⢇⠈⠉⠉⠉⠉⠙⠶⠶⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣴⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠡⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢀⠀⣰⡓⣐⣄⣶⣷⣰⣄⠀⠙⠻⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠘⠳⣄⡀⠀⠀⠀⠀⠈
⠀⢀⡏⣴⣆⡀⣿⣿⣍⣽⣿⠏⡷⢧⣀⡄⢋⠁⠦⠀⠀⠀⠀⠀⣀⣤⣠⣴⣤⠴⠊⢉⣿⢟⡶⣺⢿⣷⣾⠉⠈
⠀⠘⢦⡟⠁⠀⠉⡿⠛⠁⠉⠙⠃⠀⠺⢣⣄⠱⠀⡁⠀⠀⣠⣾⣿⣿⡇⣼⡿⢿⢸⢧⡿⣻⠟⢯⡞⠙⡾
⠀⠀⠀⠑⢰⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢠⠄⠀⠈⠙⠛⠉⠉⠁⠁⠀⠀⠉⠉⠉⠑⡄⠀⠀⠠⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⠀⢤⡘⠿⣿⣧⣾⣦⣶⠄⠆
⠀⠀⠀⠀⢀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⠘⠳⣲⣿⣿⠟⣿⠃
⠀⠀⢄⣾⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⢿⣧⣿⣻⡿⠇⡀
⠀⠀⠀⣈⣿⣿⣿⣾⣿⡿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⢿⣿⣿⠟⠃⢸⣿⣿⣟⣖⣶⡛⡏
⠀⠀⠈⠿⠿⠿⣿⠛⠛⠿⢿⣷⣾⣴⣶⣶⡄⢀⣠⣀⡀⣀⣀⣀⠀⠾⠟⠿⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣇⣀⣀⣠⣤⣿⡟⣟⡻⢋⢛⣿⣼⣿⣾⣿⣿⣿⣶⡖⢶⠀⣷⠀⡀⠈⠏⢹⣿⣿⣿⣿⣇
⠀⠚⠿⠛⠛⠛⠛⠛⠻⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⡇⣽⣼⣥⣾⣤⣴⣶⣛⣿⣿⣿⣿⣿⡄
⠀⠀⠐⠒⠒⠛⠒⠛⠛⠛⠻⠿⠛⠛⠛⠉⠈⠋⠙⠙⠛⠋⠉⠉⠉⠀⠉⠉⠋⠉⠛⠛⠉⠛⠛⠙⠻⠿⡿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠉⠉⠉⠙⣦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡆⠀⠀⠀⡠⠀⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢠⡤⣀⠀⠀⠰⣄⠀⣠⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣇⠀⠀⠀⠈⠑⠂⠀⠙⣷⡿⢿⣿⡿⢀⣠⠠⠴⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠐⠀⠀⣀⠀⠘⣿⣷⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠂⠀⠉⠐⠾⣿⣿⣿⡟⠁⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⢀⡤⢶⣶⣾⣿⣷⣉⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠈⢳⠆⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣰⣟⢠⣟⣻⣿⣿⣇⠙⠛⣆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢦⠀⣸⠟⠉⣾⣟⠺⢿⣿⡟⠀⠀⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠲⠆⣐⠦⠀⠀⠀⠄⠃⠀⠀⢹⣧⣴⣿⣿⠇⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⡌⢻⣿⡿⠋⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠰⢇⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡆⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠒⠀⡀⠀⠀⠀⠀⠀⢀⠈⡈⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⠀⠀⠀⠑⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⣠⡄⠈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⡇⠀⠀⠘⠧⠀⠀⠄⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⢰⠁⠀⠀⠀⡀⠳⣄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⢀⣄⠀⠀⡆⣾⠈⡌⠀⠀⡰⠃⠀⠈⠱⣄⠀⠈⠢⣆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣿⡄⠀⢸⡇⣠⠃⠀⠐⠁⠀⠀⠀⠀⠈⢷⡈⢄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⣷⠀⣼⠀⡏⠀⣴⡷⠃⠀⠀⠀⠀⠀⠈⣷⠼⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠈⠄⢀⠸⣧⡏⢠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢇⠹⣆⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⢠⠄⠘⣧⡉⢀⢸⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⡇⠈⠨⣿⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡀⡏⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠀⠄⢹⣏⣋⡟⡿⢛⣉⣛⣏⣽⢛⣙⠋⣿⠋⠛⢉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣻⣿⣟⣻⣟⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣼⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⡴⠇⠀⠚⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡶⣄⡞
⠀⠀⠀⠘⠛⢈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⡿⠀⠁
⠀⠀⠀⠀⠀⠀⢧⣶⣶⡆⠀⠀⠀⣠⣬⣗⣀⠀⠀⠀⠂⠀⠤⠄⠀⠀⠀⣀⠤⠒⠉⣿⣿⠏⢹⢳⡀
⠀⠀⠀⠀⠙⠒⠒⠛⠛⠃⢀⡠⠀⣸⣄⣉⣈⣷⣟⣒⣆⢀⠄⢂⣴⢖⠋⠁⠒⢴⢺⡿⠁⢀⡗⠂⣷⠤⠴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢫⣿⣀⠤⢼⡇⣿⠋⠸⡯⠿⠽⢾⣿⣿⡖⠒⠚⢁⣄⣀⣿⠃⣠⠚⠁⢸⣿⠀⢠⣼⣿⣦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣹⣾⣿⣧⣶⣤⣧⣤⣴⣁⣇⡈⣇⠀⠀⠀⠀⢸⢃⣴⡏⡀⠀⢃⣿⡄⢠⡏⠉⢹⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠂⣼⢏⣿⢻⢹⣿⠛⢿⠻⠿⡿⡿⡿⣿⣿⣷⣶⣾⣾⣼⣿⣇⣜⣺⣗⣽⣾⣗⣤⣼⡷⢲⣶⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⢷⡞⠈⠋⣿⣀⣌⣧⣖⣞⣎⣆⣆⠇⡇⡇⡏⢹⢸⠉⠏⡟⢻⢻⣿⣿⣿⣿⣿⣟⣽⣿⣏⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠿⠟⠿⣿⣿⡟⠒⠒⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣻⡳⠹⡽⣞⣦⣇⣧⢸⣸⡏⠁⠀⢺⠓⠻⡖⠊⠽⠷⠭⠄⠉
⠀⠀⠀⠀⠀⠀⠉⢁⣐⣶⣶⣤⣤⣤⡤⠤⠤⠤⠄⠀⠈⠉⠉⠛⠛⠛⠿⠿⣾⣬⣜⣌⣎⢋⢷⡈⠀⠘⠀⠀⠱⠄
⠀⠀⠀⠀⢀⣤⣽⣿⣿⣿⣿⣿⣷⣶⣶⣾⣶⣶⣶⣶⣦⠷⠶⠶⠦⠤⣤⣤⣤⣤⣤⣉⣉⣛⣛⣻⣦⠇⢀⣀⣀⣠
⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣙⣂⣂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣤⣥⣾⣧⣬⣤⡄⠠⣤⠀⡀⠀⢰⠀⠀⠀⡡⠤⠁⠀⠀⠐
⠀⠀⠳⡀⠀⠀⠀⢀⣴⠋⢳⣆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⢱⡄⠀⠀⠀⠀⠀⠀⣀⠘⢺⠿⢣⡜⠿⡖⠃⣀⠀⠀⠀⠀⠀⠢⡠⣆⠀⠀⢀⣠
⠀⠀⠀⠀⡘⠂⠂⣈⢻⡄⣼⢋⡀⠀⠐⡂⠀⠀⠀⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠛⡿⠋⠉⡄⡀
⠀⠀⠀⠀⠀⠈⠁⠉⢁⠸⢀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠑⣄⡳⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡈⠀⠀⠀⠀⢀⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⢄⣀⠴⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⠆⡀⠑⢦⢠⠖⠁⠰⠄⠀⠀⠀⠀⠀⡀⢡⠌⠉⠁⡎⠀⠀⠀⠀⠂⠉⠉⠀⠀⠀⠙⣗⢸⡏⠁⠀⠀⠀⠉⠐⠂⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⢀⡡⢬⡇⠀⣿⠤⣅⠀⠀⠀⠀⠀⠀⠈⠴⠈⠹⠁⠶⠒⠁⠀⠀⠈⠂⠀⠀⠀⡀⠀⣯⢸⡃⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⢇⠈⠳⢤⠛⠈⢃⠴⠋⣀⠆⠀⠀⠀⠀⢠⠀⠛⠂⠛⠀⢤⠀⠀⠀⠀⠀⠀⢹⣏⢇⣀⡘⣏⣀⣠⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠙⠂⠂⠀⡉⠀⠒⠒⠁⠀⠀⠀⠀⠀⠄⠈⠓⠐⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⢹⡛⢟⠻⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠂⠒⠲⠤⠐⣄⣧⣥⡔⠡⠤⠒⠂⠀⠀⠀⠀⠀⡆⠀⠀⡥⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠀⠀⠀⠀⣶⡐⠙⡆
⠀⠀⠀⠀⠀⠀⠐⢻⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⠔⠛⠢⣈⠆⠀⠀⠀⠀⢀⠘⣇⠀⠀⢰⡤⣴⠀⠀⢀⡟⢀⠀⠀⠀⠀⠀⣹⣇⢀⡇
⠀⠀⠀⠀⠀⠀⡠⡖⠋⠙⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠦⠤⠏⠀⠀⠀⠀⠀⠀⠀⢼⡄⢀⣻⣿⣿⢒⡀⣼⠁⠀⠀⠀⠀⠀⠀⣿⣷⣾
⠀⠀⠀⠀⠀⠌⠐⢇⠀⢀⠟⠀⠣⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠸⠐⣄⠀⠀⠀⠀⡌⠸⣇⠀⠙⢿⠿⠋⢀⣿⠞⡄⠀⠀⠀⠀⠀⢸⠳⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢀⢴⡄⠈⠀⠀⠀⠀⠐⢀⠘⡦⠀⠈⠀⠠⡞⢀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠑⠂⡀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠰⠆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡽⠤⡧⠬⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠗⢏⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠤⠐⠂⢆⡇⠀⠀⠀⠀⢤⡀⠀⠒⠒⠀⢀⡤
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠹⣦⡾⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠴⠖⠢⠔⢣⠤⠀⠀⠀⢰⠒⠇⢹⠋⠉⠉⠸⠐⡆
⠀⠀⠀⢀⠄⠁⠀⠀⠁⠀⠀⠊⢃⠀⠀⠀⠀⠀⠀⡆⡠⠊⠤⠆⠤⠄⠢⡀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⣄⠀⢠⡕⠀⣠
⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⢠⠀⡀⠀⠹⠁⠨⠖⠀⠐⠲⠀⠹⠅⠀⣀⢠⠀⠀⠀⠀⠃⡀⠀⢈⠀⠀⠀⠀⠀⠢⡀⢦⠂⠐⡄⢀⠔
⠀⠀⠀⠀⠀⠀⢙⠒⠶⠚⡘⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⣄⠀⠀⣾⣷
⠀⠀⠀⠀⣤⠀⠀⣾⣿⡄⠀⢸⣿⡄⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣠⡄⠀⣴⡄
⠀⠀⠀⢰⣿⡆⢠⣿⣿⣇⠀⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣇⢰⣿⣇⢠⣷
⠀⠀⠀⣾⣿⣇⢸⣿⣿⣿⠀⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⡿⢸⣿⣿⣼⣿
⠀⠀⠀⣿⣿⣿⠈⣿⣿⡿⠀⢿⣿⠇⠘⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣘⣟⠀⢻⡃⠘⢿⠏⢸⡿
⠀⠀⠀⠸⣿⠇⠀⠹⡟⠁⢀⣀⣯⡤⠤⠼⠗⠐⠒⢂⣈⣉⣩⣥⣤⣤⣶⣶⣶⣶⣶⣶⡶⠾⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣯⣭⣽⣿⣷⣶⣇⣀⣀⣀⣀
⠀⠀⣀⣀⡽⠤⠔⠒⠉⢉⣁⣀⣤⣤⣴⣶⣾⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⢉⣁⣠⣤⣤⣶⣶⣿⣿⡿⠿⠿⠟⢛⣛⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢺⣯⣭⣤⣤⣴⣖⣚⣛⣛⣿⣛⣛⣛⡛⠛⠩⠤⠀⠤⠠⣤⣴⣶⣾⣿⡿⠿⠟⠛⠛⠉⠉⣉⣠⣤⣴⣶⣿⣿⡿⠿⠟⠛⣛⣩⣭⣶⣶⣿⡿⠿⠟⢛⣋⣽⣿⣿⣿
⠘⣿⣿⣿⣿⠿⣿⣿⣶⣦⣭⣛⡛⠿⢿⣿⣶⣦⣌⣙⠓⠶⢶⣬⣍⣁⠀⠀⠀⣤⣶⣾⣿⠿⠟⠛⠋⠉⢁⣠⣤⠶⠾⠿⠿⠿⠟⠛⠉⠀⠐⠶⠿⠿⠿⢏⣭⣥⡶
⠀⠸⣿⣿⣿⣿⣷⣦⣬⣉⠛⠿⢿⣷⣶⣬⣉⠛⠿⢿⣿⣶⣄⡀⠉⠛⠿⣿⣶⣤⣈⠙⠀⢤⣤⣶⡦⠏⣩⣶⣶⡶⢟⣿⣿⡿⠟⢋⣴⣿⠟⢁⣴⣿⠟⠁⣴⡿⠁
⠀⠀⠙⠿⣿⣷⣦⣉⠛⠿⣿⣶⣤⣈⠙⠻⢿⣷⣦⣄⡀⠙⠻⢿⣷⣦⣄⠀⠉⠻⢿⣿⣦⣄⠈⠁⠠⣾⡿⠋⢁⣴⣿⠿⠋⢀⣴⣿⠟⠁⢠⣾⡿⠃⠀⣼⡿⠁
⠀⠀⠀⠘⢶⣍⡻⢿⣿⣶⣄⡉⠛⠿⣿⣦⣄⠈⠙⠻⣿⣶⣄⡀⠈⠛⢿⣿⣶⣄⡀⠉⠛⢿⣿⣦⣄⠈⠑⠠⣿⡟⠃⠀⣠⣿⡟⠁⠀⣰⣿⡟⠁⠀⣼⡟⠁
⠀⠀⠀⠀⠈⠻⣿⣶⣌⠙⠿⣿⣶⣄⡈⠙⠿⣿⣦⣀⠀⠙⠻⣿⣶⣄⡀⠈⠛⢿⣿⣦⣀⠀⠉⠻⢿⣷⣤⡀⠈⠢⣀⣴⣿⠋⠀⠀⣴⣿⡟⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡈⠙⢿⣿⣦⣀⠈⠻⢿⣿⣦⡀⠈⠙⢿⣿⣦⣀⠀⠉⠻⣿⣷⣄⡀⠀⠙⠻⣿⣷⣄⠈⠻⣏⠀⠀⣼⣿⠏⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠉⠻⣿⣷⣄⠀⠙⢿⣿⣦⣀⠀⠉⠻⣿⣷⣄⠀⠈⠙⢿⣿⣦⡀⠀⠈⠻⣿⣷⣄⠈⠳⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⠈⠻⣿⣷⣄⠀⠈⠻⣿⣶⡄⠀⠈⠻⢿⣷⣄⠀⠀⠙⠿⣿⣦⠀⠀⠈⠛⢿⣷⣄⡙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⠀⠈⠻⣿⣷⡀⠀⠈⠻⣿⣦⡀⠀⠀⠻⣿⣧⡀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢿⣿⣆⠀⠀⠈⢿⣿⣦⠀⠀⠈⠻⣿⣦⡀⠀⠀⠙⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠛⠓⠀⠀⠀⠈⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠄⠄⠀⠀⠀⠀⠠⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠰⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⢴⣁⣀⣀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⣸⣿⡟⠻⣿⣿⣿⣷⣶⣦⡵⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⠀⠀⠙⠿⠿⣿⣿⣿⠗⠢⠽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣇⠀⠂⢀⠀⠄⠀⢹⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⣈⡠⠀⡴⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠤⠔⢻⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢶⡉⠀⠀⠀⠀⢁⠟⠻⠧⣀⠀⠀⠀⠀⠀⣼⢃⡴⠋⢀⣠⡤⠖⠂
⠀⠀⠀⠀⠀⠀⡀⠒⠁⠀⠀⠀⠀⠈⠒⠠⠤⠒⠉⠀⠀⠀⠀⠉⠲⣤⣯⢊⡾⢋⠤⣲⣟⡥⠄⣠⡄⣀⢀⢔⠦
⠀⠀⠀⠀⠀⢠⠃⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⢅⡼⢋⣥⠾⣋⠥⡙⠋⢉⣤⢭⣉⡐⢴⠞⠛
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠔⡱⣣⠮⡪⠟⣻⣻⣃⣘⣊⣈⣉⡀⠁⠘⠚⢺⡞⡻⢂⡀
⠀⠀⠀⠀⢀⡃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⡋⢎⣔⡵⠞⣒⣭⣵⡖⣿⢯⣤⠮⢖⡯⢗⢶⡲⢀⠘⠽⡼⡓
⠀⠀⠀⠀⠀⡝⠒⠲⠤⠴⡆⠀⠀⠀⠀⠀⠀⠀⣰⠋⠎⠃⠘⡜⠓⡞⢻⣿⣿⣿⣿⣿⣟⡳⠶⠿⣇⠘⠵⢰⡞⠵⣀⠙⠁
⠀⠀⠀⠀⠀⡁⠀⠀⢆⠀⡇⠀⠀⠀⢀⡠⠔⣊⡝⢄⣀⡀⠀⠘⠂⠙⢿⠍⡺⡯⢶⣤⡉⢩⢵⢶⠠⣢⣀⡈⠹⣹⠫⠂
⠀⠀⠀⠀⠀⢦⡀⠀⠀⠉⠁⠒⠲⡉⠁⢔⡩⣪⢕⡡⠊⠉⡟⠢⠤⠤⠜⠀⠙⢼⡳⣯⠙⢶⣍⠸⠵⣖⡜⢣⣄⠀⠫⠂
⠀⠀⠀⠀⠀⠀⣈⢍⡳⡀⠀⠀⠐⢷⢀⠔⣊⠔⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠧⠘⠇⠀⠈⠂⠀⠀⠫⠇⡙⢃
⠀⠀⠀⠀⠀⠀⠘⡥⢒⠕⢔⢔⢜⢾⡦⠊⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢣⠔⣩⡩⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⣿⣼⣾⣇⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠆⢠⣷⢠⣾⡇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡠⢿⠟⠉⣿⣿⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⢸⣻⣾⣿⡏⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣶⣦⣴⣶⡶⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣁⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⡞⠙⣿⣶⡄⣿⡀⢰⢸⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣿⣿⡿⢄
⠀⠀⠀⠀⢀⠴⠛⢀⣴⣿⣿⣿⣿⣧⣼⣦⣷⡄⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⣿⣿⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠹⣿⣿⣿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠰⢷⣤⣿⣿⡿⡆⠁
⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠛⠋⠉⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⡈⠻⠿⠟⢠⠇
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡆⢰⠀⡄⠀⣿⠀⠀⠀⢣⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⣦⣷⣶⣿⣶⣷⣴⠇⣸⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣤⣄⣀⣀⠀⠈⠦⠠⣄⡀⠙⢦⡟⣋⣙⣿⣿⣿⣿⠶⠃⣀⡴⠰⠀⠉⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⡠⠐⠋⠁⠁⠀⠈⠉⠛⠛⠲⠤⠌⣹⣶⢤⣀⣀⣉⣗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣠⣤⣖⣋⡩⠭⠛⠛⠒⠀⠐⠀⠂⠈⠑⠢⣄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠀⠐⠲⠖⠚⠛⢲⠟⠽⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠿⠶⠤⣤⠄⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⣠⢴⠏⠀⠄⠀⣼⡇⢠⣿⣿⣿⡌⢿⠁⣙⢿⡉⢹⣦⣀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⡼⢀⡄⠀⠘⠁⣭⣿⣿⣿⣿⣿⣦⡀⠘⠆⢁⢹⡇⠈⠑⠦⡀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠀⠀⠀⣀⣿⡀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⢜⣶⣇⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠘⣿⡾⢻⡏⢿⣿⣷⣿⣿⣿⣿⣿⠟⢹⣦⣿⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠙⢿⣿⣿⣿⠟⠋⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⣻⠿⢿⡁⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠿⢛⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠎⠀⠘⠶⣿⣡⣚⡷⠊⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠿⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⣤⡶⣾⣿⣿⠶⣦⣄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠎⠹⠃⣤⡄⠀⢀⣤⡀⠟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⣘⠀⡀⠀⢼⠆⠀⡀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡿⣴⢿⣦⢸⢠⣾⠷⡜⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡊⠺⣦⠀⠀⠀⢾⡷⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⣆⠘⡟⢰⢈⡿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠈⠀⠐⠀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢹⠀⠹⠾⠞⠁⢸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢀⠏⠀⠀⢃⠀⠀⡞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢀⠊⠀⠀⠀⠱⡞⠀⠀⠀⠈⡄⣸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⡄⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⡏⠀⠀⠸⠀⠀⠀⠀⢀⡤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⣲⠟⣻⣀⣤⣄⠀⢀⠔⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣴⢛⣭⠵⠛⠉⠉⢀⣽⠔⠁⠀⢀⡞⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠈⠳⡀⠀⠀⢸⡀⡠⠒⢠⣾⣿⣿⣿⣯⣥⣤⣶⠶⠞⡟⠁⢀⠀⣠⢋⣤⠞⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠹⡄⠀⠀⠉⣿⡆⢸⣿⣿⣧⣿⣿⣃⢼⣿⢇⡀⠀⠰⠃⣼⡵⠋⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠠⠚⣿⢏⠈⠙⣻⠟⠻⢿⣿⢛⣥⣻⣷⠀⢁⡾⠋⠀⢀⡞⢀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀⣀⡀⠈⠻⢦⡀⠀⢀⣀⣬⣧⡔⣛⣱⣶⠶⠚⢷⣿⣽⡿⣼⣴⠟⠀⠀⣀⡾⠞⠉⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠻⢦⣀⡿⣿⣷⣞⠻⢿⣿⣻⠷⢾⢻⣿⡾⣿⢁⢀⣤⠾⠉⠀⣠⣴⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣛⣶⡶⠶⠶⠶⠶⣶⣿⣦⠼⣭⣿⡓⣮⣾⠛⢻⢟⡆⠹⣾⢇⣼⠟⠃⣀⣴⡾⠟⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠒⠊⠉⢁⣀⣽⣍⢿⣫⣥⣦⡟⡡⢶⡃⡩⠼⡿⢨⣾⣿⣴⠿⠿⡟⠁⢄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⣫⣿⣿⣆⣶⣻⣶⣦⣽⢛⣿⣡⣋⣵⣿⠿⠋⠀⠀⡼⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠋⠉⠉⠀⠀⣠⡴⠛⠛⠻⣿⣧⣬⣥⣿⣭⣤⡞⠋⠉⠀⣸⠋⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⠚⠋⠹⣤⡴⠶⡈⠀⠀⠀⠀⢀⣠⡞⠀⠀⣠⣾⣥⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠒⠋⠀⠘⣷⣾⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠀⠀⠀⠀⠑⠢⢄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠐⢦⣄⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠬⠬
⣤⣤⣤⣤⣤⠀⠠⠤⠐⠒⠒⠒⠒⠂⠀⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⢉⣉⣉⡉⠉⠉⠉⠉⣉⢉⢉⢉⣉⡉⠁⠀⠘⠂⠉⠁
⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠐⠒⠂
⠀⠀⠀⠀⣤⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀
⣀⣠⣤⣼⠇⠄⠤⠤⠀⠒⠒⠛⠒⠒⠒⠒⠒⠀⠒⠂⠒⠒⠒⠂⠠⠄⠀⠀⣠⡄⠀⠀⡀⡀⠴⠰⠒⠂⠀⠉⠙⠉⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢂⣀⡄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠰⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⠤⠤⠤⠤⠐⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠈⢀⣭⣥⡀⠀⣰⣾⣦⠀⠀⠀⠀⠀⠀⡀⠠⢐⠀⣀⠠⠤⠐⠐⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠸⣿⣿⠟⠁⠸⣿⣿⣿⣇⠀⠀⠀⠤⠐⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠟⠛⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⣀⠀⣀⠀⣀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠁⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣤⣤⣤⣤⣿⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⢿⡿⠿⢿⣶⣤⣈⡻⣷⣄⠀⠀⠀⢀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⡜⠉⢉⣼⣿⣿⣿⣿⣻⣛⣟⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⣿⠟⢋⣱⣿⣶⣿⣿⣶⣶⣎⣙⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣸⣤⣶⠿⣻⣭⣽⣯⣭⣽⡛⢿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⡿⢃⣼⣿⣿⡿⠟⣛⣛⠻⢿⣿⣿⣷⡘⣿⣿⣿⡇⠀⣹⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢀⣿⡟⢱⣾⣿⡿⠿⠿⠿⣿⣿⣷⡙⣿⣿⣇⣀⣀⣀⣸⣿⣿⠓⣿⣿⣿⢋⡔⠀⠉⠉⠀⢢⡙⣿⣿⣿⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢴⣼⡿⢸⣿⣿⠣⠚⠁⠈⠉⢈⢻⣿⣿⠘⣿⣟⣛⣛⣛⣿⣿⣿⢴⣿⣿⡇⠊⠀⠀⢠⡄⠀⠀⠁⢹⣿⣿⡆⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢺⣿⡇⣾⣿⡇⢆⠀⠐⠆⠀⠀⢆⣿⣿⠇⣿⣟⣉⣛⣙⣿⣿⣿⢈⣿⣿⣧⠱⡄⠀⠀⠀⠀⢠⠇⣾⣿⣿⠁⠀⠀⠈⠉⢉⡍⠉⠙⣿⣿⣿⣿⠟⠛⠛⠃
⠀⠀⠈⠉⠁⠸⣿⣿⣄⠠⣀⠀⠠⢂⣼⣿⡿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠛⣿⣿⣷⣌⣐⠲⠒⣂⣥⣾⣿⣿⠛⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⣴⡟
⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣶⣶⣾⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠋⠁