Cartoon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⢀⡠⠔⠒⠈⠉⠉⠁⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢣⠀⠀⠀⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠑⢄⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠠⠂⠀⠀⣠⣈⣀⣤⠶⢉⠀⠀⠀⠀⠀⢀⠤⠀⠷⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠉⠉⡹⠉⠉⠀⢠⠊⠀⠊⠀⠈⢄⠀⠀⡰⠁⢀⡑⠀⠈⢿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⡀⠀⠀⠀⢠⠃⠀⠀⠀⡆⠀⢠⠊⠉⣢⠈⠀⠀⠃⡜⠡⠈⣂⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠡⢌⣙⠳⠶⠋⠒⠒⠒⠐⠇⠀⠀⣶⣿⣾⢀⠒⠒⡆⣗⢿⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠳⠭⢋⠂⠀⠀⢘⢌⠓⠓⢁⠔⢹⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠁⠀⢀⠠⠎⠀⠈⠉⠀⠀⡸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⡟⢦⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⠷⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠁⠘⡀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⣠⢾⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠈⡁⣒⣤⠄⠀⠀⠀⠀⢀⠀⣀⡠⠤⠶⠈⠁⢀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡏⠉⠉⠉⣀⠴⢻⠑⢄⡀⢀⡸⠧⣄⠀⠀⠀⠀⠇⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡔⠀⠀⠀⡜⠁⠄⠂⡃⠠⠘⠃⠀⠃⠄⠑⣄⠀⠀⠘⣄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡜⠀⠀⢸⠀⡅⠀⠀⠀⠀⠀⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⡗⡈⠀⠀⠀⠀⠀⡆⠰⠂⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡟⠀⠂⠐⠎⣈⡈⢄⢀⡀⠠⢤⡦⠤⢀⡀⡠⠋⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠓⠤⣀⡀⠀⠀⢡⡼⠎⠁⠁⠈⠲⠦⠤⢼⠁⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⢆⡀⠀⠀⠉⠙⠖⠛⠻⠀⠀⠀⠀⠀⠀⢀⠀⠰⢄⠀⣀⡀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⢹⢄⠐⢶⠂⠀⢈⠀⠠⠄⠐⠂⠈⠈⠲⠀⠀⠀⠂⠉⠀⠀⠀⠀⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠙⢪⠢⡑⢄⠀⠁⠂⠠⢒⡀⠀⢀⣀⡀⠠⠤⠤⠐⠒⠒⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢢⠀⠀⠑⢌⢢⡑⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠐⠒⢲⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠈⠉⢢⢤⠤⠄⢒⠶⡂⠈⠉⢹⠁⠀⠑⢬⡒⢄⠀⠀⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠳⡀⠀⠀⠸⠘⣂⣀⡎⠸⠆⣤⣤⡇⠀⠀⠀⠀⠈⠢⡑⢤⡀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢢⡀⠘⠀⣄⣹⢛⡄⠻⠦⠴⠃⠀⠀⠀⠀⠀⠀⠈⠓⢌⠃⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢤⡅⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⢀⠂⠀⣰⠄
⠀⠀⠀⠀⡀⠢⠀⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠋⠛⠇⠈⠡
⠀⠀⠀⠀⠣⡀⠐⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⠘⠣⠤⠤⡀⠈
⠀⠘⣄⠐⢄⠡⠄⢡⠶⠈⠀⠀⠊⢠⠊⠀⠀⠀⠀⠀⠐⡀⠀⠀⠁⠀⡆
⠀⠀⠀⠑⣤⡁⠋⠀⡀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣀⣀⠀⠁
⠀⠀⠒⠀⠀⢠⡀⠈⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈⢀
⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣻⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⡀⣣⠀⢃⠀⠀⢀⣀⣀⣀⠠⠤⠔⠚⠉⠀⠀⠉⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⡄⠀⠀⠀⠀⢀⣠⠋⠉⠛⠀⠉⠉⠉⠉⠛⠻⢇⡀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠐⡀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢙⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⣴⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⢀⠉⠠⣤⠀⠀⣠⣤⡤⠶⠒⠉⠁⣀⣼⣿⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠡⣄⣀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⡦⢀⣀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⢸⠂⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠈⠻⣿⣿⠋⠀⢈⠀⠸⠟⣿⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠙⠶⠂⣀⣀⡠⠞⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⢶⠖⠤⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⣶⣶⠖⠚⢹⠉⠲⡄⣘⡀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢸⢣⠀⡸⠀⠀⠀⠉⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠢⠤⠤⠤⠀⠚⠉⠀⠀⠀⠀⡄⠾⠃⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠻⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠚⠉⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢰⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣡⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠢⣄⣠⠎⣄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠖⢉⣡⠶⠛⢧⡀⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣴⠃⢀⣰⠃⠀⠀⠀⡀⣠⣤⡴⠒⠉⠁⠀⠀⠀⠀⠻⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢆⠈⠉⠉⠉⠉⠉⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⠡⡀⠀⠀⠀⠀⢠⡆⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠓⠤⠤⠴⠋⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠠⠤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠁⡰

⠀⢀⣀⣤⠄⢇⡒⠀⠠⠁⠀⠐⠀⠀⠠⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⢰⣾⠄⠀⠀⠀⠀⠀⠀⠄⠰⠁⠀⠀⠓⠈⢒
⠈⠉⠁⠀⠀⠀⢈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣩⠹⢀⡴⠀⠠⠚⠀⠀⠂⠈⠉⠉⠁
⠀⠀⠀⠀⢤⡀⠢⠀⠀⠞⠀⠀⠀⢄⣆⣀⣤⠴⠂⠀⠀⠀⠀⠀⠀⠁⠒⠛⠃⣰⠀⡄⠀⠀⠀⠀⠀⠸⠂⠀⠀⣠⠄
⠂⠀⠀⢀⠘⢂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⣈⠀⡐⠀⢾⢧⡞⠃⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋
⠒⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡀⢄⠀⠈⠀⠀⠀⠀⠴⠶⠄⠀⠀⠉⡟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠳⢦⣄⣄⡦⠅⠁⠀⡀⠀⠀⠀⡀⠈⠀⢀⡀⠀⠀⠀⠰
⡀⠐⠀⠀⠐⠃⠁⠀⠀⠲⡄⠀⠀⢀⠧⠤⠙⠧⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢱⠀⠀⠀⠈⠀⠐⠇⡼⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠎⠀⠀⢀⠀⣀⠱⠀⠀⠀⠀⣄⠘⡶⠀⠈⢸⡀⠀⠀⠀⠀⠀⣠⠦⠌⠁⠀⠀⠐
⠀⠀⠉⠀⠀⠠⠾⠼⠛⠀⠀⠴⠂⠀⠀⠚⠛⠁⠈⣻⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⡁⡀⠀⠀⠂⠀⠀⠀⠀⠀⢀⢐⡄
⠀⠄⠀⣠⠤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠂⠒⠄⠀⢠⠀⠀⠀⠁⠀⠀⠀⢒⠂⠀⠐⡀⠈⠉
⠀⢀⠞⡁⠀⠀⢿⣷⠀⠀⠂⣰⠀⠀⢤⣆⠀⠀⠘⣆⡀⣀⡴⠌⠴⢺⡀⠀⡄⡁⠀⠀⠈⠀⢀⠟⢂⡄⠈⠀⠀⠀⠈
⠀⠸⠀⠀⠀⠠⢑⣽⠀⠱⢤⠏⠀⠀⠀⠙⠧⠀⠀⠁⢊⣡⡤⠴⠕⣋⣧⠀⠈⢮⢦⡀⢀⡀⠁⠈⢀⠀⠠⠄
⠁⠸⣄⡀⡀⢀⡴⠃⠀⠀⠀⢀⢴⠄⠀⠀⠀⠀⠀⠀⢎⣡⠴⢞⠟⠋⠁⠐⠀⠀⠁⠁⠀⠀⢆
⠀⠀⠐⢩⠍⠉⠀⠀⠐⢿⠀⠉⠉⠃⠈⢀⡼⠁⠀⠀⠉⣆⠠⠀⠂⠀⠀⠐⠒⠈⠁⢔⡮⠇⢤⠊⠀⠀⠁⠀⠀⠀⠁
⠁⠀⠀⠂⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⡀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀
⠀⠠⡌⠀⠀⠀⠐⠄⠀⡴⠀⠀⠀⠀⢐⡉⢳⣰⠀⠀⠀⠀⢠⠃⠀⡀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙
⠀⢀⠃⠀⠀⠙⠃⠀⠀⢘⠊⠀⠀⠀⠉⠋⠠⠋⠀⠀⠀⢠⠃⠀⠰⠀⠀⠀⢀⡞⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⡄
⠀⠊⠀⠀⠀⠀⢀⡶⠶⡋⠉⠀⡀⠀⠀⠀⠐⣲⡄⠀⢄⡏⠀⠀⠀⠀⠀⠀⡂⠇⠀⠀⢠⣬⣀⠄⠠⠀⠂⣀⠃
⡤⠖⣿⣆⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⠀⣀⠀⠀⢀⠀⠀⠃⠀⠠⠄⠀⠀⠢⡃⠀⠀⠀⠀⠉⠓⠢⠤⠤⠖⠋
⢀⡀⠜⠋⠀⡄⢠⠀⠀⠀⠀⡄⠊⠉⠝⠓⠨⠭⠄⠠⠀⠀⠰⠀⠀⠀⠑⠀⠈⠂⠀⠀⠈⢄⠀⠄⡀⠀⠀⠀⠰⠛⠉
⠁⠀⠀⠀⠐⢂⠝⠂⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠂⠀⠣⢄⢠
⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢂⣀⣀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢈⢁⠜⠀⡤⠈⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠸⢲⠛⠊⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⡀⡀⠄
⠀⠀⠀⠠⠄⠀⠀⠨⢨⠅⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⢯⡤⢄
⠀⠀⢀⢈⠆⠀⠀⠀⠁⠋⠃⠉⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠌⢒⣄⠀⠀⠁
⠊⠛⠃⢀⠄⠀⠀⠀⠀⠀⠏⠂⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⠀⠀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠞⠶⣶⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⡀⠈⠉⠀⠀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡤⠀⠀⡀⠀⠀⠸⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠰⣠⠉⢉⡤⠄⠀⠀⢀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠡⠄⢨⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⢠⠀⠂⡐⠰⢀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠀⢄
⢀⡄⠀⠀⠀⠀⠐⢷⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⢰⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠟⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠲
⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⠄⣐⣤⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣾⡿⣿⣿⣽⣶⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣠⣄⡀⠀⠀⠀⠀⠀⠀⢔⣠⣤⣤⣤⣾⣗⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡍
⠀⠀⠀⠐⠀⣠⣶⣿⣿⣿⣿⣷⣿⣿⣦⡀⣠⠔⣫⣶⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣾⣿⣿⣿⣟⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣏⣿⣞⣿⣿⣷⡄
⠀⠀⠀⣾⣟⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣷⠈
⠀⠀⢠⠀⢯⣻⣿⣿⣟⣿⣿⣿⣿⣿⣟⢛⠿⣿⣿⣿⣿⠿⣏⠋⢿⠿⠿⣿⢿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⣿⡍
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣽⣿⠟⠋⠉⠀⡼⠁⠳⣄⠈⠓⠬⣇⡀⠐⢻⣿⣿⣿⣟⣿⣿⢇⣿⣿⣷⣿⣇⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⣿⣿⢫⣶⣧⠞⠚⠀⠀⠀⠀⠀⠉⠐⠒⠻⠷⠾⣷⣛⣋⣭⣾⣟⣴⣿⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠺⡿⣿⠿⢿⣻⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠋⣡⣤⣶⢶⡶⠆⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠏⣉⠻⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠢⠶⠰⢀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣰⠖⠒⠢⢄⣀⡰⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠒⠀⠀⠠⡅⠀⡀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠲⠅⠀⠀⠀⠃⠀⠀⠀⠘⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⢒⠐⠣⡆⠀⠀⠀⠈⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⢀⣶⣀⢀⢠⣦⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠼⠀⠉⠁⠀⠀⠀⣐⠐⠃⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠙⠛⠁⠀⠀⠉⢀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠸⡀⠃⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢒⠈⠀⠀⣤⣀⠀⢀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⡌⣷⣦⣤⠤⠒⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⢸⡿⢿⠇⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⢠⢴⠶⢯⡇⠉⠁⡡⢒⣒⠂⢲⡒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⢧⠀⢀⡀⢰⠂⠂⠁
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠋⠠⢼⠋⠀⠀⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠳⣀
⠀⢠⠔⢲⣌⡓⣇⣀⡴⠀⠀⢖⡀⠀⠢⣀⣠⠞⠀⣀⢤⡖⠒⢦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠢⢄⠀⠀⠀⡀
⡔⠃⠀⠏⠀⠹⡖⠖⠀⠀⠀⠈⢆⠁⠀⠀⢀⢓⠏⠀⠠⠃⠀⠸⢦⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣙⢢⢀⠉
⣇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⡞⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠠⠃⢂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡗⠊
⠘⣄⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠱⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⡀⠂⠀⠁⢄⠀⠁⠐⠀⠀⠀⠄⠓⠀⣀⠀⢀⠜
⠀⠈⠓⠤⠤⠴⠋⠀⠑⠤⣀⡀⠀⠀⠀⡠⠦⢧⡀⠀⠀⣠⠜⠁⠀⠀⠀⠈⠂⠦⠀⢠⣀⠀⡀⠀⢆⣴⡁⠀⠀⠘⢘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠦⠄⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⡀⠀⡄⠀⠄⡈⠀⠀⠀⡐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣶⡌⡌⠀⠀⠀⠘⢂⣤⡈
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠛⠃⠃⠀⠀⠀⠀⠌⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠠⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣀⠄⠄⢀⠄⡀⠀⢀⠠⠤⠀⠄⠊⠄⠄⠈⠀⠁⠀⠀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠉⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢉⣼⡏⠉⠉⠻⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⠀⣼⣿⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠃⢀⣿⣿⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣀⣸⣙⣃⠇⠀⠀⠀⠀⠀⠘⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⠛⠛⠻⠿⣿⡄⠀⠀⠀⠀⣀⣻⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⠁⡀⠀⠧⣧⢹⡅⠀⠀⠀⠘⠋⠉⠉⢗⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡿⠿⠛⡿⢙⢺⣸⡇⠀⠀⠀⣀⣀⣤⣤⠸⡎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣸⠃⠀⠀⠀⠈⣸⢿⡇⠀⠀⠈⠛⠠⠛⠁⠀⣿⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⠏⠀⠀⠀⠀⣴⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡴⠃⠀⠀⠀⣀⣼⡿⠝⠁⠀⢠⠄⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣠⣴⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠖⠒⠦⠤⢤⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣴⠶⠯⣭⣤⣤⣄⣀⣀⣠⠴⣲⣿⣛⣋⣉⣀⣀⣀⣀⠉⠉⠉⠉⠉⠛⠒⠒⠲⣤⡄
⠀⠀⠀⠀⡇⡐⠒⠒⠒⠒⠒⠠⡀⡿⢸⡇⠀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⡉⠉⠛⠓⢲⡏⠀⡇
⠀⠀⠀⠀⡇⡨⠭⠭⠭⠭⠉⢉⠀⡇⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡷⠀⢸⠁⢸⠟⡆
⠀⠀⠀⠀⡇⠑⠒⠒⠒⠒⠒⠊⢠⡇⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡾⠀⢸⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⡟⢰⠇
⠀⠀⠀⠀⣧⠀⠘⠋⠒⠒⠂⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⢀⡇⣸
⠀⠀⠀⠀⢻⠀⠀⠀⣀⠀⠀⠀⡿⠀⢸⡀⠘⠒⠒⠶⠶⠦⠤⠤⠤⠤⠤⣤⡼⠀⣸⠀⣸⠖⠃
⠀⠀⠀⠀⢸⡀⠀⠀⠒⠁⠀⠀⣇⡴⠋⠛⠓⢲⢖⡶⠒⣶⡶⠶⠤⢤⡤⢤⡤⣤⡿⠞⠁
⠀⠀⠀⠀⠀⠉⠉⠙⠛⢛⣛⡛⠉⠀⠀⠀⡊⠁⠸⣧⣤⣀⣉⣉⣉⣉⣤⡾⠀⠈⠒⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡩⢭⢭⠭⡭⢭⢉⡉⣛⣓⡒⠛⠻⠿⠯⠭⣭⣁⣀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⡼⡰⢥⠯⡯⣹⣩⣏⣞⣱⡓⡞⢺⢡⢮⠏⣴⣰⠂⡰⣹⠀⠀⣠⠖⣻⠟⠙⣆
⠀⠀⠀⠀⠀⠀⢸⣥⣍⣉⣚⡒⣓⣒⡒⠀⠧⠼⠥⠃⠎⢞⣲⣲⢃⢜⡴⠁⠀⡼⠉⠉⠉⠒⢤⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠒⠾⠿⠭⠭⢤⣄⣒⣲⡾⠋⠀⠀⠀⢷⣄⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠿⠛⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡋⠀⠀⠀⣠⠴⠖⠶⣄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣫⣀⣉⠢⣀⠞⠁⣠⠤⢶⡘⣧⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠋⠀⠈⢧⠉⢀⡞⠁⠀⠀⢻⡸⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⣶⢦⡘⡆⣸⢁⣾⠙⡆⢸⡇⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣇⠀⡇⡇⣿⢸⣿⠀⡇⢸⡇⡿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣇⢸⣿⣤⣷⡇⣿⢸⣿⣿⠇⡼⢀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢆⣻⣿⡿⠷⢛⣻⢿⣯⠞⣡⠎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢦⢹⠏⢀⣠⡴⡟⣥⠏⠸⡁⠀⠀⠻⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡿⠈⠉⠉⢯⠷⡵⠁⠀⠀⠹⡄⠀⠀⠀⠈⠉⠙⠛⣛⡿⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣷⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢻⠐⢶⣤⣤⣀⣈⣩⣥⠖⠋
⠀⠀⠀⠀⠀⢴⢶⣛⠉⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠶⡾⠉⠉
⠀⠀⠀⠀⠀⠀⠙⠾⠭⠴⠞⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢟⠲⠶⢶⡶⢶⡚⠋⠁⠰⠭⢭⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠊⣡⠖⢀⡾⠀⠀⠙⢦⣌⡙⣲⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠛⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⡼⠿⠇⣤⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢰⡆⢰⣷
⠀⠀⠀⠀⡀⠋⠀⠿⣱⣿⠿⠿⡃⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢈⠁⠀⣁⠀⠀⠀⢄⣀
⠀⠠⠀⠀⠀⠀⠀⠈⠻⢫⣾⣟⠃⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⢉⣷⣤⣤⣤⣤⣴⡄⠀⠀⣤⣄⢀⣀⣠⣤⡄
⠀⢀⢐⣀⢀⠀⢠⠀⠀⠀⠀⣀⠀⠀⠀⠘⠛⠂⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠉⠉⠈⠉⠈⠉⠁
⠰⣿⣸⣫⣥⠀⢻⡄⠀⠀⠘⠁⢴⠀⣤⠘⠋⠀⠀⢹⣿⣿⣿⣟⣿⣿⣿⣿⡇
⠐⠶⢧⠈⠉⠀⢘⠧⣀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⢿⣿⣿⣟⠀⠴⢁⡤⠀⠀⠀⠀⠀⣸⣾⣧⡀
⠀⠑⠶⢆⠔⠀⠀⠀⠀⠐⡄⠀⠂⢠⢦⡀⠪⢀⠄⠂⠀⠈⠙⢄⠈⣿⣷⠀⠀⠀⠁⠁⡤⢀⠀⠄⠈⠉⢻⠋⠁
⠀⠀⠓⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⢂⠈⢌⣀⠁⢀⡀⠀⠀⣀⠀⢰⠛⠛⠀⠀⠀⡂⠀⠁⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠀⠉⠢⠀⣀⣤⣶⣶⣯⡀⢽⠃⠀⠈⠁⣼⡅⠉⠀⠀⠀⢀⣄⠀⠈⢣⠀⠀⠆⠀⣀⠀⢀⠀⠰⠁
⠀⠀⠀⢄⠊⠀⠀⠀⢳⡟⠻⣿⢠⢹⣿⡄⠀⡄⠀⠀⠀⠀⠀⣀⠐⠆⠀⠁⠀⢰⣶⣷⡀⠀⠀⠂⠀⠈⠀⠐
⠘⠧⡀⠎⠈⠁⠀⠀⠹⣧⣁⠉⠀⣸⣿⡣⠀⠐⠂⠀⡀⠀⡸⠤⠄⡐⠀⢀⠀⢸⠟⠋⠂⠀⢀⠠⣴⣤⠈
⠀⠀⠀⠨⣠⣾⣿⣿⣿⣿⡉⠀⠀⠁⠀⠀⠀⠐⢡⠂⠀⡀⠀⠀⠀⠀⠁⡀⡨⠀⠀⠀⣤⡀⠀⠀⣿⠟
⠀⠀⢠⣼⠿⡿⠛⠇⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠻⠀⠀⠀⠈⣆⡀
⠀⠀⢼⣿⣾⣇⠀⠀⣨⣿⣉⣿⠀⠈⠃⠠⠘⠃⠀⠀⠀⠲⠀⠀⠰⠃⠀⣀⡼⠒⠃⣀⢀⣀⣠⠂⢠⠃⡀⠃⡀
⢀⣰⠠⡝⠿⣿⣿⣿⣿⣿⠿⢋⣀⠠⠄⠀⠀⡄⠀⠁⠀⢀⢀⠀⡀⠠⠂⢹⣷⠀⣶⠅⣿⡟⢰⣤⠊⠇⠀⠠⠰
⠀⠆⠜⠤⣰⣆⣀⠀⣀⣴⡄⠉⣹⡇⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⢁⢀⠡⢸⣿⠀⠀⠈⠀⠀⣿⡟⠰⠀⠀⠀⠈
⠀⠈⠠⠀⠉⢹⣿⣷⣿⣿⠛⠛⡯⢥⢠⢀⢄⡠⢥⡰⢁⡀⡀⡀⡨⢎⡀⢾⣿⠀⣦⡄⣠⡆⣿⡇⠋⢐⣠
⠀⠀⠀⠁⠀⠋⠤⠸⠄⠘⠤⠐⠁⠂⠀⠃⠄⠢⠤⠃⠰⠄⠚⠤⠖⠠⠀⠀⠉⠒⠛⠃⠛⠃⠿⠐⠀⠀⠈

⠡




⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣾⣋⣹⡅⠀⠀⠸⣎⠣⣐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣂⠼⣱⠇⠀⠀⢨⣏⣙⣷
⠀⠀⠀⠀⠀⠰⣾⠋⣏⠀⢀⡤⠶⣟⢠⠻⡄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⠟⣄⣻⡶⢤⡀⠀⣹⠉⣷⠆
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣤⠄⠀⠈⠽⣿⣇⣡⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣌⣸⣿⠯⠁⠀⠠⣤⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠨⡿⣷⣶⡀⠀⠀⡨⣿⣿⣿⢠⡳⠄⣀⠀⠀⠀⠀⡀⠀⢞⡀⣿⣿⣿⢅⠀⠀⢀⣶⣾⢿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⡤⢀⠀⠞⠟⣿⣿⠀⣿⣦⡡⠔⣒⣓⢢⢌⣴⣿⡀⣿⣿⠻⠷⠀⡀⢤⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⡂⢕⡄⡈⡉⠛⡐⡎⣿⠻⣬⡳⢞⣥⠟⣿⢱⢀⠛⢉⢁⢠⡪⢐⣥⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣶⣾⣇⡢⣾⠹⣽⣮⡽⢣⠜⣮⡵⣯⠏⣿⢔⣸⣿⣴⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣉⢽⣷⣿⡷⣄⡙⢶⡏⢺⠷⢋⣠⣾⣿⣾⡯⣉⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡤⠈⠘⣽⣿⣿⣎⠿⣓⣶⣶⣚⠿⣻⣿⣿⣿⠃⠁⢤⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡴⢄⡘⣿⡿⣏⣼⣼⡻⣿⣿⢛⣧⣧⣹⢿⣿⢃⡠⢦⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣷⠒⠿⣿⣿⣏⣿⣓⣾⣷⣛⣿⣹⣿⣿⠿⠒⣿⡈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⢿⣿⣿⡿⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⣟⣿⣻⣻⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣛⣛⣛⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠤⠄⠀⠒⠢⠤⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣶⣒⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠲⠤⠤⢄⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣑⣲⣶⣤⣤
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠿⠟⠛⠛⠛⠛⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠟⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢶⣤⣶⣿⣿⠟⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠉⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⢸⣿⡋⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡴⠶⢶⣒⣶⡚⠋
⠀⠀⠀⠀⠀⠀⢀⢼⣓⠢⢄⡀⠀⠀⠀⠉⠛⠲⢤⣄⡀⠀⣿⣧⣀⣀⣀⣀⣀⣤⡤⠶⠖⣚⣋⣭⣭⣶⡾⠶⠶⠟⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⠂⠉⠓⠦⣄⡀⠀⠀⠀⠈⠙⠓⠺⢿⣿⣿⣿⣵⠶⠶⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠐⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠒⠤⣄⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⣖⣛⣻⡟
⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡉⠓⠤⣀⠀⢸⣿⡤⠀⠀⠀⢀⣀⣠⣤⠴⣖⣾⣿⣭⣷⠶⠿⠛⠛⠋⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠛⠿⠿⣛⣛⣯⣿⡿⠿⠾⠛⠛⠉⠉⠁⠀⠀⡀⠠⠄⠐⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣶⣿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⢸⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⣿⣿⡅⣀⣀⣤⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠹⢿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⠛⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠑⢿⡿⠧⢀⡀⠀⠀⢀⣀⣀⣤⣤⢤⣤⣤⡀⣀⠀⠀⠀⢀⠀⡶⣿⡷⠂⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡳⣌⠻⣷⡿⠟⣿⡿⠉⡘⢧⢻⠍⠌⢩⠃⠿⣈⠛⣶⣾⢿⣷⣾⠏⣡⢾⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣦⠛⡃⠀⠋⠍⡘⡿⠀⣷⠻⠼⢇⡌⠐⠿⠃⣉⠉⠀⠹⢃⣼⣳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣋⠇⢼⠿⠒⠆⠀⠁⢠⣶⡶⣦⣷⡶⣼⣶⠀⠀⠀⠰⠾⣿⡄⠟⡻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢋⣿⣷⣾⠷⣴⣄⠂⠰⢱⣟⣈⣷⠆⠂⢀⣄⡴⠾⣷⣞⣉⠻⡻⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⠃⡿⠋⡿⣶⣦⣍⠑⠧⡀⠹⣭⠋⢠⠖⢋⣥⡶⣿⣿⡙⣯⢢⠘⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢸⠸⣧⠀⠿⣿⡿⢻⣷⠞⠈⠦⠁⠞⠹⣾⣎⠛⠿⣿⠟⠀⡾⢨⠀⡯⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⡀⠡⡙⠳⣦⣤⣴⡞⠁⠖⡀⡶⡐⢧⠔⠀⠉⣷⣤⣤⣤⠞⣡⠆⣰⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠛⢷⣮⣌⡑⠒⢒⣚⣥⡇⠴⠀⣸⢻⣄⠰⠌⣷⣘⡃⠲⠒⡈⣄⣶⡶⠋⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣦⡀⠉⠛⠟⠿⠛⠛⠉⢐⡺⢷⣿⠀⣿⡿⠚⢈⠙⠛⠾⠶⠷⠊⠋⣴⣿⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢿⣿⣤⡀⡒⢀⣀⡀⢀⡔⠘⠙⡆⣽⣼⡏⣆⠛⠰⡄⢀⣀⣀⢀⠀⡤⣿⡿⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡘⠿⢿⣯⣈⠋⢁⠞⣻⠿⣶⣷⣼⡋⣴⣕⣾⢿⠛⡄⠙⣁⣼⣿⠿⠛⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡮⣙⢛⠋⠆⣻⡀⣩⡼⠀⢈⠹⡽⢉⠀⠹⣞⡃⠸⢋⡍⣛⢛⡩⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠋⠞⠽⡿⢄⠈⣒⠅⢾⡀⢉⣦⠅⠠⡽⢟⡀⣹⠅⠰⠈⢧⠘⡿⠹⠎⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠶⣤⠇⢨⣵⢶⠟⡀⢰⠀⠹⡴⣻⡄⠀⢤⠄⡘⢧⢘⣭⠐⣧⡾⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣠⡸⠋⣗⣤⢉⣠⠀⠙⠚⠃⠚⢜⠋⢴⡀⠺⠐⢁⢠⣈⣡⡸⡏⠓⣤⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣁⣰⡟⣺⠷⡏⣰⣿⠁⣼⡎⠛⢠⡌⣽⠀⢉⣿⣀⣶⢿⢻⣷⡄⢹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣻⠣⣨⣓⢟⣥⣬⡉⣠⢧⣄⣩⣤⣻⢝⣝⡌⢛⣃⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣻⣿⣿⣜⣽⣷⣾⣗⠦⣶⢛⡟⣾⡤⢚⡿⣶⣯⣉⣼⡿⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣏⡟⣿⣽⢼⡷⣯⣿⢻⣯⣿⣿⢻⣯⡷⣿⢼⣽⢋⣇⣿⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠋⡋⢘⠉⡯⣿⣻⣷⣷⣿⣹⣿⠏⣃⠘⠉⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢶⣧⣻⣤⡑⠛⡹⠿⡟⠿⢹⣟⢣⣿⣼⡷⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣀⠁⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠢⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠉⠉⠁⠹⠖⠂⢤⡀⠀⠀⠀⠀⠀⠀⠠⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⢦⣀⡤⠞⠉⠱⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠰⡎⢀⡠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠖⠳⠎⠀⢠⠈⠑⠲⠦⢤⣤⡤⢀⠀⢤⡤⢤⡄⠀⠐⣠⡿⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠐⣇⡠⡏⠀⠀⢸⠃⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡜⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣤⣤⡤⠾⣴⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠉⠁⠀⢀⡜⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢧⡀⠀⠒⠒⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠉⢰
⡀⠀⠀⣠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡐⠰⠆
⠀⠀⢠⡼⠆⠀⠀⡀⠀⠀⠀⢀⡀⠂⠀⠠⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠄⢠⡇⠀⠀⠈⠉⠀⠀⢀
⠈⠁⢠⡜⡀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠲⠲⢤⣌⣉⠒⠠⣄⣀⡙⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⣀⠠⠤⠒⣊⣤⠖⠁⠙⢦⣀⠀⠀⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠤⣌⣉⠓⠚⠛⡿⠛⠛⠛⣿⠟⠛⠛⠉⢀⣀⣀⣀⠠⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠈⠁⠘⠧⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡙⠀⠈⠙⠉⠁⠴⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠒⠒⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⢀⣀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠏⠀⢰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠲⠶⠶⠶⠺⠟⠋⠁⠄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠌⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢀⡁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⢨
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠆⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣐⠀⣀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠆⠀⠀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠉⠒⠢⣄⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠖⠒⠉⠉⠉⠁⠒⠢⢌⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠔⠁⠈⢀⡀⠀⠁⠀⠀⠀⠀⠈⠢⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣽⠢⠀⠑⢄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡇⠀⠀⡤⠀⠀⠤⠄⢀⣠⣾⡇⠀⠀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠻⣿⣶⡶⠿⠛⢻⡟⠀⠀⠀⢰⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠉⠻⠄⠀⠔⠋⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠶⠤⠤⠤⡤⣤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⢠⠃
⡄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠠⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢀⡎
⠱⡀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⢄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠘⢎⠀⠀⠈⠂⡤⢆⠀⠀⣀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠑⠦⡀⠄⠀⠀⡀⠀⠀⠁⠂⠤⣀⠈⠢⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠁⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠦⠤⡄⠀⠀⠀⠀⠀⠀⠈⠶⠥⣄⠀⠀⠀⠢⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄⠀⠀⠈⠃⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡸⠁⣀⠀⠀⣀⠜⠀⠀⠈⠢⣀⠌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠲⣄⠀⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⡀⠀⢨⡛⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⢄⠀⣧⡉⣷⣾⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⠀⠘⢳⡆⠀⣤⣿⡇⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢆⢸⣸⣧⡰⡶⣏⣳⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⣄⣦⢀⡈⢦⣀⣨⣯⣿⣯⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⣻⡄⡤⣀⣻⢿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣤⡟⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢈⣷⣠⣿⣴⣤⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⣀⠀⣤⣦⣤⣠⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⢦⡈⡷⡄⣾⡰⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠙⡷⣧⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢤⡴⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢚⣛⢦⣠⣾⣮⣭⣭⣚⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⡾⠛⣹⡟⣿⠙⡟⢟⠻⢿⣶⣦⣍⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠴⠊⠀⢀⡠⣄⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⣿⣏⣠⠞⢁⢣⠃⡧⠇⡈⠇⢀⣿⠻⣷⣍⠺⣾⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢯⡀⠀⠋⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⢾⡟⣿⡞⢏⡡⠞⠻⠽⠀⠈⠳⠃⠈⠋⣄⠈⠻⣳⣜⢷⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡏⣾⢡⣹⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠙⣿⠻⣧⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⢠⡏⢸⡇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠁⠀⡴⣂⠀⢹⡀⢻⡄⡇⠀⠀⠀⠀⠀⠀⡴⠉⠙⣦⠤⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⢨⠱⣾⠇⢠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⢸⡇⢸⢷⢸⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢸⠀⣿⡀⠸⣌⡸⠀⠀⠀⢄⠀⠀⠀⢀⡆⠀⠀⠀⣠⡇⢠⣸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠘⣠⡿⡏⠲⣀⠀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⣠⠞⠁⡇⢸⣿⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⣦⣿⠁⡇⠀⠀⠉⠒⠤⣤⣀⣀⣀⢠⡤⠲⣿⡁⠀⠀⠘⠮⣷⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡏⠀⠀⠀⢀⠴⠊⣿⠀⢀⡠⠴⠳⣄⣷⠙⠦⣀⠀⠀⠈⡶⢻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⣿⡀⠀⠈⠳⠦⣼⣿⡦⠋⠀⠀⠀⠀⢹⡏⠓⠚⠉⠀⠀⡇⢀⠱⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⡇⡇⠀⠀⠀⢀⠇⡇⢥⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⡦⠈⢆⡃⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢸⣵⠃⠇⠀⠀⢀⡌⢸⠀⠸⡄⠀⠀⠀⠀⡟⢨⢣⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡜⢀⠇⠀⠀⠹⣀⣤⣄⣼⠁⢸⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⡜⠀⠀⠀⠀⡟⠟⠻⠿⠆⢸⡀⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⡄⢰⢠⣏⠟⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠰⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠆⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⠶⡄⣄⠇⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠖⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠚⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢧⣠⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠈⠤⠵⠮⢤⣶⠦⢤⣀⠀⠀⠀⠀⣀⣀⣀⣀⠾⠤⣀⣁⣠⡇⠀⠀⠀⠀⠀⠀⣀⣧⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠈⠉⠉⠉⠉⠀⠈⠙⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠼⠁



⣿⣿⡿⠿⣿⡿⢿⢿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣵⣿⣵⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢚⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡟⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣄⣀⣀⡾⠀⠟⣴⣿⣯⠤⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠛⠛⢻⣄⠀⢉⣡⠀⢀⡶⢸⠏⢀⡶⢀⡟⠻⣦
⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⣶⣿⠇⣼⠟⠛⠛⡇⠀⠚⠁⡄⠀⢨⣴⠿⢃⣴⣿⠁
⠀⠀⠀⠀⠀⢸⣇⢠⣾⣟⣡⡏⣸⠏⢀⣴⣿⣷⣤⣴⣾⣿⣤⣤⣴⣾⣿⣟⣡⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣻⠟⠋⠉⠉⣀⠉⣀⠛⢁⣴⠀⣸⠃⢈⡤⢀⡉⠀⣡⠄⢈⠁⢀⡟⠀⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣤⣴⠞⠀⣿⠀⡟⠀⠰⠃⢰⡏⢠⡿⠃⢨⠁⣼⠟⠀⡍⠀⠞⠀⠘⣉⠀⠉⣿⡄
⠀⠀⠀⠀⣿⠙⠶⠟⠋⠀⣸⡇⠀⢿⣤⣴⣦⡔⠁⣦⣤⣶⠇⢰⣤⣴⣾⣧⣴⠎⣰⣿⠟⠻⢷⣿⠇
⠀⠀⠀⠀⠹⣷⣄⣀⣠⣾⣿⣧⣀⣀⣿⡍⡿⠀⢸⣿⢉⡏⠀⣿⠃⠘⠷⠟⠃⣰⣿⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠙⠛⠛⠋⠘⣷⣤⣿⠇⣿⣄⣰⣿⣆⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠛⠛⠋⠙⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⡉⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠉⠉⠉⠁⠀⠂⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠾⠿⠿⠟⠉⠩⠏⠁⠀⠀⠐⡟⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡶⢶⣶⣶⠶⢲⣶⢢⡖⠒⠒⠒⠒⠒⢶⠶⡶⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣥⣿⣤⣴⣦⣼⣄⢠⡷⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠛⠛⠿⠿⢿⣿⣿⣿⢿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⢀⣠⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢾⠟⠛⠉⠉⠉⠉⡥⠖⠒⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠄⠠⣀⣀⣀⣀⡀⠀⢀⡤⠖⢒⠉⠀⠀⠀⠀⠀⣼⣷⡤
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠀⡏⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠑⠒⠒⠢⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠢⠤⠄⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⡠⠖⢚⣉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⢠⡄⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠖⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆⠀⣀⣤⡀⠀⠈⢦⠈⢢⡀
⠀⠁⠀⠀⠀⢿⡉⢢⡀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠾⠷⠄⠀⠠⡶⠿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⢠⣇⡼⠋⣰⠃⠀⠀⠀⢧⠀⢳
⠀⠀⠰⣟⠓⢮⣳⣄⠱⣼⡇⣠⠏⠀⠀⠀⠀⠀⠀⢀⡾⣫⡴⠆⠀⠀⠀⠀⠀⠀⠀⣀⡉⠻⣆⠀⠀⠀⠀⠀⣞⢉⣉⡙⢿⣄⠀⠀⢾⡥⠶⣦⠀⠀⢸
⠀⠀⠀⠈⠓⢄⡙⠁⣠⠟⠁⢳⡀⠀⠀⠀⠀⠀⠀⣸⠇⢁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡦⠹⣧⠀⠀⠀⠀⠉⠁⠀⡝⠀⠈⢷⠀⠀⡤⠖⠋⠀⠀⢸
⠀⠀⠰⣏⣉⣈⡁⠰⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠙⢦⣄⡀⠀⠀⢀⣠⡴⠛⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⠁⣤⣉⣱⡄⠀⠀⠏
⠀⠀⠀⠀⢠⠞⣡⣄⣀⣀⣄⠙⢦⡀⠀⠀⠀⠀⣠⣿⡀⢸⣇⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⣿⠀⢸⡷⣤⡀⠀⠀⠀⣰⠋⢠⡷⠒⠋⠁⠈⠉
⠀⠀⠀⠀⠘⠋⠀⠈⠉⠉⠈⠳⣄⠙⢦⡀⠀⠀⣧⣂⡀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢀⣀⣸⠇⠀⢠⡞⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠙⢦⠀⠈⣿⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠀⠀⣿⠁⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⢄⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣠⠞⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠈⢧⡈⠉⠙⠛⠛⢛⡿⠃⠀⠀⠀⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⡀⠈⠻⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠦⣄⣀⠉⠛⠛⠛⠋⠁⠀⣀⣠⡴⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣼⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠀⠀⢀⣠⠶⠛⠙⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⢦⡀⠀⣠⠏⣹⠛⠻⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⢻⡙⢦⣀⡴⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⠲⠋⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉

⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣠⡤
⠀⠀⠀⠰⣦⣽⣻⣷⣾⣷⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣡⣾⣷⣿⣟⣭⡴⠂
⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣮⡢⣤⣀⣠⡤⠶⠶⠶⠶⢖⠒⠶⠶⡶⠦⢤⣄⣀⣤⢈⣵⣵⣿⣿⣿⣟⡋
⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣷⡝⢿⣿⣶⣶⣤⣀⣤⣘⣨⣗⣀⣴⣶⣾⣿⡟⣣⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⣸⣟⣛⣿⣿⡋⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⣾⣟⣛⣻⡄⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠈⣿⠙⣿⣽⣿⣶⣬⠛⣿⣿⣿⣿⢫⣴⣿⣿⣽⡿⢹⡿⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠹⣄⠙⠻⠛⣹⣿⣷⡯⣻⡏⢽⣿⣿⡙⠻⠟⢁⡼⠃⠀⠀⠀⣿⣿⣯
⠀⠀⠀⠀⠀⠐⣿⣿⣿⡀⠀⠀⠀⠈⠛⠶⢿⡟⠁⠈⣳⠇⢿⡏⠀⠉⣿⠶⠞⠋⠀⠀⠀⠀⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣄⠀⠀⠀⠀⡀⢀⠀⡀⠀⡟⢨⡈⣇⡄⠀⢈⢧⡀⠀⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣽⢿⣿⣷⣶⣯⣾⠾⠿⣿⣿⣷⣇⣿⡇⣿⡿⠿⣿⡷⢽⣮⣾⣾⣿⣿⢿⣷⣿⣿⡀
⠀⠀⠀⠀⠀⣼⡟⠿⣿⣿⣿⣿⣯⣥⣴⣲⡷⢀⡀⢬⣿⣿⣽⣯⡔⢀⡠⣾⣆⣤⣭⣿⣿⣿⣿⡿⠟⣿⢇
⠀⠀⠀⠀⣼⡟⢁⡖⠁⣽⣟⠈⣸⠉⠙⠋⠛⣼⣏⠂⡙⢿⠟⠉⠐⣽⡟⠋⠙⠉⣹⡌⢐⣿⡧⠙⣦⠙⢺⡆
⠀⠀⠀⠀⣿⣱⢫⣷⣄⠈⠻⢣⡿⠋⠀⢰⡇⠉⠙⢷⡀⢠⡄⢀⡞⠛⠁⢻⠆⠀⠛⢷⡽⠏⠀⣴⣿⡹⣾⡇
⠀⠀⠀⠐⢳⣷⣻⣿⣿⣄⢀⡏⣠⣤⠀⠀⡘⠁⠀⠸⣷⣼⣁⣾⡅⠀⠈⣂⠀⠀⠀⠀⣷⡀⣠⣿⣿⣇⣿⠙
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡍⠁⠀⠐⠿⠀⡶⢀⠀⣿⣿⡇⢠⡘⠀⠻⡅⠙⢷⣷⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠟⠿⣿⡿⢿⣿⣿⣿⣾⡄⣦⣀⢀⣄⣛⢰⣿⣿⣷⡈⣃⣀⣀⡴⣰⣾⣿⣿⣿⡿⠿⡿⠟⠗
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠘⠘⡟⢃⠸⣿⣿⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⠈⠀⠉⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠻⠏⠻⠎⢿⣿⣿⡿⠛⠚⢹⠏⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠒⢶⣎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠖⠋⠉⠀⠀⠀⠀⠀⠀⣸⠟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠉⠁⠀⠈⣿⠹⣆⡀⠀⠀⠀⣀⣀⣤⠞⠋⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⡞⠉⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⠙⢦⣤⣄⣠⣤⡴⠶⠋⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⠂⠀⠀⠀⢸⣷⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡆⠀⠀⠀⠀⠀⠀⠠⣄⣀⡤⠶⠚⠛⠛⠋⠙⠛⠛⠻⠦⣤⣀⠀⣼⠋⢀⣠⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢠⣀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠻⣧⡀⠀⠈⢉⡴
⠀⠀⠀⠀⠀⠀⠀⣶⡄⠸⣿⡄⠀⠙⣦⠞⠁⣀⣠⣤⣤⣴⠆⠀⠀⠀⠀⠀⠉⠻⣟⠲⠄⠀⠈⠻⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⠙⠁⠀⣴⣧⠶⠛⣩⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠸⣇
⠀⠀⢀⣠⡤⠶⠦⣤⡀⠉⠛⠶⣼⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡤⠤⠦⣤⣀
⠀⢠⡟⠁⠀⠀⣀⣀⣽⣦⣄⣀⡟⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣀⡀⠀⠀⠙⢷
⠀⣿⠀⣠⡴⠚⠉⠉⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠙⠳⢦⡀⢸
⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⢀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠙⢿
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⢦⣄⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠶⣤⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡼⢷⡄⠀⠈⠛⢯⣙⠛⠛⠛⠉⢉⣥⠞⠉⠀⠀⣼⠃⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⣴⠏⠀⠀⢻⡄⠀⠀⠀⠙⠷⣄⣀⡴⠋⠁⠀⠀⢀⡾⠉⢳⡄⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡾⠃⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⡼⢿⡄⠀⠀⠀⢀⡾⠁⠀⠀⢻⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⣿⣁⣀⣽⣦⡀⢠⡞⠁⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠁⠈⠉⠉⠀⠈⠳⠟⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢀⣀⣀⣠⣤⣤⣤⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⣴⠞⠋⠉⠉⠀⠀⢀⣠⢴⡏⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⣷
⠻⣤⣀⣀⠀⠀⣰⠟⠁⢰⡇⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⢾⣏⣠⡴⠋
⠀⠀⠉⠉⠙⠛⠻⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠙⠶⣤⣀⣀⣀⣀⣀⣀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠉⠛⠒⠲⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠡⠴⣶⣶⣶⣤⣄⠉⠻⣿⣿⣿⣿⠟⠋⣠⣤⣶⣶⣶⠤⠌⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡴⠋⠉⠉⠉⠙⢿⣷⣄⠘⣿⣿⠃⣠⣾⡿⠋⠉⠉⠉⠛⢦⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣰⠏⠀⣠⠞⢻⣷⣦⠀⢹⣿⡆⢸⡇⢰⣿⡏⠀⣴⣾⡟⠳⣄⠀⢹⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡀⠀⣿⣷⣾⣿⣿⡇⢀⡇⠃⢸⡇⠘⢸⡀⢸⣿⣿⣷⣾⣿⠀⢀⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢻⣧⡀⠘⠻⠿⠿⠋⢀⡼⢁⣤⣾⣷⣤⡈⢧⡀⠙⠿⠿⠟⠃⢀⣼⡟⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡻⢿⣶⣤⣤⣤⠶⠋⠀⣨⣿⣿⣿⣿⣅⠀⠙⠶⣤⣤⣤⣶⡿⢟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡟⢶⣤⣍⣁⣀⣠⠴⠞⠁⠈⠻⠟⠁⠉⠳⠦⣤⣀⣈⣩⡥⡶⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠃⣿⠀⣼⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⣧⠀⢿⠀⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡟⠀⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡄⣿⠀⡇⠀⡇⠀⣄⣀⡄⢠⣄⣀⠄⢤⣀⣠⠀⢸⠀⢸⠀⢸⢀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⡇⢻⠀⡇⠀⡇⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⠀⢸⠀⢸⠀⡿⢸⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠸⡆⣷⠀⡇⠐⠶⠤⠆⠐⠦⠴⠂⠲⠤⠴⠂⢉⠀⡛⢀⠃⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢷⢸⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡇⣼⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣇⢷⠸⡆⠀⠈⠙⠛⠁⠈⠛⠋⠀⠀⢸⠇⡾⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣇⢻⡀⠀⠀⠠⣤⣤⠄⠀⠀⢀⡟⣸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⢀⣾⣴⣯⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡽⢟⣿⡿⠷⠦⣄⣀⣀⣤⠴⠾⢿⣿⠿⡍⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠿⠛⠻⠟⠛⠿⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⡥⠄⠀⠀⠀⠀⠀⢤⡀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠘⣿⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠀⠀⣾⣷⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡐⠀⠀⢀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⡤⢴⠆⠀⠀⠠⠂⠀⠀⡠⠀⠁⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢌⣀⣠⡔⢈⡀⠠⣤⠐⠈⢀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⢹⣧⣼⡷⠀⠀⠀⣿⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠠⠐⢻⡀⠀⠀⠀⠙⠈⠁⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣂⠁⠀⢀⠠⠀⠐⠛⠊⡇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠑⠂⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠇⠀⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠰⠀⠀⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡻⣽⣷⠇⠀⠀⠀⣷⣿⣫⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⡻⠃⠀⠀⠀⠀⠘⠿⠿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣻⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠀⠀⠀⢱⣠⠔⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠠⠙⡄⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣄⠐⢀⡜⠁⠄⠀⢀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠀⢸⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⣻⠟⡝⡟⢷⣶⣤⣀⣀⠞⠁⠀⢀⠀⠀⠈⠧⠀⠀⢈⣀⡀⠈⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠋⢀⡬⠐⠋⠘⠁⠁⠀⠐⠦⠙⢷⣦⣀⠀⠈⠙⠂⠀⡠⠚⠉⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⣡⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⣯⡣⡀⠒⠀⡼⠁⣰⠃⠀⠁⠀⠀⠀⢳⠐⠚
⠀⠀⠀⠀⠀⠀⠐⠟⡴⢡⣇⠛⠀⡀⠀⠀⠀⠐⠂⠀⠈⠀⢀⠀⠛⢸⣻⡷⣵⡀⠀⠱⡀⠹⣄⣀⣀⡤⠀⢠⠏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⡄⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠏⠀⠇⠻⠁⠀⠀⣹⢶⠤⢍⡭⠤⠖⠁⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠑⠦⢄⣀⣀⡠⠴⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⣀⠀⢰⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠦⠤⠤⠤⠤⠔⠚⢿⢄⡀⠀⠀⣀⢀⡠⠊⠁⠀⠀⠀⡇⠀⠀⢇
⠀⢠⠊⢉⣚⠉⢹⠄⠀⢀⣀⣠⠔⠋⡽⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠑⣾⡷⠏⠀⠀⠀⠀⠀⠀⣃⣀⠀⠈
⠀⢿⢠⠋⢀⢱⠈⠓⡄⠀⠞⠿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⣠⠞⠁⠀⠀⠀⠀⠀⣀⣴⡉⠵⠮⣗⠒⣄
⠀⣰⠛⢻⠾⠊⡤⠞⠁⠀⠀⠀⠀⠘⠓⠋⢹⡏⠉⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣅⢎⣥⡼⢴⠃
⠀⠈⠋⢉⣓⣚⣆⡴⣦⣀⡠⠤⠤⠒⠒⢃⣸⠇⠉⠉⠁⣇⡀⠉⠙⠓⠒⠒⠦⠤⢄⣀⠉⢱⣌⡹⠯⣀⡼
⠀⠀⠀⠈⠓⣮⠿⠛⠉⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⡀
⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠋⠔⠋⠄⡰⠀⠀⠀⠂⠠⠀⠀⠂⠱⠘⠀⠶⠂⠋⠇⠃⡇⠱⠀⠀⠰⠂⠁⠀⠀⠴⠀⠆⠀⠸⠉⠱⠋⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠿⢿⢻⠿⡿⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣧⣤⣴⣶⣶⠶⣿⣿⣶⢰⣶⣶⣶⣶⣤⣤⣤⣄⠈⣿⡆
⠀⠀⠀⢰⣾⣿⡏⣽⡿⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇
⠀⠀⠀⣤⣬⣤⠀⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡀⠀⠀⠉⣡⣝⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷
⠀⠀⠀⠿⣦⣧⠀⠀⠀⠀⠈⠩⣗⣀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⢦⣘⣼⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⢹⣿
⠀⠀⠀⣾⠿⣟⣄⠀⠀⠑⢀⡼⢯⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠤⡮⣸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣽⣿⡇⢸⣿
⠀⠀⠀⣿⠀⡋⣏⠀⠁⠠⡽⡷⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣶⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿
⠀⠀⢰⠈⠀⠀⠸⡇⢂⠀⠀⠨⣽⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣴⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⣤⣬⣭⣅⠸⣿
⠀⠀⢸⣇⠀⠀⠀⣿⡀⢶⡖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⢦⣿⣼⣿⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⡼⠿⣦⠀⠘⣿⣷⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿
⠀⠀⣷⠘⠿⠠⠊⢉⣥⣤⣤⣦⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿
⠀⠀⣿⣤⣶⠤⠄⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹
⠀⢰⣟⣉⣐⣶⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠧⣼⣿⡛⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠇⡿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣤⣄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡠⢀⣀⣀⣀⣀⣀⣀⠀⠀⣾⣿⡿⠛⠛⠿⢿⣿⡿⢿⣿⣯⠉⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⢀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠄⣿⣿⣿⠟⠙⠛⠻⠿⢿⣿⣿⡿⣿⠇⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠏⠋⠙⠁⠈⠁⠀⠈⠛⣿⣿⣿
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠀⠀⠀⠐⠃⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟
⠀⠀⠀⠀⢸⢳⠀⠀⠀⠠⡄⠀⠀⠀⣤⠀⠳⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⡇⢄⣄⣠⠄⠀⡄⠀⠆⠀⠀⠀⠰⠀⠀⠀⠀⣏⠉
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢄⠀⡂⠀⠀⢘⠈⠀⠀⠀⢀⠀⢀⣀⢠⠔⠁⠀⠿⢉⡩⡀⠘⡀⠀⠀⠢⠀⠐⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⣿⣷⣤⣀⣀⠀⠀⠀⠀⣀⡠⠂⠀⠀⠀⢀⡜⠀⢢⣀⠂⠀⢀⠂⠀⠀⠈⠂⢁⠀⢤⡀⢀⡀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠤⢻⣿⣿⣿⠀⠀⠀⠀⠣⡈⡠⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠁⠘⠚⠐⠳⠀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠄⠀⠀⢻⣿⣿⡇⠀⠀⠂⠀⠀⠁⠨⡒⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠢⣜⠂
⠀⠀⠀⠀⠻⠿⠿⢿⢋⠋⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⠀⠀⠀⠀⠀⠀⠠⠂⠀⢠⠆⠀⠀⡠⢤⠡⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠏⠀⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠀⣀⡀⢀⢠⠀⠀⠦⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠚⠗⠀⠀⠀⠀⠀⠺⠓⠃⠠⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠡⠐⢋⡉⣂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡠⠂⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠂⠀⠀⠀⠔⠁⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡂⠐⡂⡖⠀⠁⠚⠲⡆⠀⠀⠀⠀⠀⠑⢈⣱⠐⡆⠀⠀⠀⠀⠀⣀⣠⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡅⠀⢩⢅⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠞⠁⠀⠘⠚⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣴⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠈⠉⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⠤⠀⠀⣄⣀⠈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢰⠂⠐⠺⠗⠂⠈⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠓⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠐⠀⠀⠀⣠⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⣤⣤⣶⠟⠁⠀⡟⠛⠛⠛⠛⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠝⠋⠁⠀⠀⠀⢧⣤⣤⣤⣤⣤⣤⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠁⠀⢀⠀⠤⠀⠂⠁⠙⢛⣿⣿⠿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣴⣾⣧⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠈⠉⠙⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣄⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣄⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠼⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠛⠛⠛⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⡀⠀⠂⠀⠀⠠⠶⣤⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠤⡄⠉⠻⣿⣷⣾⣀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠶⢴⠞⠁⢰⠾⡇⠀⠀⢤⡄⠀⠤⢼⠟⠛⠛⠓⠀⢀⡀⠀⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡄⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠃⢻⣤⣾⣧⠆⠈⠁⠀⡀⣠⣴⡆⠈⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⡀⠐⠀⢿⣶⡦⡤⠀⠖⠀⣶⢀⡄⠈⣿⠿⠋⠷⠖⠀⠀⡙⠛⠛⠀⠀⠐⠳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠉⠁⠚⠁⢄⡀⠀⢀⣤⣼⣿⡿⡘⢀⢠⣀⣶⣤⠀⣤⠉⠀⠀⢠⠤⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⡀⠀⠀⠀⠀⡀⠉⠩⠉⠓⢷⣿⣦⣿⣟⣛⣿⣿⣾⣆⡄⠐⠀⠐⠀⠠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠖⠀⠋⠉⠂⠠⣄⢀⣼⠟⠉⠁⠉⢻⣿⣿⣿⡿⣓⠂⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠸⣿⡇⠀⠀⠀⠀⠘⡿⢉⣿⣿⡋⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⢦⠄⠀⠞⠋⡀⠚⠟⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣾⣟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠘⠻⠷⠶⠶⢺⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣠⡤⣄⠀⠀⢀⣴⠄⢀⣴⠆⠀⢠⣾⡟⢀⣤⠀⠀⣠⡀⢀⣾⣏⡼⠁
⠀⢀⡴⠶⠶⣤⡀⠀⠀⢀⣿⡏⣴⣿⡁⠘⡇⢀⣾⡟⠀⣼⡏⠀⣰⣿⠏⢠⣿⠏⠀⣾⡟⠀⣼⡿⠋⠀⡀
⢰⡏⠀⠀⠀⠸⡷⠀⠀⣼⡿⠀⣿⡏⠛⣾⠗⠻⣿⣀⣴⣿⠣⢶⣿⠷⠖⢾⡏⣠⣼⣿⢀⣼⡿⠀⠀⡼⠁
⠸⣇⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⠛⠚⠋⠀⠀⠉⠉⣼⡏⢠⣿⠋⣇⠀⠈⠛⠉⠀⠛⠋⠸⣧⣠⠞⠁
⠀⠈⠛⠶⠶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⣴⠋⠉⢉⣿⠟⠲⢾⡟⠋⣿
⢰⣇⠀⡴⣿⡄⣰⢻⣷⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠸⣧⣠⡏⠀⠀⠀⠀⣼⣄⡀
⢸⣿⣸⠃⣿⣷⠇⢸⣿⠀⢀⣤⡄⣤⡄⠀⠀⢠⢤⠀⠀⠀⠀⣨⠉⠀⣤⠀⠀⢠⣿⣿⡟
⢸⣿⡏⠀⣿⡿⠀⢸⣿⢠⣿⣣⠇⠙⡿⢤⣤⠈⢻⠦⣤⡄⠀⣿⠀⢠⣿⡆⢠⠈⣿⣿⣿⠆
⢸⣿⡁⠀⣿⡇⠀⢸⣿⢸⣿⠁⠀⡰⠁⣼⡿⢀⠏⢠⣿⠇⣸⣿⣄⡞⣿⡷⠋⠘⠻⣿⡏⣤⣀⣤⣦⣄⣀
⠈⠛⠁⠀⠀⠀⠀⠀⠋⠀⠙⠛⠋⠀⠀⣿⣧⠞⠀⢸⣿⡴⠁⢙⣋⢤⣿⡇⠀⠰⣿⠿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⣠⠖⠚⢻⣦⣀⣀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⠀⠀⢰⡋⢀⣼⡿⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⡉
⠀⠸⠥⠂⣠⡿⠋⠉⣸⡷⠀⣰⡿⢡⠇⠀⠀⠀⠀⣀⣀⠀⠀⢙⣛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⢀⣀⣼⡟⠁⠶⣾⡋⠀⢰⣿⡵⢃⣴⡾⢛⡆⠸⣿⡀⠁⠀⢿⣄⠉⠀⢠⣴⠞⢳⠀⢀⣴⠶⣾⡏
⡼⠉⢸⣿⠙⣦⠀⠈⣿⢀⣿⠋⠀⣼⡟⠓⠋⢡⢞⣘⣿⣆⡠⣋⣻⣷⣠⣿⠟⠚⠋⣰⣿⠃⣸⡟⢀⡖
⢧⡀⠀⠓⠀⠟⠀⢠⣿⢹⡇⢀⡼⠙⠧⡤⠖⠋⠯⡥⠿⠃⠸⢭⠼⠟⠀⠻⢦⠤⠚⠙⠷⠖⠻⣧⠞
⠈⠛⢶⣤⣤⣤⣾⠟⠃⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣟⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠿⠏⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣫⡵⠾⣿⣿⣿⣿⡟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠘⠉⠁⢼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢢⠄⠀⠀⠀⠀⠀⠠⣥⣴⣶⣿⣿⣟⣿⡽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡠⠅⠀⠀⠀⠀⠀⢀⠚⠀⠀⢠⠀⣤⠡⡄⠀⠀⠀⣰⣶⠾⠿⠾⣿⣏⡉⠙⠟⠷⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢉⣙⡾⢷⣦⠀⠀⢰⠀⢆⠀⠀⠠⠐⠒⠇⠄⠀⠀⣀⣃⡈⠲⠀⠀⢈⠙⢷⡆⠀⣄⠀⠀⠀⠀⠀⠀⠀⠃
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣈⣥⡀⠀⢠⢈⣀⠀⠰⠐⡀⠖⠀⢀⣴⣾⣿⣭⡿⢷⣬⡄⡈⡀⠈⣿⡄⢏⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡝⠻⣻⣦⣄⠀⠄⠈⠑⠀⠉⣀⣾⣿⡟⠻⠿⠟⠀⣸⢣⠥⡶⠀⠀⢹⡇⠈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣧⡀⠛⠟⢿⣿⣶⢶⣶⡶⢿⠏⠀⠙⢏⡒⠦⠖⢒⠠⣸⡽⠄⠀⠀⣸⡇⠀⡘⢇
⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠒⠅⠈⢛⣸⠏⠀⢋⢻⡞⢷⣏⡀⠀⠀⠀⠀⠀⢀⣛⠂⠀⠀⠀⠀⣰⡟⠁⠀⠀⠈⢃
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠰⠖⠉⠀⠀⢀⣨⣿⡆⣿⣿⣶⡆⣧⢀⠀⠠⠬⠀⠀⠀⠠⠴⠞⣻⣶⡄⠀⠀⠀⠀⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠒⠐⠀⠨⣾⣿⡇⣿⣿⣿⣿⠋⠉⢀⢀⡀⠀⠀⠀⢀⠀⣼⣿⣿⣧⠶⡀⡐⣀⣦⣝⡱⢠⣄
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠦⠀⠀⠀⠀⠈⠉⣿⡿⠿⠿⠛⠱⠿⠿⠿⠿⢿⠛⠛⠋⠻⣷⣹⣿⡽⣯⡽⣟⣿⣽⣿⣿⣿⣿⣿
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢤⣤⣀⣿⣀⣀⣠⣠⣴⣠⣿⣿⣦⣀⣀⣀⣀⣸⣿⣿⣿⣿⣥⣠⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢋⣾⣯⣽⣿⣕⣋⣉⣉⡉⢹⠉⠉⣉⡉⢉⣁⣈⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⠘⠛⠉⠉⠉⠉⠁⢐⣿⠻⣿⣋⢛⣻⡿⣿⠛⠛⢻⡿⠿⣻⣿⣿⣝⣛⣿⡿⠁
⠀⠀⠀⠀⠢⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⣀⣷⠇⢹⣿⢿⣿⣷⣎⣛⡑⢯⣌⣲⣠⣾⡲⠵⠿⡿⣷⣦⡞
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠉⠦⠄⣀⠀⠀⠀⣀⣰⡜⣿⣿⣧⣤⣬⢿⡯⡹⣿⠿⠿⢿⣿⣿⣴⣆⡠⠃⠩⡭⣿⢖⠵⡄⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠉⠀⠀⣦⣹⢿⣿⠟⠛⣿⣿⡇⣊⡜⣋⡐⠸⣿⣿⣝⣿⣿⣿⣩⣙⣧⠈⣾⣏⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⢰⡀⣽⠟⣾⣿⠁⠀⣹⣿⣻⣿⣿⡟⡆⠀⣿⣿⣿⣿⣿⣯⣿⣿⣩⣩⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢷⣿⣦⣿⣿⣤⣤⣿⣯⣽⣟⣿⣎⠡⢠⡉⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣿⣟⣽⣻⣇⡮⠤⠼⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣴⣶⣿⣷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣾⣿⡿⢉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣸⣿⣿⠁⡈⠀⠏⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣤⡀⠀⠀⠀⠸⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⡆⢰⡁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡇⢠⣼⣿⣿⣿⣿⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣦⠠
⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⣿⣿⣿⣷⣤⣀
⡌⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠺⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠀⠘⣿⣿⣿⣿⣿⣿⣍⣳⣦⣄⡀
⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣾⠿⠛⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠙⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⡳⡀
⠀⠀⠙⢯⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⡀⣀⣤⣴⣿⣿⣿⠏⠀⣰⣮⡟⢋⠝⠫⠟⠉⠛⣋⠀⢂
⠀⠀⠀⣨⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣍⠋⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⠷⠏⠀⠀⢀⡰⣟⠁⠚⢋
⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠋⠕⠛⠻⢿⣿⣿⢻⣿⣿⣿⢻⠇⢀⣠⠴⣂⡛⠰⠀⠀⠰⣿
⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠈⢻⡿⢿⠛⠋⠞⢰⣿⠃⣾⣿⠿⢿⣷⣦⡀⣽
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⢻⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣀⣼⣇⡼⠁⠿⠁⠂⠀⠀⠈⢻⣿⠈
⠀⠀⠀⠀⣌⣉⣉⣥⣤⣶⠒⠻⣿⡛⠿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣯⡴⠂⠀⠈⡐⠀⠀⠀⣸⡏⡄
⠀⠀⠀⠀⣿⡘⣿⣿⣿⣿⣷⡀⠹⣿⠃⠀⢙⡄⠀⠈⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⠿⠋⣀⣀⣀⣀⣴⣤⣶⣶⣿⣾⣷
⠀⠀⠀⠀⣿⡿⣾⣥⣌⠉⠛⢿⡆⢭⣄⠺⣿⣿⡄⠀⠀⠙⣧⣶⣎⢻⣶⣦⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢃⠔⠋⡍⠉⠛⠋⠉⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣧⣴⡤⠀⠀⠉⠁⠛⠓⠋⠓⠋⠉⠁⠀⠀⠀⠈⠻⠟⢸⣿⣿⣷⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⢣⡴⣣⣤⣤⡄⠤⣀⡀⠻⣯⡙⣿⣿
⠀⠀⠀⢰⣿⣿⣯⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣷⣤⢸⣿⣿⣿⣿⣿⣄⠙⢿⣦⡉⢻⠟⠁⠰⡾⣟⣷⣾⣷⣌⢻
⠀⠀⠀⢸⡿⠛⠛⠻⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢿⣧⠙⣿⣸⣿⣻⣿⣿⢿⣿⣇⡾⣿⣿⣆⡀⢀⡀⢈⢯⣼⡏⢿⣿⣿
⠀⠀⣰⣾⢿⡟⣫⠄⢀⡤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⡧⢈⣿⡏⡽⣿⣤⣈⣿⡿⠀⢸⣿⣿⣷⡈⣷⢸⣷⡽⣇⢸⣿⣿
⠀⢀⣿⣷⣟⡽⠧⢀⡌⢀⣀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢠⣟⢻⡟⠰⡄⣿⣿⣿⣿⠃⠀⠀⠻⣿⣿⣷⡀⠘⡇⢻⣽⣎⣿⣿
⠀⢸⣿⣿⣿⠂⣠⣾⣷⣿⡿⠛⠁⠀⣠⣴⣶⣾⣿⣿⢿⣇⣀⠠⣶⣶⣿⣶⣤⣼⣟⣫⣩⣿⣿⣿⣿⡟⠀⣠⣤⣄⣉⣿⣿⣇⣠⣿⡀⢘⣿⣿⡏
⠀⠀⢿⣿⣯⡄⢹⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣉⣁⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠃
⠀⠀⠈⢿⣿⣿⡜⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠻⣿⣷⠿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠻⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢛⣿⣿⣿⠿⢻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣖⠒⠲⠤⣄⡀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⣙⢦⡀⠀⠙⠪⣧⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡉⠛⠂⠀⠀⠈⠃⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⣂⡀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠎⠀⠀⠀⠀⡀⠀⠀⡀⠀⠙⠦⡀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢦⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠣⡀⠀⢠⡠⣄⡠⠴⠃⠀⢠⠖⠉⠀⢀⠲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠆⠀⠀⠀⠀⠈⠒⢢⠀⠀⣘⡚⢣⠉⠋⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠄⠒⠂⢊⠔⠤⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢢⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣨⡘⡻⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠒⠀⠀⠂⠬⣐⠒⢒⣛⢆⢳⡎⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢉⠆⠐⠎⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣯⠋⠉⠉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⡏⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣰⡟⡹⢽⡲⢒⢒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠀⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣀⣠⠤⠤⠤⠤⣄⡀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠃⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠙⣧⣴⣾⡥⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⢀⡇⠀⠀⢠⡄⣸⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⣷⢠⣷⣸⡟⠛⢷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠒⠾⠷⠶⠞⢡⠿⠋⠈⠟⠀⠀⠈⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢀⣴⠾⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣤⡄⠀⠀⢹⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠀⠀⠀⠈⢁⡤⠶⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠦⣤⡀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⠛⠁⠀⠀⠀⢰⠏⠀⠀⣀⣄⠀⠙⣆⠀⠀⠀⢀⡞⠁⣀⣄⠀⠀⠙⣆⠀⠀⠘⠳⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡃⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣶⠀⢹⠀⠀⠀⢸⡇⢸⣿⣿⣶⠀⠀⢸⠀⠀⠀⠀⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⡇⠀⠀⠀⠀⠀⠘⠦⣤⣀⣙⡛⠁⣠⠟⠀⠀⠀⠈⢧⡈⢙⣛⣁⣀⣤⠏⠀⠀⠀⢀⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣷⠀⠀⠀⠀⠀⢰⣶⡶⠦⠭⣍⣉⣁⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡹⢳⡀⠘⣧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⢰⡏⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣄⢧⠀⠘⢧⡀⠀⠀⠀⢻⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⢨⣿⡟⠀⠀⠀⣰⠏⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⣿⢸⠀⠀⠈⠳⣄⠀⠀⠀⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠀⠀⢀⡾⠃⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⣽⣸⠀⠀⠀⠀⣿⠳⣤⡀⠀⠻⢿⡁⠀⠀⠀⠁⠀⠀⠙⣿⣿⠟⠁⢀⣠⣾⠋⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣱⠃⠀⠀⠀⢀⣿⢀⣸⣽⣷⢶⣤⣉⡓⠶⠤⠤⠤⠴⢚⣉⣠⣴⣶⠛⠳⠿⢦⣄⣀⣀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⣻⡿⠟⠋⠉⢀⣸⣷⠉⢿⠙⢿⣍⣛⣿⠿⠉⠉⣿⡒⢻⣷⢦⣤⣤⣈⡉⠻⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠶⡶⠋⠉⠿⠶⠿⢷⡀⣀⣥⣤⡀⠀⢸⡉⣉⠉⠁⠀⠘⣯⠉⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⡇⠀⠀⠀⢰⢒⣾⠳⣿⣿⣿⣿⠀⠘⣧⢼⠀⠀⠀⠀⣿⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣶⠾⣧⣀⣀⣀⣬⡼⠇⠈⠻⢿⠿⠟⠀⠀⠙⢿⣷⠶⢴⡶⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢸⡉⢹⣏⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠉⢛⡿⠿⠖⠒⠒⠛⠛⠛⠛⠛⠉⠉⠉⣧⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠷⢾⠃⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡟⠳⢽⣀⣿⠀⠀⠀⠀⣼⠋⠉⠉⠹⣆⠀⠀⠀⢀⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡼⠁⠀⢰⡏⠉⠙⠛⠛⠛⢻⡆⠀⠀⢰⡟⠛⠛⠋⠉⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠺⣧⣤⣤⣤⣤⣠⡿⠀⠀⠀⠀⣷⣀⣠⣤⣤⣤⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⡴⠿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⡀

⠀⢀⣀⣀⣤⠶⢾⣿⠿⠿⣿⣶⣤⡀
⠀⢣⡀⣩⡧⣤⠎⠀⠀⠀⠀⡈⠻⣿⣦⡀⠀⠀⠀⠀⠀⢀⣠⠞⢉⡳⢤⣀⣠⣤⣤⣤⠤⢤⣀⡤⠾⡉⠙⢦⣀
⠀⡿⣹⣿⢁⡎⠀⠀⣶⣀⣀⢹⡀⠹⣷⢹⠓⢦⡄⠀⢰⠉⠀⢀⣞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣸⣀⠀⠀⢱
⠀⡇⢹⠇⡜⠙⠉⠉⠀⠁⠉⠉⠱⡀⢹⡈⡇⡴⠁⢠⠊⠀⡤⠊⢿⠁⢀⠔⠉⠓⠒⠒⠒⠚⠲⡄⠀⡟⠻⣦⠀⠈⢢
⠀⣇⢼⡴⠁⠚⠙⠀⠀⠀⠚⠙⠂⠳⣤⣷⡏⠀⠀⢹⠄⢠⠏⠀⢸⣤⡎⠀⣀⡀⠀⠀⢀⣀⠀⠸⣤⣇⡴⠛⣦⠀⢞
⣠⠊⠀⣇⡀⠘⢗⡒⠾⠖⠒⡾⠀⣤⡏⠸⡄⠀⠀⠸⡄⢸⠀⠀⢧⡀⠀⠀⣁⣁⠠⠄⢈⣈⠀⠀⠀⡸⠀⠀⣳⠀⡞
⢧⠀⡴⣏⠓⠒⠬⡓⠦⠖⡞⠚⠉⣁⢧⠀⡽⠀⠀⠀⠳⠞⠀⠀⠀⣿⡷⣄⣘⢯⣉⣉⣡⣯⠤⢿⣿⠃⠀⠀⠙⠚⠁
⠀⠹⡀⠈⡷⠀⠀⢻⠛⣻⠀⠀⠸⡅⢀⣟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⡄⠈⢱⡬⢥⠏⠀⢰⠊⢹
⢀⡴⢳⡀⡇⠀⠀⠘⡦⡇⠀⠀⠀⣇⡞⠈⢧⠀⠀⠀⠀⠀⠀⢀⡜⢇⢠⠇⠀⠀⣇⣸⠀⠀⠸⣆⡎⢣
⠛⠠⠤⠽⣇⠀⠀⣸⣁⣱⡀⠀⣠⣏⣀⣀⣨⠇⠀⠀⠀⠀⠀⠛⠲⠼⢿⡀⠀⢀⣇⣹⡀⠀⣠⣏⣠⡤⠗
⣤⣤⣤⣤⣬⣵⣾⣥⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣮⣤⣤⣭⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⡠⠄⠒⠀⠀⠈⠁⠀⠀⣠⣔⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠖⠉⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⠜⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡴⠃⣰⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣉⣀⢀⠀⠀⡀⡀⠐⠨⡢⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣼⠇⢰⠃
⠀⠀⠀⠀⠀⠀⢠⡲⢿⣿⣿⣿⣟⠳⢖⣒⡚⠵⡲⣦⣄⢱⡀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣠⣿⠏⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠿⢿⣶⡾⢿⡟⠛⠛⠂⠉⠫⣷⣿⣆⣠⢊⣠⣴⠶⠛⠉⠀⠀⠀⠀⠠⠤⢀⣠⠞⠁⢀⣼⣿⠏⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠒⢁⡴⠊⠙⠒⠦⢄⣒⠤⣄⣈⣿⣿⣿⣿⣭⣤⣤⣤⣀⣀⠀⠀⠠⠄⠠⢤⣀⣀⢠⣾⣿⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢀⡙⢿⣿⣿⡿⣿⣿⣯⣭⣭⡭⠭⠍⠉⠒⠂⠒⠈⠉⠹⣿⣿⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠋⠉⠙⠛⠛⠿⢶⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠤⠀⠀⢽⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣾⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠋⠉⠉⠉⠙⠻⠟⠋⠉⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠋⠉⠉⠉⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⡀
⠀⠀⠂⠈⠁⠀⠀⢀⠄⠂⠂⠀⠉⠁⠉⠀⠉⠁⠉⠁⠐⠐⠠⣈⠁⠂⠂⠠⠤⠤⠤⠄⠀⠂⠂⡩⠄⠒⠐⠂⠀⠉⠉⠉⠀⠀⠉⠉⠀⠂⠂⢄⠀⠀⠈⠁⠐
⠀⠀⡆⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠑⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠔⠀⠢⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⠀⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌
⠀⠀⠀⠀⠀⠡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠌⠀⠀⠀⠀⠀⠀⠀⢂⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡰⠁
⠀⠀⠀⠀⠀⠀⠑⠌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⡐⠀⠄⢀⣀⣀⣀⠀⠄⠀⢊⠡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⢑⠀⠠⠄⠀⣀⣀⠀⠠⠄⠐⡨⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠉⠛⠟⠿⢿⣿⣿⣓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠤⠄⠒⠂⠄⠀⡀⢲⣆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢹⠖⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿
⠀⠀⠀⠀⠀⢿⣷⣶⣿⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⢐⣋⣠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿
⠀⠀⠀⠀⠀⠈⠛⢿⡿⡻⡿⡿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣸⣿⣿⣿⡿⣷⣄⢀⣠⣤⣤⣶⣶⣾⣿⣿⣿⡿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣾⣾⣾⣿⣿⣿⡀⢀⣀⣤⣤⣶⣷⠋⠉⠉⠁⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠓⠛⠛⠋⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠀⠀⢀⠀⡀⡀⡠⢸⠠⡂⢠⠠⡀⡄⡂⠄⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢖⠂⣆⠗⠁⠇⠀⠣⠸⠀⠚⠘⠀⠃⠃⠁⠀⠀⡏⢀⠇⠄⠐⢰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠤⠄⠤⢄⠈⠁⠀⠈⢁⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠎⠉⠀⠁⠈⠀⢀⣀⠀⠈⠑⠒⠖⠢⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠔⠉⠁⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠠⡉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡀
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠐⠢⠭⢥⡝⠀⠀⠁⠀⣀⠖⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠄
⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠷⣮⡍⠁⠈⢣⠀⢀⣀⠆⠁⠀⠈⠙⠔⠆⠤⠤⠦⠀⠀⢀⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⠀⠀⢸⢸⢀⠆⠋⠁⠀⠀⠀⢹⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢇⠀⢁⠏⡼⠀⠀⠀⠀⠀⠠⡘⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠃⢣⠀⠀⠀⠀⠀⢠⠕
⠀⠀⠀⠀⠀⠀⠈⢢⣀⠜⠀⠀⠶⠀⠀⠀⡀⡄⢂⠀⠀⠀⠰⡇⠀⠀⠀⠠⠦⠀⠀⠣⣤⢠⡀⡰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡙⣦⣀⠀⠀⠀⠀⠀⢀⣠⠞⠓⢤⣀⠀⠐⠐⠀⠀⠀⠀⢀⡠⠔⠁⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⣿⠐⠒⢲⣙⠷⡀⠈⠑⠀⠓⠋⠁⠀⠒⠒⠂⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⡿⠃⠀⠸⠄⢠⣆⠀⠀⠀⣀⠀⣀⠐⠤⣦⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⣈⠀⠛⠂⢸⠀⠉⠉⠂⠴⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⢀⠄⠉⠁⠰⠦⢼⡀⢀⢀⠀⡀⡀⢄⡒⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠐⠃⠴⠻⠦⠐⠛⠒⠀⠀⢘⠁⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡃⠀⠐⠀⠀⢀⠀⡀⠐⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⡁⠀⢈⢩⡀⠀⠀⡀⣄⡄⠀⢈⡁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣷⣄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣠⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⡘⢷⣄⢤⣶⣶⣿⣟⣛⣿⣿⣿⣿⣟⣻⣿⣶⣶⡤⣠⣾⢃⣼⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢿⣿⣿⣿⣿⣾⣿⣧⣤⣭⣙⢿⣯⣛⣛⣛⣟⣻⡿⢋⣭⣤⣴⣿⣵⣿⣿⣿⣿⣿⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣍⣻⣿⣿⣷⣽⣿⣿⣿⣿⣫⣾⣿⣿⣟⣩⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⢿⣿⣟⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⢻⣿⡿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⣼⣿⣿⣆⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣰⣿⣿⣧⠀⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⣼⣿⡟⢉⢻⣶⣮⣍⠛⠿⣿⣿⣿⣿⡿⠛⣉⣵⣶⡟⣉⢻⣿⣿⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⣿⣿⡇⠀⠈⢿⣇⠹⣿⣿⣿⡿⢹⣦⡘⣿⣿⢋⣴⡏⢿⣿⣿⣿⡏⣸⣿⠋⠀⢸⣿⣿⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀⠈⠻⣷⣬⣉⣩⣴⣿⣿⣿⡿⢿⣿⣿⣿⣦⣍⣉⣥⣾⡟⠁⠀⠀⢰⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠉⠛⠿⠿⠏⠈⠀⢹⣯⢹⡟⠀⠀⠹⠿⠿⠋⠉⠀⠀⠀⢀⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠘⢷⣿⣿⣿⠃⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⠿⣤⣀⠻⠟⣁⣠⠾⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣿⣿⣿⣿⣿⣼⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣹⣧⣽⣿⣿⣿⣿⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣿⣿⠿⣿⣿⣿⣿⣿⣿⣴⣿⣟⠛⠛⠛⠛⣹⣿⣷⣿⣼⣿⣿⣿⣿⠻⢿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣡⣶⣿⣿⡟⢸⣿⡟⠉⣿⣿⡀⢰⡆⢀⣿⣿⠋⢻⣿⡏⢻⣿⣿⣶⣄⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⣿⡇⣿⣵⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣦⣿⣼⣿⠉⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢻⣿⢏⡀⢻⣿⠟⣠⣿⣿⣿⣿⣆⠻⣿⡟⢀⡙⣿⡿⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠣⠸⣟⠘⡏⢿⣿⣿⡿⢹⠗⣿⠇⠸⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢻⡿⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠿⠶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣥⣴⣶⣶⣶⣶⣦⣤⣉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠏⠙⠛⠛⠛⠛⠛⠟⠻⠿⣿⠂⠀⠀⠀⠀⠀⣿⣿⠉⠁⠀⠀⠀⠈⠉⠁⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⢇
⠀⠀⠀⠀⠀⠀⠀⢀⠿⢿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⡞⢙⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠊⣇⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣀⡄⠀⠀⠀⠀⠀⠠⢬⣤⡄⠀⠀⠀⠀⠀⠀⣴⡆⢰⡤⢧⣦
⠀⠀⠀⣀⣢⡷⠠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠛⠤⢀⡠⣦⡶⡀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⣴⣿⠧⠘⠀⠐⠛
⠀⠀⠀⠐⠋⠀⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠌⣁⠠⡉⠁⢴⣤⣤⣤⡀⠀⣠⣤⣶⣾⠟⠋⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠑⠀⡁⠂⢁⠂⠄⢀⠀⠀⠀⠀⢀⠀⠀⠠⡊⠄⢈⠀⠊⠀⠀⠀⠐⢀⡘⠙⠛⠣⠄⠻⠋⠁⢡⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠂⠀⢀⠤⣀⠨⣀⠄⠆⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠂⠀⠀⠀⠐⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⡀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠁⠀⠃⠀⠖⢂⠢
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⢀⠠⠐⠻⣀⠇
⠀⠀⠀⠀⠀⠀⡔⣀⣡⠉⠑⠐⠀⠀⠀⠀⠐⠒⠒⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⠮⡄⢨
⠀⠀⠀⠀⠀⠀⠃⠘⠁⠑⢀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⢣⡄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠂⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠙⣦⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣠⡾⢙⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢿⣿⠁⢠⡖⢉⠾⢩⠹⢦⠙⣦⠄⢨⣿⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢠⡈⡄⣡⠀⢸⡆⢠⡀⢄⣡⠊⠀⢼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣻⠦⣤⣽⣿⣴⣤⠀⡝⠇⢰⣴⣾⣿⣧⡤⢾⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢳⡄⢾⡈⠛⢋⣿⣶⣦⣷⣾⣏⠛⠛⣸⠇⢰⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠳⣶⣼⣿⣿⣿⢫⡿⣿⢻⣿⣿⣿⣤⡶⠋⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠘⢦⣐⢀⠉⣉⣯⠝⠉⡇⡝⠙⢯⣏⡉⢁⢀⣠⡾⢹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⣶⣬⠉⠉⠁⠒⡻⣷⣻⣓⡿⡓⠂⠈⠉⢩⣴⣾⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢸⣿⣿⣿⣷⣶⣋⠒⠐⢛⡓⠀⢊⣻⣖⣿⣻⣿⣿⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣸⣿⣿⣿⢗⣡⠘⡡⠚⣉⠙⠢⡙⠢⣑⢿⣾⣿⣿⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠘⢿⣏⣵⠾⠒⢩⠀⠼⠉⠙⠆⢨⠕⠚⢶⣜⣿⡏⢈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠞⡶⠁⠀⢀⠷⡤⠚⢀⠌⠢⣤⢇⠀⠀⠙⡞⢇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⣦⠬⠴⠣⢄⠀⢀⠤⠒⠬⢤⡄⢰⣧⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⢆⠠⠞⠀⠡⠉⠁⠂⠀⠢⠀⢲⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢻⣷⠿⣄⣉⡙⡄⠐⢉⣇⣸⢷⣿⡏⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⡌⠳⡟⢇⡚⡿⠊⣤⡾⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⣉⢰⣏⡲⢗⣿⠘⠠⣧⠿⢚⢿⠊⡹⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⠀⢡⣿⢗⡈⢹⡴⢦⠉⢐⢿⣧⡁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠺⠁

⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠱⡀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡄⠀⠆
⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠎⠀⠀⠀⠀⠀⠑⠢⣶⣧⠀⠀⠀⠀⠀⠀⣢⣿⡤⡇⠀⠀⠀⠀⠀⢀⣿⠗⠊
⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⢼⣿⡀
⠀⠀⠀⠀⠸⠃⠻⠀⠀⠀⠀⠀⠐⢢⣼⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠸⡜⡇
⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠎⠘⠄⠀⠀⠀⠀⠀⠰⠀⠡⠀⠀⠀⠀⠀⠀⠐⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⣠⣀⠔⠁⠀⠀⠘⡀⠀⠀⢀⠄
⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠳⢄⣶⣀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠈⠙⢿⣶⠄⠀⠀⠺⣿⠁⠀⠀⠀⠀⠀⠳⣿⡴⠊
⠀⠀⠀⠓⢲⣾⠆⠒⠈⠀⠀⠀⠀⢿⡏⠑⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣰⢿⡟⠀⠀⠀⠀⠀⠟⢻⠀⠀⠀⠀⠀⠀⠀⡟⢹⠀⠀⠀⠘⠃⣇⠀⠀⠀⠀⠀⢸⠋⣷
⠀⠀⠀⠀⠚⠟⠃⠀⠀⠀⠀⠀⠸⠈⠛⠐⠆⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢯⣉⠙⠛⠳⠦⣤⡀⠠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠳⣦⡀⠀⠀⠙⠳⣜⢦⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⡓⠶⢽⣦⡀⠀⠀⠈⠙⢧⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠥⠆⠀⠀⠈⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⠖⠋⠙⠲⢄⠀⠀⠀⠤⠄⠈⠙⠦⣄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠁⠀⠀⠀⠀⠈⢳⡤⠚⠑⠲⡀⠀⠀⠈⠑⢦⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⣄⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⣄⠀⠀⠀⢀⡀⡇⡀⠀⠀⣰⡃⠀⠀⠀⣠⠴⠒⠈⠁⢠⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢈⡒⠤⣤⡼⠟⠛⣿⠞⠉⠁⠀⠀⠀⣜⣀⡤⠤⣄⣸⢦⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡔⣄⠀⠠⢀⠂⠀⠀⡔⠊⠙⢢⠀⠀⢀⣈⣉⠙⢧⠀⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣆⠀⠀⣠⠖⢤⠤⠧⠦⠴⢃⡴⢄⡀⠉⠈⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠉⠑⠋⣠⠋⠀⠀⠀⣠⠏⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢊⠑⡄⠀⠀⠀⠀⠀⢹⣀⣀⠀⣧⡀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠙⠁⣄⠈⠀⠘⠲⣄⠀⠀⠀⠀⠀⠈⡆⢣⠘⣆⠀⡼⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⣤⢤⡤⣄⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢸⠘⡴⡍⠋⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣃⣸⡀⣘⡂⠉⣉⠑⠢⢄⣀⠀⢀⣘⣯⠇⢱⢄⡴⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢬⣉⣁⠠⣴⣸⡈⠿⢆⠀⡐⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡷⠐⠚⠷⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢸⠙⠉⠉⠉⠉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣸⠗⠀⠀⠀⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢺⣤⣤⣧⣀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠰⢭⡃⡴⠧⠭⡿⣉⣉⡩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠥⠭⠭⠥⠤⠕⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠗⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣠⣀⣀
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠉⠁
⠀⠀⠀⠿⡇⢠⣶⠄⠚⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣤⣀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣶⠁⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠉⠀⢀⡾⠁⠀⠀⠀⠀⡀
⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠐⠁⠀⢠⣤⣶⠂⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⠀⠐⠊⠀⡀⠀⠀⠈⡡⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠀⠙⣿⡿⠀⠀⠀⠀⠈⠀⠀⣰⣦⣠⣤⡴⠞⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣇⡀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣽⣿⣷⡀⠘⠿⠀⠀⡀⡤⢠⣶⣿⣿⡿⠛⠉⠁⠀⣤⡀⠀⠀⠙⠛⠛⠛⠋⠉⠉⠉⠛⠛⠿⠿⣶⣤⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⣿⠿⣿⣿⣦⣤⣶⡿⠋⠈⠁⣸⣿⡏⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠈⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⣿⣦⣾⣿⣿⣿⣿⠁⣶⠖⣸⡿⠿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁⠱⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣿⣿⣀⣼⠟⠉⠀⠀⠀⠀⠀⢀⣴⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠
⠀⠀⠀⠂⠀⠀⣀⡀⠀⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷
⠀⠀⠀⠀⠀⣰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣠⠀⢂⢘⡀
⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⣿⣿⣿⣿⣿⣧⠀⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠀⣀⣀⣸⠉⠢⡄⢸⢆
⠀⠀⠀⠀⣸⡿⠟⠛⠳⣤⣤⠀⠀⠀⡀⠀⠘⠿⠟⠀⠹⣿⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡀⢰⡌⠁⢱⠀⢀⠀⠘⠂
⠀⠀⠀⠀⣿⣤⣴⣶⢤⣀⠉⢠⣄⡀⠐⠆⠰⣦⡤⠠⡀⠿⢿⣿⠃⠀⠀⠀⠈⠙⠻⠿⠏⠀⠀⠀⠿⠀⡠⠌⠀⢀⡀⠄⠺⠟⡛⠂
⠀⠀⠀⣀⣿⣿⣿⣿⠈⣿⣿⣶⡄⠀⠋⠉⠐⠺⠁⠀⠉⠘⣮⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡌⠑⠀⠀⣰⣾⠟
⠀⠀⠀⠀⠀⣸⣿⣿⣀⠿⣿⣿⣷⡀⠀⠀⠀⠀⢀⠈⠁⠀⠘⠁⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣌⣡⠀⠉⣁⡀⠀⡀
⠸⠂⠀⠀⣀⣿⣿⣿⣌⣰⣿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉
⠀⠀⠀⠀⠙⠁⢀⣽⣿⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀⣶⣦⣀⣀⠀⠀⢀
⠀⠀⠀⠸⠈⣿⣿⣿⣿⠃⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠐⠠⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠈
⠀⠀⠀⠀⠰⡿⣿⡿⠁⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠠⠖⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⢴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡹⡇⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣼⠋
⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⣀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⢀⠀⠀⠀⠀⠀⠐⣄⠛⠛⢻⣿⠏⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠰⣦⡄⠀⠀⠀⠀⠈⠛⣻⣿⠏⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾
⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿
⠀⠀⠀⠈⣤⢣⣄⠀⠀⠀⠀⡐⠢⡖⠀⠀⠀⣠⣄⡄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⢐⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠸⠈⠁⠀⠀⠀⠀⠉⠙⣇⠀⠀⢀⣾⠿⠋⠁⠀⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠩⡵⠒
⠀⠀⠀⠀⠀⣾⣿⠈⠻⣦⣄⠂⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠛⠁⠀⠀⠀⣸⠿⠀⠀⠀⠀⠈⠉⠉⠛⠉⠛⠋⠉⠻⠈⠀⠀⠐⠈⠀⠀⠘
⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢈⣶⣶⡄⠀⠀⠀⠀⠂⢸⣿⣇⠀⠀⠀⣿⣶⣦⣤⣤⣀⣀⣀⠀⠀⠀⣀⣀⣤⡄⠠
⢴⣶⠀⠀⢸⣿⣷⣶⣤⠀⠀⠀⢸⣿⣿⠇⡀⠀⠄⠀⠀⠈⠉⠁⠀⠀⠀⠹⠃⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⢸⠇
⠀⠉⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡂⠀⠠⠂⠂⠀⠀⢀⠆⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡈⠀⡈⢉⣂⡃⠉⠉⠁⢀⡘⠚⢙⠋⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠤⠁⠘⠿⠛⠛⠛⠀⠀⠀⠘⠛⠻⠷⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⡀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠔⠂⠀⠁⠀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠁⢢⡄⠀⠘⣒⠌⡀⠀⡠⠔⠁⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣖⢃⠉⠀⠥⠀⠐⠈
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⡐⠁⠀⠀⠹⣆⢡⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠈⢁⠦⠀⠀⠒⠚⠂⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⡚⠛⠒⠒⠒⠶⠶⣤⣤⡄
⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡪⠗⠀⠀⠀⠀⡈⠁⠀⣀⡘⠿⠉⠉⠉⡉⠉⢙⡖⢲⣛⡭⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠒⠄⣀⠀⠀⠀⠰⠛⢬⡂⠈⠀⡊⠄⠀⢰⠊⠁⡑⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⠀⠃⠀⢪⣠⣤⣤⣊⡁⠴⢉⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠢⠤⢆⣀⡄⠀⠀⠀⠀⠀⠂⣂⣠⠄⠀⠀⠨⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠉⠉⠙⠒⠒⠚⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⣀⠤⠔⠂⢈⣁⠨⣧⣀⢠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⢔⡠⠖⠉⠑⠠⢀
⢀⢴⡚⠉⣁⡤⣔⣲⠭⠕⠒⢉⣀⡄⠀⠀⠀⠀⢀⠄⢀⣀⣀⠤⠤⠒⠊⠁⠀⠑⢅⠀⠀⠀⠀⠀⠉⠒⢄⡀
⡇⠃⢹⡩⠾⣍⢁⡠⠴⠒⠋⠉⢚⢤⠀⠀⡀⠐⠁⡞⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀
⡇⠀⣼⠃⠀⢸⠀⠀⠀⢀⠔⣋⣑⣤⣤⠎⠀⠀⠀⠳⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢈⡵⠂
⡇⠀⣿⡄⠀⣾⠀⠀⢐⣤⠚⣀⢨⣯⣕⠐⠢⠁⠀⠱⡘⢆⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢀⣠⠴⠊⡡⢧⡄
⣇⣆⡇⡇⠀⡇⠀⢶⡉⠙⠈⠀⠀⠉⠉⠙⠲⢄⡢⢹⡀⢈⣳⡀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣶⠉⣀⢔⡪⠚⠉⠓⢦⣀
⠀⠈⠷⣇⣀⣧⠶⣟⢍⡓⠦⣄⡀⠀⠀⠀⠀⢀⡹⢦⠿⣉⠀⠘⢄⠀⠳⣄⣀⣠⠤⠴⠖⠒⢋⣉⢿⣔⡪⠖⠉⠀⠀⠀⣠⢴⡟
⠀⠀⠀⠁⠸⣿⣗⠦⣕⡪⡂⢄⠉⠒⢄⡠⠖⠉⣠⣜⣄⡈⠓⢤⡈⠳⣠⣏⡂⢀⠤⢄⣒⠭⠕⠚⠉⢈⣱⠆⣀⡤⠖⠋⣁⠜⣳
⠀⠀⠀⠀⠀⠈⠪⢑⢄⡉⠛⢷⣬⣀⢠⣧⠴⣫⡞⠣⣀⠉⠢⣀⠉⠲⣌⠓⠒⠒⠉⠁⠀⠀⣀⡤⠞⣉⢿⣞⠉⢀⠴⣊⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⣐⠀⢈⣯⣀⠴⠊⠀⠣⣀⠈⠳⢄⡈⠑⢤⡀⠙⠢⣄⢀⡠⠖⠋⢁⠤⣪⢕⣩⡽⢚⡵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋⠁⠀⠀⠀⠀⠈⠑⢤⡀⠙⠲⣄⡈⠳⣄⣠⣏⠂⠀⣊⣵⡯⠖⢋⡨⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠙⠢⣄⠉⢓⣲⠿⠋⠁⣠⢔⡩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⣹⠫⠒⣀⠔⣪⠔⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣻⣆⣤⣖⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣉⣀⡐⠀⠐⠒⠮⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢟⣛⣩⣭⣭⣛⣓⡀⠀⠀⠀⢮⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣋⠵⣾⢿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢿⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡼⠁⠈⠀⠀⠀⠀⠐⠒⠲⠄⠀⠀⠀⠀⠀⠀⠸⣷⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⠁⠀⠀⢀⠤⡀⠀⠔⡡⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡤⣄⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣧⠃⠀⠈⢀⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠁⠀⢰⠚⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⡇⠀⠀⠀⠀⣄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢸⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢙⠂⠤⠞⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣏⠀⠀⠀⠀⠀⠈⣏⠉⠁⠀⣠⠔⣻⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢠⢂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⢇⡉⣉⡠⣺⠏⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⡠⠚⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠉⠒⠚⠁⠀⠀⠀⠀⣠⠞⠁⠀⣀⠴⣌⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠀⠀⣀⣠⡴⢾⠁⠒⠒⠉⣁⡠⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠝⠋⢋⡀⢀⡞⢰⠒⠊⠉⠁
⠀⠀⠀⠀⠀⡠⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠒⠒⠒⠉⣀⣤⡆⠀⠉⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡴⠂⠤⠤⠤⠤⠖⠚⠦⠔⠒⠋⠁⡼⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠃⠈⠙⠲⠤⣀⡉⠑⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠒⠒⠲⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠤⣄⢀⣀⣠⠋⠑⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⡭⢷⡄⠀⢀⣀⣀⣀⣈⠑⠲⠦⢤⣤⣀⣀⡀⠀⣀⡁⠀⠀⠀⠀⠀⢸⠀⡟⠈⠀⠀⠈⠉⠉⠉
⠀⠀⠒⠄⠀⠀⠀⠀⠀⡰⢮⡠⠚⠁⠀⠀⠛⠉⠉⠉⠁⠈⠉⠁⠢⢤⣀⡀⢀⠉⠉⠉⠉⠴⡦⠀⠀⠀⢠⠋⡰⠃
⠘⢌⠢⡀⠈⠑⠢⢄⡘⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡀⠀⠀⠀⣸⠣⠤⠔⣊⡭⠛⠁
⠀⠈⠱⣈⠢⡀⠀⠀⠈⢳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⠏⠙⠋⠉⠁
⠀⠀⠀⠈⠑⢌⠳⢄⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠿⠿⣿⣿⣿⣿⣷⡾⢋⣿⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣧⣤⡛⣼⣷⣟⣯⣿⣶⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⣿⣯⢳⣿⣾⣴⣿⣿⣿⣿⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣷⡟⣛⣻⣿⣿⣿⣷⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣽⡿⢿⣿⡷⢺⣿⣿⣿⣿⠟⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⢨⣌⣳⣾⣛⣁⣀⠈⠁⣝⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡶⣢⠀⠆⢠⡄⢩⣉⣤⠀⠦⢰⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⢃⢺⡇⢈⣅⠘⢉⠛⢼⣦⠛⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣭⢿⣿⡷⡸⠆⠁⠸⢿⢶⠞⠃⠘⠿⠁⣋⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣷⡾⢡⣜⠋⣘⠷⢦⡤⢈⡸⠇⣿⠀⣶⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣯⠥⠿⢋⢈⣼⣷⣾⠃⡸⠧⣴⣠⡐⣋⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⠛⡫⢿⡇⣩⡞⢛⡁⠉⠘⠃⣀⠙⢸⠟⠳⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⢛⢻⠟⡡⣦⣾⡏⠶⠸⢃⠞⠐⠇⠉⠀⡄⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⡟⡥⣠⣾⠿⠃⠐⠃⢠⠀⢠⡆⠀⢄⠀⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠬⢔⣾⡧⠀⠊⠀⠀⠀⠉⢰⠀⠘⠀⠀⠘⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣾⣿⡟⣹⠀⠀⠀⠀⠆⡀⠀⠀⠇⠀⡆⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠳⣿⡇⠀⠀⠀⣐⣷⣠⣀⣴⣾⡾⢻⣤⡰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣻⣿⣤⣀⢀⣼⣿⡉⠀⠀⠈⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⢿⣿⠟⠉⡹⢛⣉⠙⠷⠦⣼⠚⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠛⠉⠀⠀⠸⣷⠋⠀⠳⢴⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣿⣵⣶⣌⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣟⣻⣿⣿⣿⣿⣿⣷⡀⢙⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⣿⣽⣿⣿⡗⡸⡿⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡯⠉⠀⠀⠀⠀⠀⠉⠻⣿⣿⠇⢹⢳⣇
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⣤⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⣠⣤⣤⡀⠘⣿⣯⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣟⡂⠀⠀⠉⠙⠛⠷⠆⠀⢹⣿⣿⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣣⣄⠠
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣯⠳
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⢤⠀⠀⠀⢰⣴⣿⡿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠠⠹⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⡠⠐⢹⣿⣿⣿⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⢫⡑⠒⠒⠈⠁⠀⠀⢸⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢮⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠨⠂⠠⠀⠬⣔⡀⡀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠍⠳⣦⡄
⠀⠀⢔⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠉⠀⠀⠘⡆⠀⠀⠀⢾⣿⠿⣿⡀⠀⠀⠹⣿⡀
⠀⠀⠀⢄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢸⡟⣀⡘⣿⠠⠴⠂⠙⠣
⠀⠀⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠈⠀⠟⠋⠋⠀⠈
⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠘⠀⠀⠀⠰⠶⠄
⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⢀⣀⠀⠀⣀⣀⣀⠀⠀⢰⢴⠾⢿⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠁⢢⠄⠀⠀⠀⠈⡿⢉⣻⠁⠤⠀⠒⢒⣦⡤⠟⠀⠀⠀⠢⣄⣀⢀⡀⣀⣀⣂⣀⢀⣀⡀⠄⠀⠀⠂⠈⢳⡄
⠀⠀⠀⠀⠀⠀⡶⠲⠤⠜⣉⡐⠶⢶⣯⣤⢴⣶⣶⠖⠉⢉⠠⠀⠀⠀⠀⣀⠎⠈⠋⠉⠩⠥⠄⠀⣙⣟⠁⠒⢂⣠⠤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠉⠉⠑⠚⠳⡞⠉⠤⡧⢂⣠⠴⠓⠀⠀⠀⠙⠛⠓⠒⠒⠒⠒⠒⠚⠁⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⢄⣀⡀⠀⠀⠀⡏⣀⡤⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠁⠀⠀⠀⠀⠀⠀⠀⣴⠶⡂⠀⠐⠌⠉⠁⠈⠉⠏⠓⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⡾⠷⠒⠚⠛⠿⠿⡶⠦⣄⣈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⢣⣤⣤⣤⣤⣤⣴⣧⣄⣀⠈⠙⠲⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠭⠁⠀⠰⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣶⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⠀⠠⠶⠖⠶⠶⠶⠶⠶⢿⡿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⡀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣧⡴⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠛⠛⠛⠛⠙⡿⣟⡛⠛⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⣶⣇⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⣄⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⢀⣠⠆⠀⡁⠀⢀⣤⡼⠔⡈⠀⠺⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⣦⣤⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠊⡍⠁⡀⠀⡿⣚⢉⡀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠑⠠⢀⠀⠀⠀⠈⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢆⠀⠀⠀⡇⠀⢇⠀⠃⠀⠸⡇⠀⡁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠢⢄⣠⣶⣿⣷⡀⠐⡀⠀⠀⠀⠀⠀⠀⢀⣴⠗⠀⠀⡇⠀⢻⠀⠁⠒⠒⠁⠀⡷⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⢸⠇⣹⠿⠋⢁⠰⢅⢀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⢀⠀⢸⠀⠀⠄⠤⣆⠀⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠠⠈⠱⣄⣴⠾⠋⠀⠀⠀⠀⠀⣦⣼⠀⢸⠀⣍⠀⠀⣿⠁⡄⠀⣠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉⠉⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⠿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣤⣤⣤⣄⡈⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣤⣤⣤⣤⣀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠀⢸⣧⠀⠀⣿⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⣠⡼⠏⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡾⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠊




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⢸⣿⣿⡿⠋⠉⠁⠀⠀⠀⠈⠉⠉⠛⢿⣿⣶⣶⣶⣶⣿⡿⠛⠉⠉⠁⠀⠀⠀⠈⠉⠙⢿⣿⣿⡇
⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⣤⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢸⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⢧⠂⠌⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠓⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡇⠀⠄⠀⠀⢄⢻⢄⡹⠬⠇⠿⠂⠀⠀⢈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢷⡄⠀⠀⠀⢠⣌⠃⢇⠚⢾⠀⠀⢀⠚⠉⠹⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⣶⣄⡀⠀⠀⠎⢉⠗⢁⣴⡶⠿⡀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡿⢿⣯⣽⣷⣄⣾⣷⣠⡿⠻⣿⡏⣻⠀⠀⢸⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⢀⣳⡈⡛⠁⢾⣯⡟⢛⡹⢛⡿⡦⣤⠍⠀⠀⢸⡇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⣇⣀⡀⡉⠉⠁⠀⢀⣬⣧⢸⣧⣤⣁⠀⡀⠀⠀⢠⣾⠃⠰⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢠⡯⠙⠽⠋⢻⠴⣾⣿⠿⢻⣾⡿⢿⠟⡛⡃⢠⠐⠚⠁⠠⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣃⣔⡾⠓⠫⣾⢍⣴⠃⢸⠋⠑⣨⢀⠀⠉⢠⣾⣿⠆⣤⡈⠃⠈⡳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣽⡶⠄⢠⣀⠀⢰⡆⠈⣠⠀⠀⣼⡧⠀⠀⡿⣉⣢⡜⠃⠳⡄⠀⠴⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢠⣿⣯⢺⣿⠊⠀⣼⡇⡀⢻⠀⠛⢈⠿⠠⠀⠙⢿⠂⢫⡄⢲⣄⡀⠠⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⡼⢈⡏⣸⠷⠀⠀⣟⣅⢣⠀⠀⠸⣧⠀⢶⡀⠀⠀⠐⠘⠃⠀⠀⢠⡀⢰⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢧⡝⢧⠀⢼⡇⢸⣯⡄⠀⡄⡀⠹⠏⠉⢷⣤⠀⠀⠈⢀⠰⡄⢪⡇⠮⠉⠁⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⣽⡗⢸⣷⡀⠀⠈⢿⠀⠰⣭⠛⠀⣤⡛⢤⠟⠃⣠⠀⢠⠆⠐⠉⠂⠘⠆⣠⡵⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⠹⢩⠄⠛⠃⠀⠀⠀⡞⢂⣠⠸⡀⠈⣷⡔⠀⠀⠈⣷⡄⣦⠲⣜⡛⣷⢰⡌⠧⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣦⡀⢠⡀⠐⣤⠀⣆⠀⢈⣋⠠⢷⠀⠘⠟⢃⡼⠟⠻⠇⠀⡀⠘⢷⢐⡦⢀⠠⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠔⣧⠀⣿⠰⠟⠀⠸⡷⠀⢸⣧⡀⢸⢸⣧⠀⢤⠠⡄⢰⣤⣼⡍⣝⠈⢁⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠰⠟⢈⣿⡇⠀⠀⣀⠀⠀⠸⠋⡃⠀⡙⠟⠗⢆⠀⢳⣄⠈⣷⣿⡙⢓⠇⠷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢁⠸⣄⠀⢹⡄⢸⣆⠀⡀⢈⣷⣀⢠⢹⡆⠘⠿⠀⢹⣿⠿⠳⡾⣦⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠳⡛⣧⠈⢿⠀⠛⣨⢧⡌⠠⠽⠇⠈⠛⠀⠀⢀⠈⣍⣦⡿⡋⢈⢋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⣄⠀⡄⠀⠀⠠⠓⡂⢿⡰⣠⡀⢶⡐⠂⠀⢺⠄⣿⣉⣼⡿⢋⣸⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⢂⣤⣄⣠⠶⠚⠛⠛⣮⣻⡑⠶⡛⢷⡄⠈⣰⣿⣎⢿⣶⣾⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢉⣤⠠⢿⠟⢁⣤⠎⠀⣄⣀⠘⠏⠀⠘⠚⣶⣄⣀⡜⠁⠻⢊⣿⠙⠿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⣽⢿⡄⠊⠀⠀⡾⣽⠋⣤⣀⠏⠀⠈⢿⠦⣦⠀⠀⢿⣏⣹⢸⠈⠂⣸⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠸⠏⠁⠘⠆⠀⠀⠀⠀⠁⠀⠀⠏⠉⠀⠀⠀⠀⠘⢁⡀⠀⠈⠻⣿⣜⣸⠀⣿⣃⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣠⣤⡴⣤⢄⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣄⠀⢻⣿⣿⢾⣿⡿⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣧⣥⡶⠞⠉⠉⠉⠀⠀⠀⠀⠉⠙⠓⠦⣠⠀⠀⠀⢶⡿⣻⠄⠈⠻⣿⡿⡿⢿⠶⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⣿⣿⠋⠀⠀⠀⠈⠉⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⡟


⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣿⡏


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠒⠚⠀⠈⠋⠙⠨⢝⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣪⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠰⠫⢶⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠤⠶⣒⢖⠒⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢈⡤⠶⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢠⠊⣍⢳⠀⢎⠀⠀⡎⠀⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⢤⠀⠀⠀⢰⡌⠈⠈⠁⠘⠀⠀⠈⠂⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⡱⠶⠦⢤⣔⠁⠙⠓⢲⡼⠀⠀⠀⠀⠀⠀⢀⣠⠖⠐⠁⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠉⠀⠀⠀⠀⠀⠙⢦⡰⠁⠈⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⣼⣧⠎⣀
⠀⠀⠀⠀⢀⡀⢠⠔⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠉⢦⢄⡀⠀⠀⠀⡀⠀⠊⠀⣀⣹⢁⠞⠠⢀⡈⠉⠐⠂⠀⠠⠤⢀⡀
⠀⡤⠖⠋⠤⢤⠊⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠉⠚⠣⠤⠤⠤⢼⡀⢧⠞⡂⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠄⣀
⠀⠇⠀⠀⠀⣇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣐⡣⠀⠀⡀⠄⠀⠐⠈⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠓⠆
⠀⠘⠂⠉⠉⡏⠳⢦⣀⠤⠀⠀⠀⠀⠀⠀⠀⢻⠀⠭⠐⠠⣤⣤⣄⣀⣀⣀⡀⠷⡀⠐⡡⠀⠁⠀⢀⣀⡠⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠸⡇⠀⠀⠈⠙⠓⠦⢤⣀⣀⣀⣀⣸⣀⡀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠰⠦⡤⠴⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⡶⠖⠋
⠀⠀⠀⡐⢊⡳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠒⡤⣤⣀⣀⣀⣀⠀⠀⠀⠇⠀⠀⠀⣀⡀⠤⠤⠒⠒⠈⠉⠀⠀⠀⢠⠃
⠀⠀⠀⡇⠀⠈⠑⠩⢉⠓⢤⣄⣀⡀⠀⠀⠀⠀⣀⣠⣄⠀⡇⠀⠀⠀⠀⠈⢩⡓⢺⡃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢑⠒⠤⣄⡀⠀⠉⠲⠚⠋⠉⠛⠛⠛⠉⠉⡏⠃⢸⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢸⠀⠀⡏⠈⠉⢶⡰⢤⠄⢦⠴⠠⡆⠒⣶⠇⠀⡟⠒⠶⠤⠤⣀⣀⣸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢸⠀⠀⡇⠀⠀⣿⠄⢸⠀⢸⠘⠀⡇⠀⣇⣦⠴⠋⠉⠳⡄⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣸⠀⠀⡇⠀⠀⣿⠀⢸⠀⢸⢀⠀⡇⠀⡇⠀⠀⠀⢀⣠⡇⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⣿⠀⠀⡇⠀⠀⣷⠀⠘⠀⠸⠴⠀⡧⠀⡟⠛⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠙⠛⠛⠁⠀⢸⣿⠀⣀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠟⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⢀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠦⠤⢤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠠⢤⣄⣀⣉⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡁⠀⠀⠀⠀⠀⠀⠈⠛⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⢀⡤⠶⠀⠀⠰⣒⡒⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣀⡀⠘⠉⣰⣀⡀⠉⠉⢀⣿⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢞⠝⣩⠧⡄⢈⣉⡀⢀⠔⢁⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠁⠋⠀⢀⣹⠀⠶⠀⡨⠛⠉⠁⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⢣⠀⠀⠀⢸⣯⣴⠶⠾⡇⠀⠀⢀⡞⠳⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⢀⠜⠳⢤⣀⡾⢿⡁⠀⣠⠷⡄⢀⡸⢷⡀⠀⠀⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⡶⠛⢷⣤⡀⣩⡃⢀⡿⢯⡀⢀⣽⣅⣠⠾⠓⠶⣄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣠⡾⠋⠀⠀⠀⠈⢻⠉⢷⡾⢧⣠⡷⠛⠰⡏⠀⠀⠀⠀⠈⢧⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡎⢠⡾⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠁⡼⢹⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠳⣄⠀⢱⡀
⠀⠀⠀⠀⠀⠀⡼⣴⠏⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠇⠈⣧⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠙⢿⣶⣧
⠀⠀⠀⠀⠀⡸⠹⡿⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⠀⠀⣿⡄⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠈⢷⠹⣇
⠀⠀⠀⠀⢠⡇⠀⠁⠀⠀⠀⠀⢀⡤⠞⢹⡆⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⣿⠙⢦⣀⠀⠀⠀⠀⠈⠇⢹
⠀⠒⠒⠒⠚⢧⡀⠀⠀⢀⣠⣖⣉⣀⣀⣬⣧⣤⣤⠴⠧⠤⠤⠾⠷⠤⠤⠤⠷⠤⠤⠽⢷⣤⡀⠀⠀⠀⣸⣧⣤
⠀⠀⠀⠀⠀⠀⠙⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠋⠛⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠙⣿⡇⠀⠀⣼⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣸⡿⠀⠀⣼⡟⠀⠀⡀⠀⠀⠀⢠⣾⠂⠀⠀⢀⣶⠆⠀⠁⢀⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠷⠶⣾⡿⠀⣠⡾⠛⣿⠂⢠⣿⡗⢩⣿⠀⣾⡧⠊⣿⠂⢻⣿⠃⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣿⠇⢰⡟⢁⣾⡇⢀⣾⣯⢤⣾⠏⣼⣿⢤⣼⠟⢀⣿⠃⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢿⣄⠈⠛⠁⠘⠛⣽⡏⠙⠋⠁⢰⡿⠙⠛⠉⠀⠀⠛⢋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠃⠀⠀⠀⣴⠞⣻⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⡀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣴⡆⢀⣴⡷⠀⠀⢰⣄⠀⠀⣶⠄⠀⠀⠀⠀⠀⠐⠛⠟⠁
⠀⠀⠀⠀⠀⢠⣶⠿⣿⡟⠉⠙⢦⠀⠁⢀⣤⠉⠉⠉⠛⠛⢻⣾⢿⣶⣿⣯⣤⣀⣠⣼⠟⠀⣼⡟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠹⠅⣰⣿⣀⣀⣤⠏⢀⣠⣌⠉⢰⣛⡆⠀⠀⣼⠏⢠⡿⢁⣭⣭⡍⢉⣡⣤⣴⡟⠀⠀⢠⣴⠶⣤⠀⢀⣴⠆⢠⣶
⠀⠀⠀⠀⠀⠀⣰⡿⠉⠉⠉⢹⡄⢹⡿⠁⢀⣼⢛⡿⠀⣸⡏⠀⣾⡷⢋⣿⠋⣴⠟⠉⢠⡟⠀⠀⣴⡿⢁⣼⠇⢀⣾⠏⣠⣿⠃
⠀⠀⠀⠀⠀⢠⣿⡃⢀⣀⣤⠟⠁⣿⣧⠶⠋⢰⣿⣥⢾⣿⠀⢸⡟⠁⢼⣇⡤⢿⣤⡶⠻⣧⣴⠞⢿⡥⠊⣿⡤⢺⣿⠔⣿⠏
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠐⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣤⣤⣾⣯⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣬⣿⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣶⡾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⡆⡄
⠀⠀⠀⠀⠀⠀⠀⡀⣤⣻⢸⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⡇⣟⣤⢀
⠀⠀⠀⠀⠀⢀⣴⠇⡇⡟⣸⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣇⢻⢸⠸⣧⡀
⠀⠀⠀⢠⣤⣾⣿⠀⡇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⠀⣿⣷⣤⡄
⠀⠀⠀⢸⣿⡿⢿⠀⡇⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⢸⠀⡿⢿⣿⡇
⠀⠀⠀⣿⡇⢧⢸⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⡇⡾⢹⣿
⠀⠀⠀⣿⡇⢸⠘⢸⢡⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡌⡇⠃⡇⠸⣿
⠀⠀⢠⣿⠀⠀⡇⢸⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⡇⢸⠀⠀⣿⡄
⠀⠀⢸⣿⠀⠀⡇⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢸⠀⠀⣿⡇
⠀⠀⢸⡏⠀⠀⠃⡌⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢡⠘⠀⠀⢹⡇
⠀⠀⣾⡇⠀⠀⠀⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⢸⣷
⠀⠀⣿⡇⠀⠀⠀⠃⠀⠌⣐⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⣂⠠⠀⠸⠀⠀⠀⢸⣿
⠀⠀⣿⠁⠀⠀⠀⠂⠠⠤⣀⣉⠓⠺⣵⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣮⠕⢚⣉⣀⠠⠤⠀⠀⠀⠀⠘⣿
⠀⢀⣿⠀⠀⠔⠀⠀⠒⠒⠀⠤⠭⠕⣲⣭⣛⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣭⣖⠫⠭⠤⡀⠐⠒⠀⠀⠢⠀⠀⣿
⠀⢸⣿⠀⠂⢀⡀⠤⠄⣀⣒⠢⠬⣍⡒⠮⢭⣛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣛⡭⠕⣒⣩⠥⠔⣒⣀⠤⠄⢀⡀⠐⠀⣿⡆
⠀⢸⣿⣍⣐⡒⠤⢭⣑⡒⠤⢍⣓⠒⠬⣙⡒⠬⣙⠢⢝⠻⣷⡀⠀⠀⢠⣾⠟⡩⠔⣋⠥⢒⣋⠥⠖⣚⡭⠴⢒⣊⡭⠤⢒⣒⣨⣿⡇
⠀⠈⠉⠛⠻⠿⢿⣶⣦⣭⣉⣒⠂⠍⠑⠂⠈⠁⠀⠉⠀⠁⠀⠙⢆⡴⠋⠀⠈⠀⠉⠀⠈⠉⠐⠊⠩⠐⣒⣉⣭⣴⣶⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣤⣤⣀⡀⠀⠀⠀⣀⣴⣾⣷⣦⣀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⡿⠿⠿⠟⠿⢿⣶⡶⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠄⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢧⠀⠀⠀⠄⡉⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⢀⡂⠀⢀⠀⠈⠀⢀⠔⠃⠄⠀⠀⠈⠀⠀⠀⢣⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡵⢋⠄⠈⠑⠀⠐⠠⠀⠐⠀⠀⠀⠠⡀⠀⠀⢀⡠⠠
⠀⠀⠀⠀⠀⠀⣗⠔⠁⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠂
⠀⠀⠀⠂⠀⠀⣳⠂⠀⠁⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠈⠀⠄⠘⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠠⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠔⠃⠀⠀⠀⠀⠀⠁⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠰⢤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⢇⡀
⠀⠀⠀⢰⣉⠔⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆⠘⣄⠀⠀⠀⠀⠀⠀⠁⢀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⣴⠀⠰⠀⠉⠀⠠⠀⠀⠀⠀⣀⣀⠀⠀⡀⠐⠈⠀⠀⠸⠀⠐⠂⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⣀⣀⠀⠀⡀
⠀⠀⣲⠿⡳⠲⠲⠟⠒⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠐⡖⠛⠒⠒⠲⠒⠖⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢄
⠀⠈⠉⠀⠁⠈⠈⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢐⡼⠁⠀⠀⠐⠉⠁⠀⠀⠀⠁⠀⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢤⢤⣀⣀⣤⣄⣠⡤⠴⠶⠶⠦⢤⣀⠈⡀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⣤⣀⣠⣤⣤⣠⡤⠶⠶⠶⠶⡤⣄⡀⢠
⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣬⣬⣽⣮⣥⣤⣤⣅⣀⣀⣁⣀⣘⣻⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣥⣤⣬⣭⣮⣥⣤⣤⣤⣄⣄⣅⣠⣈⣟⣧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠈⠀⠏⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠸⠂⠋⠀⠀⠀⠀⠀⠙⠉⠀⠉⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢨⠅⠀⠀⠀⠀⠸⠀⠎⠀⠀⠀⠠⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠹⠀⡌⠀⠀⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠰⢠⣤⣄⣀⣤⢤⠔⡄⢤⣀⣀⣤⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡤⠄⠀⢀⢀⡰⣀⣀⠀⠠⢤⣤⠠
⠀⠀⠀⠀⠀⠀⠀⢢⡐⠂⠀⠀⠉⢀⠃⠃⠈⠉⠀⠀⠒⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠒⠋⠉⠉⠙⠀⠇⠇⠘⠉⠉⠙⠛⢠⠆
⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠂⠒⠈⠀⠀⠀⠁⠒⠂⠒⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠀⠐⠒⠒⠀⠀⠀⠈⠀⠐⠒⠒⠐⠈⠀⠀⠀⢄⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠚⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠊⣉⠥⢤⣤⣈⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⡴⠃⣠⠤⣤⠤⢄⡀⠈⢳⡀
⠀⠀⠀⠀⠀⣰⠃⣠⢎⠀⠀⠀⠳⡀⠙⠢⡀⠱⡄⠀⣀⣀⣀⡼⢡⢎⠀⠀⠈⢧⠀⠈⢢⠀⢳
⠀⠀⠀⠀⢀⡇⢠⠇⠈⢧⠀⠀⠀⠑⡄⠀⠘⣆⠙⠉⣉⣀⣀⢀⠃⠈⢆⠀⠀⠀⠳⡀⠀⡇⢸⡇
⠀⠀⠀⢀⡼⡇⢸⠀⠀⠀⢣⠀⠀⠀⠘⢆⠀⢸⢰⠋⠁⠀⣸⢹⠀⠀⠈⢣⠀⠀⠀⠱⡄⡇⢸⢳⡄
⠀⠀⠀⠘⠧⢷⡀⢣⠀⠀⠀⢣⠀⠀⠀⠈⢧⠎⣼⠀⠀⠀⢻⠈⢧⠀⠀⠀⢳⡀⠀⠀⡹⠁⡼⠚⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠑⢤⣀⣀⢳⣀⣀⡤⢋⡴⠃⠀⠀⠀⠈⢧⡈⠓⠤⣄⣠⠵⠖⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠭⢭⠭⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠤⠴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠢⡀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⠒⠉⠀⢳⡀⠀⠀⢀⡸⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠤⠄⠀⠒⠂⠒⠂⠀⠀⠒⢤⠄⠀⠀⠀⠀⣧⣀⠀⠐⣜⢡⠔⡡⠚⠁⠈⣆⠀⢀⣀⡀
⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠀⡼⢷⠢⢆⡙⠉⠁⢸⠀⠀⢙⡏⠉⡀⠀⠀⠀⢸⡔⠁⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⢦⣼⡮⠤⠥⢄⣤⣸⡀⠀⠈⠀⠀⡇⠀⠀⢠⢸⠁⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⡟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⠘⠛⠢⠤⣤⡂⠀⠀⠈⠉⠑⠒⠴⠏⠉⠉⡟⣼⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡇⡇⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠉⠉⠒⠤⣄⣀⡀⠀⠀⠀⣰⠃⡿⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠉⠉⠀⡀⣀⣉⣙⣲⣾⠁⠀⣧⠒⠂⢄⡀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⣇⣀⣀⣀⣀⣹⣷⣄⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣶⡶⠿⠿⠿⠿⠿⠻⢏⡉⠉⠁⠀⠀⡗⠀⠀⠀⠈⡆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢵⠋⠉⠉⠉⠁⠀⠈⠙⠷⢾⢿⠟⠛⠛⣋⣉⣉⣁⡤⠤⢤⣶⡶⠖⠂⡇⠀⠀⠉⠦⠖⢛⡿⠃⠀⠑⠢⠴⡣⠛
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠉⣏⠻⡍⠀⠀⠀⠀⢀⠟⠉⠀⠀⠀⡇⠆⠀⠀⣠⣴⣋⣀⣤⣤⠤⢤⡜⢁⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⡗⠀⠈⠢⣄⠀⠎⠁⠀⠀⠀⠀⢰⣷⠆⠒⠛⠛⢿⡿⠛⠛⠛⠛⠓⠂⡅
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⠈⠳⠆⠀⠀⠀⠀⠐⢿⣿⡦⠀⠀⢠⡿⣧⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⠀⠀⠈⢦⡀⣀⣀⠤⣼⡏⠙⢄⢠⡳⠁⠛⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄⣈⣁⣀⣤⣤⡶⠤⠶⠚⠻⣛⠋⠉⣿⠇⠀⢸⡳⠣⡤⢠⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢦⠀⣿⠀⣠⠳⣇⢀⡵⣠⡛⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢋⢣⣿⠛⣅⡾⠃⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢢⣞⣁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠠⣉⡐⢬⣳⣄⠀⠀⣴⣫⣴⣾⡟⠍⠉⢉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠉⠛⠿⣷⣌⢻⣆⣼⣿⣟⠫⠭⠭⠻⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠄⠘⠁⠀⠀⠀⠀⠀⠉⠛⢿⠿⠿⡋⠄⠀⠀⠀⠄⠈⠉⠛⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡤⠤⠄⠀⠒⠂⠁⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠧⣀⡀⠴⠂⠒⠒⠒⠒⠒⠒⠒⠚⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠲⠒⢲⠖⢉⣰⣄
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠸⠒⢇⣠⡤⠵⠶⠒⠛⠉⠁
⠀⠀⠀⣼⣇⣀⣀⣀⠀⣀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⢈⣧⠀⠀⠈⢦⡀⠀⠀⠀⠀⣀⠔⠉⣀⡴⠗⠒⠋
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠾⠿⠡⠹⠛⠛⠶⠚⠛⠿⠿⠾⠿⠿⠿⠭⠀⠀⠀⠀⠱⡄⢤⣴⡾⠵⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠉⠀⠐⠂⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡔⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡂⢟⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡀⠳⠄⠀⠀⠀⠈⠁⠒⠀⢤⠄⢒⢍⣢⡷⠖⠛⡁⠐⡖⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠉⠙⠛⠒⠂⠠⠼⠶⠿⠋⣁⠄⠂⣁⣤⠖⣇⡀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⡜⠙⠆⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⣠⡽⣾⠚⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢃⡀⠀⠀⠀⠈⠉⠁⠂⠤⢈⡉⠀⠀⡀⠶⠂⠛⡋⡕⣈⡴⠄⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠠⠴⠒⠲⠤⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠈⠁⠒⠐⠠⠄⣀⠀⠀⠀⠀⠙⡁⠀⣀⣶⠷⠟⠋⠁⠀⠀⠀⠀⠀⠸⠥⠾⠤⠶⠶⠶⠶⠈⣉⣉⣑⡖⠀⠈⢢⣄⣀⣀⣠⣤⣀⣀⣈⣁⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠴⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢄⠀⠀⢀⠇
⠘⢻⣿⣾⠒⠒⠉⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⢠⣤⣤⣾⣷⣶⣦⡀⠀⠀⠀⠀⠀⡀⢠⡀⡀
⠀⣺⣿⣿⡇⠀⠀⠀⠀⠞⠛⠛⢿⣿⣧⡄⠀⣠⣼⣿⣿⣿⡿⠟⠛⢻⣷⣦⡄⠀⠠⣰⠿⠻⣿⣶⣦⣤⠀⢄⡀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠈⢿⣿⣿⠟⠃⠀⠀⠀⠀⣿⡟⠁⠀⠀⠁⠀⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⠀⠀⠘⠿⢿⠧⢀⠑⠀⠊⠘⠋⠀⠀⠀⠀⠀⣄⣀⠀⢀⣽⠿⢋⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢃⠀⠀⠀⠀⠀⢀⣠⣾⣿⣧⣤⣦⡄⠀⠀⣴⡄⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣀⣼⠀⠀⠀⠀⠐⣿⣿⣿⣿⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠻⠿⠀⠀⠀⠀⠀⠈⠛⠛⠿⠛⠛⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠲⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣴⣶⠖⠛⠻⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠈⠁⢳⡦⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣹⡗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⢀⣸⣿⠆⡀⣀⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠐⠳⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣏⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠤⠤⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠙⠻⠿⠟

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠔⠠⠠⠔⠉⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠢⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠄⠀⠀⠘⠀⠀⠀⠀⠀⠸⠀⠈⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡁⠔⠒⠀⠤⠤⠊⠉⠒⠉⠈⠂⠒⠈⠁⠢⢄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡖⠀⠀⠀⠀⠀⠀⠀⢐⠀⣐⠀⠀⠀⠀⠀⠀⠀⠑⠽⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⢦⡀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⢀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡅⠀⠑⣄⠀⠀⠀⠀⠈⠑⠠⢀⡀⠀⢀⣀⡄⢀⣀⡤⢊⣁⡀
⢰⢷⠂⠀⠀⠀⢤⡤⠠⠤⠤⠤⠤⢤⢤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⢚⢦⡀⠀⠀⠀⠀⠀⢸⠒⠀⠀⠒⠊⠉⠀⠹⠈⢂⠘⠆⢂
⢸⠾⠆⠀⠠⠤⠴⠷⠤⠤⠤⠤⠤⠴⢴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⢁⡱⣤⡀⠀⠀⠀⡀⠀⠀⠀⢀⠤⠄⣀⢰⠀⠘⠀⢠⠈
⢸⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢠⡯⡄⠀⠒⠒⠒⠒⠒⠒⡆⠛⠑⢄⠀⠀⢹⣷⡄⣌⣧⡢⢀⣀⠃⠀⢀⠔⠁⠀⠀⠀⢹⡄⠀⡇⠀⣶
⡼⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠸⠧⠧⠤⠤⠤⠤⠤⠤⠤⠧⠤⠴⠧⠤⠤⠼⣽⠿⠛⠃⠈⠢⣨⠀⠀⡘⠠⣀⠀⠀⠀⡌⡇⠀⠁⠀⣿
⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⡱⠒⠀⢀⠀⡀⠀⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣱⡂⠀⠂⠠⢀⣀⢀⠜⠀⠀⠀⠘⠀⡇⢀⠟
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠉⠀⠒⠀⠤⠄⠀⣀⣀⠀⠀⣠⠁⡈⢠
⠈⠂⠀⠐⠂⠀⠀⠀⠀⠖⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⡆⠀⠀⠀⠀⠆⠀⣈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠩⠓⠾⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠇⠠⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠐⣈⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠂⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢴⠀⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠛⠂⠀⠀⠀⠀⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢤⠀⠀⠀⠀⠀⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⣀⢀⠀⣀⡅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣄⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠲⣤⣤⠒⠚⠉⠉⠈⠉⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠈⠙⠓⠛⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠛⠦⠤⠤⠤⠤⠤⠮⠽⠯⠥⢤⠭⠽⠤⠤⠤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡴⠟⡋⠈⠉⠉⠈⠃⠒⠶⠤⢄⣀⠀⠀⠀⠀⠀⢀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠐⣿⡇⠀⢀⠴⠦⠀⠀⠀⠀⠤⣠⣭⠉⠙⢿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢷⣄⣰⢋⡙⠢⠀⠀⠰⢋⣭⢱⡀⡠⡿⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡖⠀⠳⣝⣣⠜⡏⠈⠛⢬⠭⠞⡁⠀⢰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠞⠃⠀⠘⠦⠖⠃⠀⠀⠒⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠠⢤⣄⣀⡤⠔⠂⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⠈⠉⠉⠁⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⠉⠉⠓⠒⠉⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⡇⠘⢦⡀⠀⠀⡠⠃⣸⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⠘⡄⠀⣹⢖⠚⡅⢰⠃⠀⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠦⠀⠀⠀⠀⠀⠘⣤⣯⡙⢻⣧⡎⠀⠀⠀⠠⠆⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢾⣏⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡐⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇⠐⢼⣈⡀⠀⠀⠀⢰⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⢦⠈⣿⡇⠀⠀⠀⠈⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡷⢄⠑⣼⡇⠀⠀⠀⠀⢹⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣇⠀⠑⣼⡇⠀⠀⠀⠀⠈⡄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣭⠑⢦⣸⠁⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠶⠶⠶⠶⠦⠾⠦⠶⢤⣤⣤⣷⣤⣤⣤⣤⣤⣿⣵⡶⠿⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠿⠶⠶⠖⠒⠒⠒⠒⠛⠺⠶⣤⡄
⠀⠀⠀⠀⠴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⢰⡶⢶⣦⠀⣀⡀⠀⢀⣀⣀⠀⢀⣀⣶⠀⢀⣀⠀⢀⣀⠀⠀⠀⣴⡶⣶⠄⢀⡀⣀⠀⠀⢀⣶⣶⣶⣶⢰⣶⣀⠀⢠⡶⠀⢀⡀⠀⣶⠆
⠀⠀⠀⠀⠀⠀⣾⣧⡾⠏⣾⠋⣿⠀⣿⠋⣿⢲⡟⢹⡟⢰⣿⣽⡇⢸⡟⠁⠀⢸⡿⢀⣿⠀⣿⠋⣿⠃⠀⠀⢁⣿⠁⠁⣸⡏⣹⠇⣸⡇⠸⣯⣙⠠⠟
⠀⠀⠀⠀⠀⠰⠿⠂⠀⠀⠿⠾⠋⠰⠿⠀⠿⠸⠷⠾⠇⠘⠷⠞⠀⠿⠇⠀⠀⠘⠷⠾⠋⠰⠿⠐⠿⠀⠀⠀⠼⠿⠀⠠⠿⠂⠿⠀⠿⠀⠷⠾⠟⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⠠⡀⠀⠀⠀⠱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠎⠀⠣⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠀⠀⢤⠆⠀⠀⠀⠀⢀⡄⣠⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠃⠀⠀⢠⠀⠰⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠦⡄⠀⣀⠀⠈⣀
⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠖⠙⠀⠀⠀⠐⢚⠂⠄⠀⠀⠠⠉⠂⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠐⡎⠈⠀⠀⠁
⠀⠀⠘⣾⠀⠁⢀⣤⡋⠀⠁⠀⠀⠀⠈⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⡂⠐⠆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⢁⡀⢀⠁⠀⣤⠶
⠘⠃⠚⠋⠀⠠⣄⣤⠄⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠁⠀⠀⠀⠀⢠⣥⣄⣦⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠈⠁⠀⣤
⠀⠐⠀⠀⠀⠀⠀⠐⡌⠀⠃⠀⠀⠀⠊⠁⠈⠙⢃⠀⠀⠂⠀⠀⠐⠃⢠⡏⠁⢠⠀⠠⠀⠀⠀⠐⠀⠉⠸⠉⠁⠀⠀⠠⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠐⠢⡄
⠀⠀⠀⣤⠤⠄⠄⢲⠀⠀⠀⠀⠀⠀⡔⠆⣠⠀⠀⢀⠖⠀⠀⠠⠀⠐⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⠉⡀⠀⠀⠀⠀⠁
⠀⢀⠀⣧⡀⠀⠐⠲⠤⠄⡀⠀⠀⢄⢠⠄⠃⠈⢲⠀⠀⠀⠀⠀⠠⠴⠄⠓⠊⠸⡁⠃⠀⠀⠀⠀⠁⠛⠔⠓⠂
⠄⠀⠰⠋⠉⡗⠠⡄⠀⠒⠀⠀⠀⠈⠁⠀⠈⠤⡎⠀⢫⡶⠀⠘⠀⠙⠃⠀⠀⠘⠃⡤⠁⠀⠀⣷⠀⡷⠀⠀⠀⢠⡤⢴⡆
⠈⠃⠀⠀⠠⡀⢀⡀⠀⠀⠀⠀⠀⢀⡀⢈⣀⣈⠇⠀⠀⠰⠄⠀⣀⠀⢄⣉⣱⡄⠀⠀⠀⠀⠀⠀⢰⣳⠀⠀⠀⣽⢷⠈⠙⣄
⠈⠀⠚⠀⡀⠉⠚⠐⠀⠇⠀⠀⠀⠸⠉⠀⠃⠒⠀⠀⠗⠀⠂⠀⠋⠒⠂⠀⠐⠂⠀⠀⠀⠀⠀⡴⢾⢹⠌⠭⠉⠏⠘⡀⠀⡋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣴⣦⣤⣤⣤⣤
⣿⣭⣏⣹⣍⣯⣥⣭⣹⣯⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣵⣿⣽⣿⣯⣭⣽⣭⣭⣭⣭⣭⣯⣭⣭⣭⣽