Vizsla Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠋⠈⠉⠝⠋⠀⠀⠁⠀⠈⠳⢶⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠞⠂⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⢻⣆⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣄⡀⠀⠀⢠⡟⣠⣶⣿⣦⣄⢀⡠⠀⢈⢻⡆⢿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣏⡻⠯⠀⠀⠀⠲⣷⣿⠋⢉⣭⠿⠻⢧⣤⣿⠀⡧⢸⡌⠉⠓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⠋⣤⣤⡀⠀⠀⠀⠈⠻⢗⠾⣏⠀⠀⠀⡾⠉⣷⢇⣿⠋⠀⠀⢸⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⣦⣴⣦⣤⣽⠀⠀⠀⢢⡀⠀⠀⠀⠁⠀⠚⠁⠀⣏⡾⡏⠀⠀⠀⠻⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⡿⠃⠀⠀⠀⠀⠙⣆⠀⠀⢤⡌⢳⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⡈⠙⣅⡀⠀⠀⠀⠀⠀⢉⣠⣭⣦⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢻⣶⣾⠟⣳⠶⠶⠶⣾⣽⡿⣿⢃⣿⣿⣿⣿⡀⠀⠀⠀⠀⣧⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⣝⠃⠰⠁⡌⣥⣾⣯⣵⠞⣣⣾⣿⠻⣿⠙⣇⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⡼⠿⣄⣀⣴⠿⠛⠋⣠⣤⣶⣿⣿⣿⠀⠘⠀⢿⣧⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣶⣶⣿⣿⠋⠀⠀⠙⣿⡄⠀⠀⠈⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠻⣿⡀⠀⠀⠀⢻⡇⠀⠀⠀⢠⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⢿⡄⠀⠈⢷⠀⠀⠀⣼⠁⠀⢀⡄⠛⠉⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠒⠒⠲⣤⡏⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠁⠀⢀⡾⠀⣴⠞⠛⠛⠛⠒⠦⡀
⠀⠀⣀⣀⣀⣀⣀⣸⣷⡀⣀⠀⣴⢀⣴⣿⣆⣀⣀⣀⣠⣿⣤⣀⣠⣤⣤⣀⣠⣾⣷⣼⣷⣆⢀⡆⠀⡄⢠⣿⣀⣀⣀⣀⣀⡀
⠀⠀⠛⠛⠛⠛⠛⠛⢿⣿⣿⣾⣿⡿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣾⣿⣿⡟⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠺⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠞⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢹⡐⣝⢤⡄⢠⢀⡇⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠇⠞⠐⠻⠛⠟⠗⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠛⢿⡟⠉⠁⠈⡐⢤⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⡆⠑⠺⣧⡙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡟⠀⣠⣼⡆⠀⠀⣆⢀⣼⣿⣏⣿⣿⣿⣿⡟⢻⠇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠓⣿⣿⣶⡿⠿⠟⠂⠴⠿⠿⢭⡈⠉⠾⢻⣿⣿⣿⠀⠷⠃
⠀⠀⠀⠀⠀⠀⢰⣻⣿⡇⠀⢸⣿⣧⠀⠀⠀⡀⡠⠖⠒⠶⣷⡄⠸⣾⣿⣿⡟⠴
⠀⠀⠀⠀⠀⠀⢸⠈⣛⠉⠀⠀⢻⣯⣷⡀⢰⠗⡦⠶⣐⣧⣿⣿⣴⣿⠃⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⢀⡏⣿⣿⣷⢮⠈⣿⡿⣿⣿⡯⣹⣿⡇⠀⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⡟⠈⢻⣾⡄⠻⣿⣿⣿⣷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠛⠀⠈⠿⣷⡾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⡀⠀⠀⠀⢪⠉⠉⠙⡿⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⢠⢿⡀⠀⠀⠘⠀⠀⠀⠈⠡⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡊⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠩⠁⠉⠉⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠣⢈⠄⠀⠀⠈⢂⠀⠀⠨⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⢠⠚⠧⠀⠒⠃⠂⠀⠀⠋⠀⠃⠀⠀⣼⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡆⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢠⣌⣠⡀⢀⣀⡀⠀⠀⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⡀⠘⡟⡍⡀⠘⣄⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡆⠀⣀⣀⣠⣤⣄⣀⣀⡶⠉⠃⠀⠀⠈⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠗⠋⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢠⠋⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠈⠳⡄⠀⢰⡀⠀⠀⠀⠀⠀⢨⠃⠘⠆⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠚⠛⢦⣀⡇⠀⠀⠀⠀⠀⠀⠀⠶⠀⣀⡤⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢰⠏⠑⢦⡀⢹⡄⠀⠀⠀⠀⠀⣤⠄⠀⣼⠉⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣸⠀⠀⢸⠉⡹⠁⠀⠀⠀⡠⠚⠁⢀⡸⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡰⠃⠀⣠⠞⠀⣧⠀⠀⢀⡞⠓⠒⠒⠉⠀⠀⠀⣡⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⡀⡀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠠⠤⠤⣤⠤⠤⢤⣀⣠⣤⣤⣄⢀⣤⠤⠄⠤⡤⠤⠤⣄
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⡀⠤⠶⡦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⡀⠀⠀⠀⠀⠀⢸⣿⡉⠛⠛⠋⠀⡗⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⡇⠀⠀⠈⠁⠒⠄⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⣿⡇⡠⠀⠀⢉⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⡜⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢻⣿⡄⢰⠃⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣽⡆⠀⠀⠀⠀⠸⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⣻⡇⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢀⡇⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠋⠀⠀⠈⠀⢀⠈⡁⠈⠁⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣼⣿⢻⣿
⠀⠀⠀⠀⠀⣾⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠠⡀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠁⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠉⡀⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠑⢦⣀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠠⠀⠀⠀⣠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⢺⣃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠠⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠼⠀⠫⠄⠠⠆⠶⣀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣷⣶⣶⡶⠶⠷⠖⠆⠀⡀⢀⠐⠄⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⡦⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⣴⠀⢰⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠎⢀⡀⠉⠀⠛⢀⡀⠰⡿⣧⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⡿⣠⡤⢿⣿⠄⠀⢧⣾⣿⢤⣘⢻⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⣿⣇⠀⠈⡛⣡⠀⢨⣿⠃⠀⢈⣯⣷⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢨⣽⡀⣻⣧⣿⣿⣟⣿⠃⠀⠀⢿⣷⢩⣿⣱⣿⣿⠈⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡨⡿⢷⡁⢻⡾⣻⡿⠃⠀⠀⠀⠀⠸⣿⢷⣿⢣⡟⣃⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢧⣼⣷⣼⣷⣿⠁⢰⣾⢟⠾⣲⠀⢻⡿⢡⣿⡇⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠻⣿⣿⣿⠇⠤⠀⢑⣾⣖⠉⠀⠈⢿⣿⡿⡱⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣽⡟⣿⠁⢠⣾⡿⣯⣿⣷⣆⣀⣽⢿⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣼⠀⣿⣿⣿⣟⣸⣿⣿⠇⣿⢠⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢿⡆⠻⡆⣿⣿⡟⠉⢹⣷⣟⣰⡇⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣾⣷⠀⣇⢠⣿⣇⠙⢿⣿⣻⠟⣰⣿⣍⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⢦⡵⢽⠋⣿⡝⣿⡃⠃⣿⠟⣣⣾⢹⢿⢹⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠔⢚⠀⠀⠀⠃⣠⢿⡇⢸⡿⣤⠻⠎⠙⠚⠻⠳⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣭⠴⣿⣢⣼⣿⣄⠁⠈⢀⢿⣦⣶⣆⠈⠃⢰⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣿⠜⠁⢠⣿⡿⠿⡿⠋⢸⣿⢿⡾⠿⢿⣷⡀⠀⠙⣿⠏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣴⡏⢂⣴⠟⠋⠁⣠⡄⠾⡿⢻⣤⣀⡀⠀⠴⣿⣀⡈⢻⢷⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣠⣿⠋⣤⣠⣴⣌⣟⢘⡇⠠⢠⢎⣄⣠⣴⣬⠻⣿⡀⣎⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⢀⣋⣧⣿⡿⣿⠻⠨⡍⢿⣀⠿⠌⡿⢻⣿⣿⣧⢱⣀⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠸⣮⣿⣿⣿⣧⢽⡂⢠⡀⡾⠟⠚⢀⠁⠙⢿⣿⢿⣿⣿⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢿⣿⡇⣻⣧⡤⡛⠮⠽⠆⠰⣾⣿⣄⡄⠛⣿⢻⣿⡿⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢠⣸⣿⣧⠘⣾⣧⢙⡦⣷⡆⠸⣿⢿⣿⠰⠞⠉⢾⣿⣤⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⣿⣿⣿⡄⢻⣟⣯⠉⣿⡆⢰⣧⣾⢋⣶⡞⣾⣿⣿⣿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠸⣿⣿⣿⡝⢽⣿⡾⣄⣿⡷⠸⢫⣿⣿⣿⣧⣿⣿⣿⡟⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠙⠛⠛⠃⠘⠛⠛⠛⠛⠃⠀⠛⠙⠟⠛⠃⠛⠛⠛⠁⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡉⠘⠾⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⡟⢧⠀⠀⢸⠃⣿⠋⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⣷⡄⢴⣶⡆⢣⡏⠀⢀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢸⣇⣠⣛⣤⡸⣧⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⡿⣿⣈⠚⠝⣫⠷⢟⠛⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠊⠉⠁⠉⠱⡄⢸⡜⠋⠛⠁⠀⠀⢱⡏⠀⠈⠆
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢰⠙⡸⡷⡀⡠⠀⠀⠀⠘⡈⠂⠀⡆
⠀⠀⠀⠀⢀⠜⠁⠀⠀⡠⠂⠀⠀⣀⠔⠉⠀⠁⠈⠈⠇⢀⡀⢀⠄⠀⣀⠘⠦⠄⢀⡀
⠀⠀⠀⢠⠃⢰⠀⢠⡴⠁⣰⣶⣛⣓⡠⠤⣖⣈⣽⡿⠀⠀⠹⢿⢾⣴⡷⢤⡄⠀⠀⠈⢑⣢⣤⡀
⠀⠀⠀⠈⠢⣀⡙⠪⠤⠤⠄⣤⢤⠤⢤⣴⠿⠛⠈⢡⣠⣀⡀⠀⠀⠈⠈⠒⠤⡀⠈⠛⢄⡈⣄⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⡄⠀⠀⢘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣘⡌⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢦⡀⠀⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣦⡆⠀⠀⠙⠳⠄⣠⠀⠐⡁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣰⡟⠁⠀⠈⠀⠀⠀⠘⠆⠀⠀⠚⠻⣎⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣿⣿⡟⠀⠀⢀⡀⢬⣤⣔⣤⠀⢀⣠⣿⢀⡛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⣦⡆⣿⣿⠠⠀⣐⡿⢿⠶⣅⠛⡏⠸⣿⣯⣴⢟⣉⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡵⠟⠋⡄⡇⢻⠘⠿⡍⠢⠔⠀⠙⠀⡓⠀⠡⣩⠦⢭⣩⡾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠸⠏⠐⡄⢰⡇⢻⠈⣷⢰⠃⢹⠿⠏⠀⠜⠀⣀⣡⣄⡀⡈⢷⣰⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢨⡀⠠⣿⠇⣽⡀⠙⣧⡁⢈⡄⠀⢠⡗⠀⠱⠋⠁⡀⣀⣀⡹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠘⠁⠀⠻⡇⠸⠇⠀⣿⣷⡀⣡⡄⣸⠎⠀⠃⡰⠾⣫⣤⣾⡧⠸⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣷⣇⠀⠰⣼⡟⠑⢉⡅⠵⠈⠀⠀⠊⠲⢿⠿⠿⠃⠶⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠠⢰⠈⠹⠂⠐⣿⡧⠁⠸⠀⠀⠠⠀⠠⠀⠀⣀⣤⡀⠁⣰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⣀⡆⠀⠀⣧⠶⡀⢶⣄⠀⠀⢀⠀⣠⡾⠿⠾⣿⡄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⠇⢀⣸⣟⣄⡠⠜⠉⢳⣦⣼⣯⣾⣿⠿⣿⢿⣿⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⢀⣿⡃⣯⡓⠀⠀⣠⢴⡟⢉⢰⠶⠒⢺⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣯⠥⣈⠁⡀⠀⠗⣠⠸⡌⢣⡏⡈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠘⡗⠈⠉⡿⠂⢀⠠⢻⢇⣙⠟⠓⠂⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣇⢻⡄⠐⠂⠔⠁⣠⢠⣈⠋⡲⠀⢢⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢩⠀⠈⠆⠳⡄⠀⡤⠿⡳⠂⠞⠃⠹⢀⡾⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⠳⠀⠀⢀⠙⠦⣀⠀⠸⠀⢦⡐⠤⣎⡸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⡦⠀⠳⠀⠢⡳⡄⢩⣧⣔⣅⡒⢤⠚⣩⠜⡔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠀⠀⠀⣆⡀⣕⢦⣙⠋⠂⠀⣋⡉⠁⠀⠗⢁⡖⠘⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⠃⢀⣠⠀⡽⣧⣠⡄⠘⢧⡘⢐⠝⠒⠊⠁⠀⡟⣀⣶⣠⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠛⠚⠃⠛⠈⠀⠛⠀⠘⠓⠚⠒⠒⠀⠐⠂⠂⠛⠘⠋⠐⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢉⣀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⡤⠔⠒⠒⠂⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⡞⠉⠀⠀⠀⢲⡀⠘⡕⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢠⡿⠀⣟⠐⠃⠘⡆⢸⢿⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡠⠟⠋⠉⠉⠉⠐⠺⣷⠀⠑⢹⠈⢧⠀⠀⠀⠀⠀⠀⠀⡜⡏⢀⡟⢰⣿⣇⠱⠀⢰⣹⣻⣜⡇⢸⡍⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣠⠰⠀⠀⠀⠠⡆⠀⢸⣷⢦⠘⣶⣼⡇⠀⠀⠀⠀⠀⢰⣱⠃⢸⣇⠺⣾⢇⡇⠀⢨⣜⠯⡻⣿⢸⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢁⣇⠀⠠⡄⢀⠤⢼⡀⠘⣿⡏⣇⠘⢿⡇⠀⠀⠀⠀⠀⢘⠇⠀⠘⣿⡀⠁⠈⠀⠀⠀⢈⠁⢐⢿⡾⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⢿⣿⢫⢦⡇⠀⡀⠀⢰⢶⡝⠆⣿⡇⢸⠀⠈⢷⡀⠀⠀⠀⠀⠸⣄⠀⠀⢻⣷⡖⢠⣭⣭⣽⡌⣧⠎⢸⠁⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠾⢸⡙⡎⢅⣥⠀⠀⠀⠌⣥⠂⢰⡏⡄⠈⠇⠀⠈⡇⠀⠀⠀⠀⠀⠈⠳⣄⠈⣿⠀⠀⠙⠿⠋⠀⢸⠀⣽⠀⠏
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⡆⠘⠁⢱⠀⡆⠀⠀⠀⢢⠀⢀⣿⡇⠱⠀⠘⡄⢀⠇⠀⠀⠀⠀⠀⢀⠞⠉⠓⠋⠦⣤⠖⢹⠦⠴⡟⠀⠘⠢⠂
⠀⠐⠶⢲⡶⢶⠟⢳⣴⠂⣇⠀⢀⡾⡶⠀⠀⠀⠀⠀⠰⢿⣿⣷⣄⠀⠀⡿⠿⠶⠶⠶⠖⠀⢀⠏⠀⠀⠈⠀⢀⡞⠇⢸⡇⠀⢷⢀⣀⣀
⠀⠀⢠⣿⣇⣼⠀⣼⣠⠞⠉⠑⠉⠀⣷⣞⣛⣒⡄⠀⣴⣟⡀⣾⢉⡷⠚⠁⢀⡖⠋⠉⠓⡶⠋⠀⣀⠀⠀⢆⠈⢹⠀⠀⢠⠀⠈⢯⠀⠘⡆
⠀⠀⠈⠙⠿⠿⠶⠻⠋⠀⠀⠀⠀⠀⠧⣿⣥⣟⣁⡴⠿⠹⠥⠿⠶⠃⠀⠀⢸⠀⠀⢀⣸⢡⡞⠁⠀⠈⠀⠈⢢⡀⠀⣞⡡⠀⠈⠹⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠉⣣⢨⠀⠀⠀⠀⠀⠀⠀⠃⢀⡏⠀⠀⠀⠀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣼⠀⠀⠀⠀⠀⠀⠀⠘⠀⢣⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡟⠀⠀⠀⠀⠀⢠⡠⠂⠀⡀⡇⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠐⠒⠒⠀⠚⠀⠐⠃⠋⠀⠓⠃⠂⠀⠐⠒⠂⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠹⣷⣄⠀⣠⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠠⠄⠀⠄⠀⠤⢀⡀⠤⠠⠀⠀⠄⠤⠀⠤⠀⠀⠀⠀⣸⡧⠄⠀⠲⣤⢆⣿⣀⣀⣀⡤⠚⠀⠉⢿⡇⠀⠀⠻⡆
⠀⠀⠀⠀⠀⣿⣷⢸⣿⡇⣿⣷⠸⢿⣿⡇⣾⡿⢿⣷⢸⣿⡇⠀⢀⣿⣿⣷⠀⠀⠀⢏⠀⠀⠀⠘⠙⢏⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣿⢸⣿⠃⣿⣿⠀⣼⣿⠁⢿⣷⣌⡉⢸⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠈⠑⠦⣄⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⡏
⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⣿⣿⢠⣿⡟⠀⣀⡙⢿⣷⢸⣿⡇⠀⢸⣿⢸⣿⡀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⡟⣼⣿⣷⡆⢿⣧⣼⣿⢘⣿⣧⡄⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠸⡿⠿⠇⠀⠛⠉⠉⠉⠉⠁⠤⠍⠉⠁⠈⠉⠛⠋⠛⠿⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠳⡄⠀⠀⢀⡇⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢹⡄⠀⢸⠀⣆⢰⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡜⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠐⠀⢆⣇⠀⢸⣀⡄⠘⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣼⡄⣃⣘⡿⠀⠀⠻⣇⣼⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠁⠀⠀⠀⠈⠉⠁

⡿⢿⠿⡿⡿⣟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣻⣿⣻⣿⣿⡻⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠉⣿⠋⠁⠀⠉⠑⠖⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡏⣰⢛⣾⣇⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠘⢐⢡⠛⢿⢻⡄⢰⠇⠀⠀⢠⠆⠀⢀⡬⢆⢸⡉⢳⡀
⠀⠀⠀⠀⠀⢀⠴⣯⠀⠀⠀⢸⡞⢾⡀⠀⠀⡀⠈⡀⠀⠀⠉⠠⢶⣩⣿⣾⠀⡇⡆⠱⡄
⠀⠀⠀⠀⠀⣧⡀⣿⠀⠀⠀⢸⣇⠈⢠⢆⢼⡯⠥⢄⣀⠀⣠⠀⠀⠀⢀⡸⠀⢷⠃⢠⡙⡄
⠀⠀⠀⠀⠀⢣⣢⢻⣄⢀⡄⠘⢿⡀⠈⠁⣈⣤⡀⢀⣀⠱⠉⢀⠀⠰⠋⠀⣼⠎⠀⠀⡟⠙⣄
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⠀⠀⣧⠀⠀⢩⣉⣰⠈⣓⠆⠀⢸⡄⣀⣦⡜⠋⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠈⡻⠀⠀⠀⢸⡿⠀⠀⠈⢉⡏⠉⠁⠀⠀⠀⣰⠏⣽⡇⠀⠀⠀⠀⢀⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠏⢧⣴⡶⠟⢲⠾⣦⡀⠀⠀⢠⠃⢼⣿⣇⠀⠀⠀⠀⢸⣿⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⢸⠐⠒⢻⣶⣤⣯⣽⣄⣠⠞⠐⠋⣿⡿⡄⠀⠀⠀⠸⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⢻⣿⣿⠀⠹⠀⠀⠀⠀⣸⡇⠱⡀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⣇⠸⣿⣿⡆⢀⠀⠀⠀⢠⣿⢣⠀⠉⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⡹⢀⡇⠙⡇⢸⠀⠀⢀⣾⡟⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠇⢸⠀⠀⢻⡀⠀⠀⠨⠏⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠛⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⠄⠀⠀⠀⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⣲⣿⣣⠞⠁⠀⠁⠀⡆⠑⢈⡍⢿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⣼⢀⣿⡽⣃⠰⣖⢶⠀⠀⠁⠳⣴⢀⡓⢽⡟⣎⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠹⣦⡟⣿⣿⠺⠏⠷⠹⡏⡀⠀⢀⢾⠻⢏⠿⢘⣷⣹⡆⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣽⡷⣿⡇⡇⣿⣆⠄⠀⠀⡃⠃⠀⠈⡘⠀⠀⠀⣸⣿⡇⣇⣷⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⣁⠃⢻⡇⣿⢿⣿⢇⡇⢰⡷⠂⢀⠀⠘⣆⢠⠊⣿⣿⡇⢻⡏⢸⣣⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⣤⣺⣷⠸⣿⣿⣼⣧⡟⡥⠂⠐⠂⠂⣹⣜⣷⣿⡿⠛⣾⣃⣄⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠆⢻⣿⣿⣿⣇⢷⡞⢢⠐⢦⢟⣿⣾⡿⣇⢈⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡀⢸⣿⡿⣿⢏⢀⡝⠛⠛⠁⠀⣿⡿⠁⣿⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣼⣿⣧⣿⢚⣨⣴⣾⣶⣄⢪⣿⡇⠀⠙⠳⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢿⣟⠙⢻⣯⡙⠟⣹⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣯⠀⠹⣿⣝⠉⣿⣵⣾⡿⠇⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣀⢻⣧⠘⣏⠻⠟⣿⣮⣷⠦⢣⡎⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧⣘⡻⣷⣤⡼⣿⣕⡏⠿⠷⠂⣾⢡⣶⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣿⢤⣟⠛⢻⣾⣹⣿⠙⡧⣺⡏⢰⣏⠞⡁⣴⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣟⠀⠻⣷⡌⣿⠁⣽⡣⣧⣾⠋⣿⣵⣠⢷⢈⡁⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢀⠜⣿⣷⣻⣮⠻⡛⠏⢹⣷⣿⣉⢀⡿⣬⣶⣿⡎⠟⡎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⣾⣏⡼⢍⢛⡻⣧⣿⠷⣈⣁⣾⣴⢾⡋⢫⡥⣾⣁⢠⠙⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣰⡿⠩⢷⡊⣶⡛⠿⣿⣆⢨⣿⡉⣽⣿⣭⣷⡼⠏⢟⠳⠂⣹⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠁⣀⣍⣀⣰⣿⣺⣿⣟⣷⣿⢣⣿⣿⡟⠉⠰⠿⠉⠀⠀⢫⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠷⡀⠀⢺⣯⡡⣭⠀⠀⣟⠚⢻⡿⠿⠽⠿⢖⣀⢒⠄⢀⡠⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⢠⣭⣽⡄⢻⣷⡶⣞⠋⠁⠀⠉⠁⣀⢴⣿⡷⣫⠎⠛⡡⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠓⠛⠲⠶⠷⠙⠿⠛⠃⠀⠈⠘⠛⠉⠛⠿⠺⠿⠇⠈⠑⠳⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⣶⠛⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣴⣿⣷⣿⣿⣍⣿⣾⡛⣻⣿⣉⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣸⠀⠐⢿⡿⠛⠛⠛⠋⠉⠉⠻⣿⣥⣿⣉⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠻⠇⠀⠗⠋⠀⠀⠀⠋⠀⠀⠀⣀⣤⡤⠀⠙⣿⣾⣏⣹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⣆⠘⢋⠕⣶⡤⠀⢿⠿⠻⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⡹⠀⠀⠀⠀⠀⠀⠁⠖⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⠠⠦⠀⠀⠀⠀⠀⢰⣏⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣒⠒⠂⠀⠀⠀⣠⣾⣿⠟⣿⣴⡀
⠀⠀⠀⠀⡰⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣀⣀⣤⣴⠞⠋⠸⡏⣴⣩⡷⣿
⠀⠀⠀⢠⠁⠀⠀⠀⠀⣾⣀⣀⣀⣠⣤⣤⣄⣀⠀⢀⣀⢀⣠⣤⣤⣀⠀⠀⣽⡿⠛⠁⠀⠀⠀⢳⣾⣭⣷⠏
⠀⠀⠀⢸⡆⠀⠀⠀⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠙⠻⢍⣻⡁⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠙⡿⣷
⠀⠀⠀⢸⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣷⠀⠀⠘⠿⣻⡋⠛⠻⣄⠀⠀⠀⢠⡾⠁⣸⠷⣄
⠀⠀⠀⠀⠉⠛⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢠⡟⠀⠀⠀⠀⣀⣀⣴⣶⣸⣆⡴⠞⠋⠀⢰⠏⠀⠈⠓⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢶⣤⣤⣤⣹⣻⣿⡃⣘⠀⣶⠀⠀⠀⠉⠉⠀⢸⢧⣿⠞⠉⢻⡄⢾⠀⠀⡠⠀⠀⠀⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣟⣴⡟⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠑⠿⣠⠞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⢹⡟⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠘⠄⠀⠀⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠄⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠙⠀⡀⢸⣿⣀⣠⡤⠶⠶⣄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⠹⡿⠓⠚⣛⣓⠢⢄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠈⢢⠘⣧⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⣷⣤⠶⠿⠿⣿⣯⡒⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢲⡀⠘⡇⣿⠀⠀⠀⠀⠀⠈⠀⣻⡧⠞⠋⠀⠀⠀⠀⠀⠈⢻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⢄⠘⢦⠘⢾⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠛⠄⠀⠀⣃⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠋⠉⠀⠀⠀⠀⢀⣀⣀⣤⠴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢀⡠⠤⠖⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢶⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⡏⠉⠉⠙⠛⠛⠛⠋⠙⠛⠲⢶⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⢉⣿⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠁⠼⢳⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣃⠆⠂⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡧⢻⠄⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⢿⣿⢇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠷⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣶⣿⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣔⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣳⡅⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⡼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣿⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣝⠠⠄⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⡇⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣾⣿⠄⡵⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢼⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⡴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⢿⣿⢿⣿⡿⠿⢿⡷⣶⣦⣤⣤⣤⣀⣀⣹⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⡋⠈⠋⠉⠈⠀⠀⠀⢻⣿⣿⣿⣻⢿⠿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢀⣀⣠⣤⣤⣼⣿⡟⠟⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠁⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠸⠗⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠠⡶⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⢲⠶⢝⣠⠀⡈⠀⠀⠀⠀⠂⠈⠑⢩⣶⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⠀⠀⠀⠰⠔⠿⠟⠀⠁⠀⠀⠀⠀⠠⣄⣠⣿⠋⠀⢰⡀
⠀⠐⣿⡀⠀⠀⢀⠤⣤⣼⣫⣽⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⠷⠂⠀⠀⠀⠀⠀⠀⠙⠙⠛⠀⠀⠿⠇
⠀⠀⠘⠗⠀⠉⠀⠀⠀⠀⠉⠺⣿⡄⠀⠀⠀⠀⠀⠀⠘⡿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡆⠀⠀⣧⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠸⠞⠐⠚⢹⡄⣠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠖⠀⠀⢀⢀⣀⣀⡀⢀⠀⢠⣌⠛⠃
⠀⠀⠀⠀⣀⣀⣶⣼⣧⣤⣿⠃⠀⠈⠁⣴⠖⠀⠀⠀⠀⠀⢀⡀⠠⠀⢀⣠⣴⠏⠁⠀⠀⠀⠀⠀⠈⢰⣒⣀⠈
⢀⣤⣄⠜⠋⠈⠉⠛⢻⣿⡏⠀⠀⢤⡤⢹⣶⡶⠀⢀⣀⡀⠀⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⢠⣆⠀⠀⠌⠉⠁
⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣭⣿⣶⣶⣠⣭⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋
⠀⠀⠀⠀⡴⣶⡆⠀⠨⠟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠛⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠨⡿⠤⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠈⣿⣤⡀
⠀⠀⠀⠀⠀⠘⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢲⣿⣿⣧
⠀⠀⠀⠀⠀⠈⢫⣦⡄⠀⠀⢠⣾⣿⠟⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⡄⠼⠏
⡀⠀⠀⠀⠀⠀⠈⢻⡁⠀⢀⣿⡏⠁⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⢀⣛⡁⠀⠉
⠏⠀⣤⡀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠸⢿⠁
⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣬⣿⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢂⠈⡀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣼⠁⣶⣶⣆⡄⠀⠂⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣶⣿⡿⢿⣿⣖⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠠⠙⠄
⠀⠀⢀⣠⣴⠶⠆⠀⠉⠑⠲⢤⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠠⠀⠀⠀⢠⡇⠀⠀⠀⠀⣂⠈⡄
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⠳⠖⠚⠉⠀⠀⠀⠀⠀⠐⢦⡀⠀⢸⡇⠀⠀⠀⠀⣿⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣶⡾⣷⡀⠀⠀⣴⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣦⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⢻⣦⡀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⢿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⡿⣿⡿⠃⡄
⠀⠀⠀⠀⢀⣠⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠚⠛⠹⠛⠉⢁⣄⠸⣿⣿⣿⣿⣷⡼⠁
⠀⠀⠀⢠⣿⣿⣿⠟⠁⠐⢻⣿⠋⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀⣀⣠⣶⣿⣿⡿⠿⠾⠿⠟⠋
⠀⠀⠀⠉⠁⠛⠋⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣴⣶⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⣀⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣹⡇
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣦⡿
⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢸⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠟⣻⡟⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣟⣁⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠑⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠓⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⡽⠋⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⢤⣈⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠚⠛⠉⠀⠛⣆⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠉⠒⠄⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠤⢄⣀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠑⠲⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠒⠛⠢⣄
⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⢀⡞⠉⢀⢰⣶⣠⡀⠀⠀⡰⢅⠀⠀⢀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣼⠀⠀⠀⠀⠀⢙⣿⣀⣤⣶⣀⠲⡠⠁⣠⣢⠤⠀⠀⠀⠀⠘⠳⢦⣄
⠀⠀⠘⣄⠀⠀⠐⠋⠋⠉⠉⣙⣻⣿⡷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⠶⣄
⠀⠀⢀⡞⠱⠦⠤⠒⠊⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠝⠳⡄
⠀⡰⡯⠐⠲⣆⠀⠀⠀⠾⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢰⡄⠀⢀⡃⠒⠀⠀⠀⣈⣴⡶⠶⠶⠾⢤⡄⣠⡤⣴⢂⠠⠲⠆⢀⠀⠀⠀⠀⠀⠀⠃⠠⡌⢳⡶⠾⠟⠒⠦⠴⢿⡓⣦⣄⣀
⠀⠙⣺⠛⠳⠶⢒⣋⣉⣉⣀⣀⢀⣤⣴⠿⣿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠘⣷⣆⢸⠀⠀⠀⠬⢷⠁⠍⠏⠉⠓⠲⠦⢤⣤⣤
⠀⢀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⡔⠀⠘⣉⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣋⢸⠀⠀⠀⢀⣸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠻⣧⣸⣠⣄⣀⢀⣐⠀⡉⠠⣩⣴⡼⠟⢫⣤⡙⢿⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡧
⠀⠀⠀⠈⢹⡋⠛⠛⠛⠛⠒⠛⠛⠛⢩⠀⠀⣼⡯⠔⠉⠉⠓⠆⣤⣶⣤⣀⡀⠀⠄⢄⡀⢀⠀⠀⠀⡞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⢷⣦⣀⡀⡀⠀⠀⣄⣀⣷⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠰⠀⠀⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉⠁⠈⠙⠿⢼⣐⡜⣁⢀⠀⠀⠀⠀⠀⠀⠉⠀⠁⣠⣀⠀⠀⢠⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠿⢧⣤⣥⣶⠾⠶⠛⠛⢶⣙⡀⡏⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⠀⠀⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢢⣄⣀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣿⡟⡇⡀⡄⠀⠂⠀⠂⠀⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣱⣹⡡⡐⣐⡀⡀⢀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣵⣿⣿⣿⣟⡙⠐⢡⢃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠮⢼⣔⣐⣃⣩⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣾⠂⠀⠃⣼⣧
⠀⠀⠀⠀⢀⠞⢻⡇⠀⢹⣿⣇
⠀⠀⠀⠀⣿⣷⣾⡇⠀⠸⣿⣿
⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣁⡌⠙⣦⠀⠀⠀⠀⢀⣴⠿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠘⣧⠀⠀⠀⡼⢋⣀⠀⠀⠋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠸⠲⢄⠀⠂⠀⠉⠀⠚⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⣶⣬⠀⠀⠈⢧⣀⠘⠟⠻⢆⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣈⣿⠀⠀⠀⠈⢻⣧⣤⣴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠉⡿⠿⠟⠒⠙⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⣿⣇⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⢿⣿⣦⣀⣀⡴⠁⠀⠀⠀⠀⠀⢂⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠈⣽⡯⠰⣿⣦⣄⣀⣀⣭⣿⣦⡐⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⠀⢀⣀⣀⡈⠙⠿⣿⣿⣿⣿⠃⠻⣦⣀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⠉⠀⠉⠻⢶⣦⣶⡿⣿⠃⠀⠀⠈⠙⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣩⣿⣿⡾⠃⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⢶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠲⢦⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠈⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡎⢦⣤⣤⣤⣤⡰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠐⣿⣿⣿⣟⢥⡹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣘⣿⣿⣿⣿⣶⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠉⣻⣿⣿⠃⠀⠀⠀⠀⠀⠻⢿⠈⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉

⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣧⣃⣻⣤⣭⣭⣭⣬⣥⣭⣥⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣠⣌⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠁⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⣴⣦⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠈⠁⠀⣙⠋⠀⠂
⠀⠀⠀⠀⢠⣾⠛⠉⠀⠈⠉⠺⣷⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠉⠉⠉⠛⢿⣆
⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⠀⠀⠸⣷⠀⠘⠓⠶⠀⣀⠀⠀⢸⡟⠀⠀⠀⠀⡀⠀⠀⢻⡆
⠀⠀⠀⠀⣿⡀⠀⠀⠐⠀⠀⠀⢸⣿⠀⠀⠉⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠑⠲⢤⠤⠤⠤⠤⠤⠀⠒⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠛⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡐⣤⡄⢸⡆⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢦⢧⠈⠁⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠈⠘⠀⠄⡀⠀⠀⠂⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡌⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠛⠢⠀⠠⠔⠊⠀⠀⢀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠊
⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡁
⠀⠀⠀⠀⠀⠆⠈⠋⠀⠴⠃⠶⠉⠀⠴⠇⠠⢺⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣶⣤⡀⢀⣼⡷⠈⠲⢶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⢁⣀⣀⣀⣀⠈⠙⢿⣿⠙⣥⣚⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⣠⣾⡿⠿⠟⠛⠿⢿⣶⠄⠱⣷⣶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⣸⣿⠋⠀⣠⣤⣤⡀⠀⢺⣿⡄⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⣿⣏⠀⢸⣿⣿⣯⣾⠄⠀⣿⣧⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⢹⣿⡀⠈⢿⣿⣿⠟⠀⢠⣿⡏⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠻⣿⣦⣀⣀⣀⣀⣴⣿⠟⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⡀⠈⠛⠿⠿⠿⠛⠋⠁⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣶⣦⣤⣤⣤⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠈⢧⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣻⣿⣄⠸⣇⠔⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢿⠿⠿⡿⣷⠁⠈⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠏⡁⢰⡄⢠⣒⣣⣴⡀⠉⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⢲⣶⣖⣾⣿⠋⣩⡘⠦⠙⠀⡁⣿⣿⣽⡿⣳⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢹⣿⣿⠏⣀⢈⣃⠠⣄⠀⠻⣿⣿⣋⣴⡿⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣿⡟⢘⣵⢿⣿⣿⣾⣧⡤⢛⡟⠙⠋⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⡿⢛⣻⣛⣩⣿⠛⠚⠻⣄⡀⠄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡟⠉⠙⠋⠁⠀⠀⠔⠁⠀⠠⢞⣼⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣵⣴⣀⠀⢶⣒⣤⠴⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣏⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠤⠶⠾⢿⣿⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⠿⠟⠛⠉⠉⠉⠉⠙⠒⢸
⠀⠀⠀⣀⣠⣴⣶⣿⣶⣶⣴⣤⣀⣉⠙⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠛⠋⣉⣥⣤⣶⣴⣶⣶⣦⣤⡄⠀⠀⢸
⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣷⢦⣀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣤⠖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⢸
⠀⠀⠀⠉⣉⡻⡀⠀⣿⣷⣶⣾⣿⠉⠓⣍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⠔⠻⣿⣿⣭⣿⣿⠆⠈⠙⠛⠛⠋⠉⠀⢸
⠀⠀⠀⠈⠻⣿⣿⣦⣞⣻⡿⠿⠫⠤⠶⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⣦⣀⣹⣿⣿⣿⢟⣀⣀⣤⣾⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⠿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⡻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢻⣟⢻⣿⣿⣿⣿⣿⣿⣿⣇⢶⣿⢇⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢾⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠒⠋⠉⠉⠁⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣿⣿⣿⣟⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠐⠂⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⣄⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣽⣿⣿⣿⣿⣦⡘⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠘⠿⠿⢿⣿⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⣿⣿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢠⣤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠂
⠀⠀⠀⠀⠀⡀⠸⢖⠀⢜⡷⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⡀⠀⢿⣇⢨⠻⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢈⡦⣤⣜⣭⡺⠗⠚⢶⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⣷⣾⣦⠟⠋⠀⠀⠀⠀⠀⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠛⠉⣤⡖⠀⠀⠀⠀⠉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⣰⠀⠀⠀⠀⠀⠠⠐⠂⠀⠒
⠀⠀⠀⠀⠀⢠⣤⣶⡀⡿⣘⡟⠃⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠸⡛⢹⡿⣿⠻⠀⠀⠀⠀⠀⢫⡤⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⢆⣻⢿⡀
⠀⠀⠀⠀⠀⠐⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠛⠛⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⢀⡀⠘⠇
⠀⠀⠀⠀⠀⠠⠋⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡀⠀⢨⣹⣄⡀⠀⡀
⠀⠀⠀⠀⣄⣀⠀⢘⡏⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⡆⠐⠊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠟⣙⢉⡟⠃⠀⠁
⠀⠀⠀⠀⠛⠛⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣾⣷⣿⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠴⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⣀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢿⡿⠿⠿⣿⣿⡛⣹⣏⠁⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢋⣩⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠐⣿⣿⣿⡿⠻⡷⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠊⣿⣿⡅
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣿⣿⠃⠀⠀⠀⠁⢀⡰⠎⢠⠄⠀⠀⠀⠀⠀⠀⠐⠏⠀⠉⠹⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠎
⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡤⣶⣦⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣀⣴⣥⠞⠀⠀⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠒⠲⣆⠀⠀⠀⠀⠀⠀⣿⣁⡈⢥⣈⡀
⠀⠀⠀⠀⠀⢸⣾⠟⠁⠀⠀⠀⠸⣾⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠉⠁⢀⣀
⠀⠀⠀⠘⠳⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡙⠀⢈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠓⠀⠐⢢⣦⣷
⠀⠀⠀⠀⠀⠰⣿⣧⣀⡀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⡁⠀⢿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡔⠂⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡿⢿⣿⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠤⠴⠆⢠
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠠⢜⢿⡿⠋⠙⠻⢤⡀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣾⣷⡀⠀⠂⢴⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢽⣶⠶⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠪⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠉⠀⢰⠀⡠⢀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀⣀⠀⡆⠀⠉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠀⠀⢄⣉⣡⣍⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠿⠷⠂⠐⠾⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣡⣌⣉⡠⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⡀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⠢⠧⠴⠜⡆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿
⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠛⢦⣼⣧⡶⠛⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⣿⠿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠈⠁⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠿⣿⠀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣿
⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣷⣶⣶⣆⣀⠀⠀⠀⠀⠀⢀⣠⠀⣀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠀⣄⡀⠀⠀⠀⠀⠀⣀⣰⣶⣶⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡇⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⢸⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⠤⣀⡀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡷⣿⣿⣿⣷⣶⣶⣦⣿⠏⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣞⡛⢿⡇⢻⡿⣿⣿⠿⡎⠉⢁⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⣦⣤⣬⣽⣿⣷⡠⡁⠐⠶⠿⠃⠀⣰⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣗⡒⠻⢿⣿⣿⣾⣦⣄⣀⣀⣼⣿⣿⣿⣿⣿⣟⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡆⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣯⢳⣦⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡿⡏⠙⢻⣿⣿⣶⣀⡀⡀⣉⠙⠛⠛⣻⣿⠘⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡇⠁⢀⡀⣿⠿⣿⣿⣿⣿⣿⣧⣴⣿⣿⢿⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣹⡿⣿⣟⣿⣿⣿⢿⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⢩⣿⣿⣷⣿⣿⣿⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⢸⠛⠛⢛⣿⡟⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠰⣤⣴⡦⡰⠛⠁⠀⠀⠈⠐⠄⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⠀⠀⡀⠀⠀⠀⠀⠎⠀⣿⣿⡷⢲⣶⣿⣷⠁⣤⡀⡀⠀⠀⠀⠀⠈⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢷⣿⣿⣟⣦⣍⣩⣾⣿⣶⣾⣿⣷⣆⡀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⣿⡀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠙⠈⣽⢃⠁⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠸⡟⠿⠿⣿⠟⠟⠙⠃⠀⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⣶⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠼⣿⡃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠄⠀⠀⠐⠂⠠⠀⠀⠄⠀⠀⠀⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⢴⠾⠋⠶⣴⣦⣀⣠⠀⠀⠶⣦⣔⣋⣽⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣄⡀⠀⠀⠀⡼⣏⢀⣀⠀⢰⣮⣻⣿⣿⣿⣆⠸⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠿⠿⠿⠿⠶⠤⠀⠀⠠⣿⣦⣼⣿⣿⣿⣿⣿⣿⣆⠰⣦⠀⠀⠀⠀⠀⠀⢃⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣌⡃⠀⠀⠀⠀⣴⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠂⠘⠛⠉⠉

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣸⣟⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠀⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⢼⣿⣿⣧⠀⠀⠀⠀⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⢰⣿⣿⣷⡀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⡼⣿⣿⡄
⠀⠀⠈⣿⢿⡿⠐⣿⡇⠀⠀⠘⢻⠿⡿⡇⣻⡟⠀⠀⠀⣿⢿⡿⡇⣻⡇⠀⠀⠀⢻⡿⣿⠗⣰⣿⡄⠀⢸⡟⣿⡿⢀⣀⠀⠀⢻⡿⣿⡇
⠀⠀⠀⣿⢸⡇⢸⣿⣇⠀⠀⠀⣾⠀⣧⠀⣿⣿⠀⠀⠀⣿⢸⡇⠀⣿⣿⠀⠀⠀⢸⡇⢸⡀⢨⣿⡁⠀⢸⡇⣿⠀⣽⣿⠀⠀⢸⠇⣿⠀⣸⣇
⠀⠀⠀⠋⠘⠃⠈⠋⠛⠁⠀⠀⠛⠀⠛⠀⠉⠙⠋⠀⠀⠛⠈⠋⠀⠋⠙⠃⠀⠀⠘⠁⠘⠁⠘⠙⠃⠀⠘⠁⠙⠀⠙⠛⠁⠀⠘⠀⠙⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⣶⠀⠀⣴⣆⠀⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣲⡂⢸⣿⠂⢸⣿⡇⠈⣿⡏⠀⣿⣷⡀⢺⣿⠀⠀⠀⠀⠀⠀⣴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠇⠻⠻⠃⠸⠛⠃⠐⠟⠷⠀⠛⠻⠁⠿⠿⠂⠀⠀⠀⠀⠰⣿⢿⣦⣤
⠀⠀⠀⠀⠀⠀⢠⣿⣥⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⣿⢿⣿⡟⠁
⠀⠀⠀⢀⣀⠀⣿⣿⣿⠈⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠸⠃⠃
⠀⠀⠀⢹⣿⠹⢻⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⢀⣼⣿⡄⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠤⢶⣦⣄⡀
⠀⠀⢈⣭⡈⠀⠈⠀⠈⣠⣄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣧⠀⢨⣿⣷⡄
⠀⠀⢠⣿⣧⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠿⠂⠀⠀⠛⠛⠛⠛⠀⠘⠀⠛⠛⠒
⠀⠀⣿⣿⣿⢀⣤⡀⢸⣿⣿⡇⣤⡄⠀⣾⣿⣿⣆⣤⡀⠀⠀⠀⣼⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⡀
⠀⠀⢸⣿⡟⢰⣿⡄⠀⣿⣿⠃⣾⣧⠀⠈⣿⡿⢠⣿⡆⠀⠀⠀⠘⣿⠳⠀⠺⣷⣤⣤⣄⡀⠀⠀⠘⣿⢳⠉⠘⣷⣄
⠀⠀⠘⣿⡇⢸⣿⡿⠀⢿⡿⠀⣿⣿⡄⠀⣿⡇⢸⣿⡿⠁⠀⠀⠀⣿⠀⠀⠀⢸⠟⠛⠻⣿⠀⠀⠀⣿⠀⠀⠀⡿⢿⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠋⠀⠀⠀⠁⠘⠛⠉
⣶⣶⡷⠿⠶⢾⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣾⣶⣶⣶⣷
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⡔⠋⠀⢂⢀⠉⠓⡄⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⡴⢏⠀⠀⠀⢈⠷⡄⠀⠀⠀⢠⣜⢿⣿⣿⣿⢟⣤
⠀⢸⠀⠀⠀⠀⠠⠀⡀⢹⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣘⠀⠈⡆⠀⠀⡎⠀⠘⠀⠀⠀⣿⣿⡞⣿⣿⡟⣾⣿⡇
⠀⠰⡀⠀⠀⠠⠀⠀⠀⡼⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠰⡀⢠⠃⠀⠀⢣⠀⡰⠀⠀⠀⢿⣿⢣⣿⣿⣧⢿⣿⠇
⠀⠀⠙⠮⣄⢀⣀⡤⠞⠁⠀⠀⠀⠀⠻⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠑⠧⣀⠀⢀⡠⠗⠁⠀⠀⠀⠈⠱⢿⣿⣿⣿⠧⠉

⠀⠀⠀⣀⠤⠀⠠⢄⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠤⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀
⠀⢀⠎⠀⠀⠀⠀⠀⢙⣄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⢠⣪⠖⠉⠉⠲⡄⠈⢢⠀⠀⠀⣴⢫⣵⣶⣮⡝⣿⣷⡄
⠀⠘⠀⠈⠉⠀⠀⠀⠠⢬⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⠐⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⡼⣿⣧
⠀⠘⣄⠀⠠⠀⠀⠈⠙⡜⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠰⡱⡀⠀⠀⠀⠀⠙⡶⠀⠀⠀⢷⡹⣿⣿⣿⣿⣿⣬⠃
⠀⠀⠈⠒⠤⢠⠠⠖⠊⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠈⠺⠦⣄⠀⠤⠊⠀⠀⠀⠀⠀⠙⠮⠛⠿⠿⠟⠁

⠀⠀⢀⢤⣖⡀⠐⠦⣄⠀⠀⠀⠀⠀⣠⠴⠶⣶⣦⡀⠀⠀⠀⠀⠀⢀⠔⠂⠀⣀⠒⢄⠀⠀⠀⠀⠀⣠⣶⣾⡿⣶⣦⡀
⠀⢠⠃⢿⡿⠇⠀⠀⠈⢣⠀⠀⠀⣼⣇⢀⣀⣿⣿⣿⣶⡄⠀⠀⠰⠁⠀⠀⠀⠉⠲⠂⠱⠀⠀⠀⣾⣿⣿⣿⣷⣾⣹⣿⡆
⠀⢀⠀⠀⠀⠀⠀⣿⣿⢄⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⢠⡆⠀⢸⣿⣿⣿⣏⣹⣿⣿⣿⣷
⠀⠈⢾⣿⣶⠀⠀⠉⣋⠎⠀⠀⠀⠹⣅⠈⢻⣿⣿⣶⡿⠁⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠀⠚⠉⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠋

⠀⠀⠀⠀⡠⠔⠲⢦⡒⡄⠀⠀⠀⠀⠀⢀⣤⣦⣔⠲⣶⠀⠀⠀⠀⠀⠀⢀⡠⠒⢒⢄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢤⡀
⠀⠀⠠⠊⠀⢀⣴⠄⠹⡇⠀⠀⠀⠀⣴⣿⣿⠟⢙⣷⡜⠀⠀⠀⠀⠀⡔⠁⠀⢀⠎⠀⡇⠀⠀⠀⠀⢀⣴⣿⣿⣫⣿⡿
⠀⠀⣧⠀⢴⠟⠁⠀⡰⠁⠀⠀⠀⢈⢿⣟⢁⣴⣿⣿⠏⠀⠀⠀⠀⡎⠀⣀⠔⠁⢀⠎⠀⠀⠀⠀⢠⣿⡿⣻⣿⣿⠟⠁
⠀⠀⣎⡳⣤⣀⠤⠊⠀⠀⠀⠀⠀⢸⣦⣙⠿⡿⠟⠁⠀⠀⠀⠀⠀⠑⢍⣀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠳⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠘⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠈⠣⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⢀⣨⠽⠓⣶⣦⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡖⠛⠉⠁⠀⠀⠸⣿⣿⠃⠀⠀⠀⢸⣇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⢀⣿⡈⠀⠀⠀⠀⠈⠙⢦⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣸⠿⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⢀⠟⠂⠠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣿⣿⣿⣷⣴⣶⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠉⠉⠉⠉⠉⠛⠻⠿⠿⠶⠶⠶⣦⣦⡀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰
⠀⠀⠀⠀⠀⢰⣶⡶⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠙⣿⢳⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠨⣄
⠀⠀⠀⠀⠀⣼⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⣶⣿⢿⣶⡆⠄
⠀⠀⠀⠀⠈⠉

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⡀⢀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠉⣉⣭⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠈⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡄
⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢠⡟⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⢠⡟⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢀⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣼⣿⣄⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠈⠉⠉⠛⠲⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠤⣀⡉⠉⠓⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠲⣤⠤⠤⣌⡑⠢⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⣼
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣤⣤⠀⠀⠀⠛⠄⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⢠⡟
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⠁
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⡟⠰⣀⠔⢋⣤⣶⣿⣷⣶⣶⣶⣶⣦⣤⡄⢸⡄⠀⠀⠀⠀⢘⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡈⢳⡀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣉⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉⠓⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠲⣄⠀⠀⠀⠀⠀⢠⡟⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⡟⠀⢠⠞⢉⡓⠦⣄⡀⠀⠀⠀⠀⢀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⢦⠈⢣⠀⠀⣸⠁⣰⠋⠀⣉⣉⣛⡲⢍⠓⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠈⢣⡼⡟⢓⡏⣰⠃⣠⠞⠉⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣄⣀⣀⡤⠔⠉⠀⠀⠀⠀⠀⢣⡴⠚⠳⠇⡰⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠔⡞⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠊⠁⠀⠀⠀⠀⠀⢇⠀⠀⠐⡄⣸⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠼⠃⠀⠲⢏⣤⠴⢺⠟⠉⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠲⣄⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡭⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠶⠶⠒⠒⠒⠒⠒⣲⠞⢳⡀⠀⠀⠘⢦⡄⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⢦⡀⠀⠈⢳⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⡄⠀⣏⢱⡀⡀⠘⠁⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⡜⠀⢸⠃⠀⢹⡈⢿⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⢄⣀⣀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡀⣀⠀⡞⠀⠀⡼⠀⠀⢺⠠⠴⠚⠉⠈⠒⣄⠀⠁⠀⠀⠤⠄⢄⠀⠀⠀⠈⠉⠉⠛⠒⠒⠶⠶⠶⠦⠄⠀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠇⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠰⡀⠀⢄⠀⠀⠀⡵⠀⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠘⠂⠀⠀⠁⠀⠐⠃⠐⠢⠤⠀⢫⠀⢣⠀⠉⠓⠚⠓⠋⠉⠉⠐⠀⠀⡀⠀⠈⠀⠒⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢚⡏⠲⢦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⢀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣌⣷⠀⠀⠈⠙⠲⢤⣑⠢⢄⡀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⣁⡤⠖⠋⠁⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠀⠈⡗⢄⡀⠀⠀⠀⠈⠙⠲⢌⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠔⠊⡁⠴⠒⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠓⣾⠀⢰⠇⢸⠉⠓⣄⡀⠀⠀⠀⠀⠀⠑⠢⣍⡐⠤⣤⠴⠂⣉⡥⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⣾⠉
⠀⠀⠀⠀⠀⠀⠀⢧⣤⠇⠀⢸⠆⠞⠀⠀⠦⢿⠢⢄⠀⠀⠀⠀⠀⠀⠉⠒⠷⡖⠈⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠊⠉⢠⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡄⠀⠀⡀⢸⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⡼⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠎⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣅⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠸⠰⠀⠀⠀⠁⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢴⡦⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠿⠃⠀⠀⠈⢿⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣤⣴⣶⣶⣦⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⣶
⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠸⣿⣶⣤⡉⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⢿⣿⡿⠀⣠⣤⡄⣠⡄⠉⣻⣿⠘⣿⡄⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁
⠀⠀⠀⣰⣿⣮⣧⣿⣦⠀⠀⠀⢀⣴⣶⣶⣿⣿⣥⣤⠙⠻⣿⡟⠋⠀⠹⠿⢷⣆⣆⣦⣤⣄⡀⠀⠀⣴⣿⣼⣵⣿⣆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⢻⣧⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣹⣿⣿⣿⢿⡇⠀⢠⣿⣿⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣧⠈⠛⠀⢸⡿⣿⣿⣿⡇⣿⡆
⠀⠀⠀⠁⣿⣿⣿⣿⠈⠁⠀⢸⣿⡟⠛⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠛⣿⣿⠀⠀⠀⠈⠁⣿⣿⣿⣿⠈
⠀⠀⠀⠀⣿⡿⢹⣿⠀⠀⠀⣸⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢿⣿⡀⠀⠀⠀⠀⣿⡇⣿⣿
⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠈⠻⣿⡄⠀⠀⢀⣿⡇⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠉⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠻⡇⠙⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⠏⠠⠒⠈⠀⠀⠀⣿⣏⠀⠔⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢁⠀⣀⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠂⠀⠀⠀⡐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢄⢈⢀⡁⠀⠨⣒⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣉⣁⣧⡀⠀⠈⠘⠢⠄⡀⠀⠀⠀⠀⠐⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡗⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠉⠀⠀⠀⠃⠀⠀⠀⠀⠆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠄⠀⠐⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⡄⠀⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠁⠠⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⣾⠃⠀⠀⢳⣿⡟⠀⣦⠀⠀⠂⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠈⠀⠀⡀⣠⣞⣧⡄⣴⡟⠀⠀⠀⠸⡹⣷⣄⣷⠃⠀⠀⠸⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠠⡀⠙⠛⠾⣿⣿⣏⠀⠀⢀⠀⠀⠰⠉⢻⣿⠒⠀⠀⠀⢳⡄
⠀⠀⠀⠀⢀⣤⡶⠊⠈⠛⠷⠀⠀⠀⠀⠀⠀⠀⠙⢯⣻⡀⠀⠀⢀⠀⠀⠾⢿⣦⡀⠀⠀⠈⠻⠄⠀⠀⠀⠀⣀⡀⡤⠀⠀⣴
⠀⠀⠠⢶⣯⣿⡇⠀⠀⠀⠀⠈⠛⠷⣽⡀⡀⠀⠀⠀⠈⠙⠀⠀⠈⠀⠀⢠⡿⢹⣱⣄⡀⠀⠂⠀⠀⠀⣦⡀⠈⠋⠀⢀⣾⡟
⠀⠀⠀⠀⠀⢉⠻⣄⡀⠀⠀⠀⠀⠀⠈⠛⠿⣴⣄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠙⣽⢟⡟⣦⠀⠀⠀⠀⠉⠻⠛⠒⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢯⣷⣄⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⠁⢈⣿⠃⢎⡆⠀⠠⢄⠀⠀⡀⠴⠄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠁⠀⠀⠀⠀⣾⠀⠈⠁⠴⠿⠃⠀⠀⠀⠀⢀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠀⠌⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⣌⡀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⣤⠀⠀⠀⢀⣆⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⢾⠏⠀⣘⣴⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠈⠛⠲⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⣁⠔⠁⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⢶⣼⣿⣷⠀⠀⣹⣿⡇⠀⢴⣧⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⣋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⣇⣿⣿⡇⠀⣿⣷⢠⣿⣇
⠀⠀⠀⠀⠤⢀⣀⣀⡈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢥⣸⣿⣿⢺⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⢙⣷⣤⡶⠶⠶⢶⣤⣾⡋⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⣀⠀⠀⢀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⡀⠀⠀⣀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣰⡾⠋⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠙⠷⣆⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢿⡄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢠⡿⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣿⠀⠀⢰⣟⢙⣷⠀⠀⠀⠀⣾⡋⢻⡆⠀⠀⣿⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢰⡟⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⢹⡆⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢀⣾⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢷⡀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠁⠀⠀⠀⠀⠀⠠⣿⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠻⠷⢶⣤⣀⡀⠈⠹⠏⠁⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⠶⠶⢿⣶⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣦⣤⣤⣤⡴⠟⠁⠀⣀⣠⡴⠾⢛⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⠀⠀⣀⣀⣠⣤⡶⠟⠋⢁⣤⡶⠛⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉⠀⠀⣠⡶⠟⣁⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠘⠋⠁




⡶⣶⢶⢶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⡶⢶⣶

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢴⠔⢜⣫⠝⣠⠀⠀⠀⠀⠀⠀⠀⠰⣄⠸⠟⣀⡖⠀⠀⠀⠀⠀⠀⠀⣀⣄⢰⡶⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡀
⠀⢰⣿⣷⢸⣿⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢦⣯⠜⢳⣶⠻⣼⡵⠋⠀⠀⠀⠀⠐⠿⠿⠏⠺⡾⢒⣕⡏
⠀⠀⣿⣇⡼⠿⡌⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠛⠂⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⢠⣶⣶⡆⢴⢶⠀⠨⡪⣇
⠀⢸⠉⠉⡆⠀⡗⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠈⠙⠁
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣶⡶⠖⢶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣄⠶⡠⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⢰⣶⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⣠⣿⡇⢙⠸⣿⣤⠈⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣤⣤⢧⣤⣬⣥⣄⠀⠀⠀⠀⠀⣠⣼⣧⣤⣿⣄⣀
⠀⠀⣾⡚⠷⣿⡾⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢾⣿⡿⣿⣿⠟⠀⠀⠀⠀⠘⠁⣿⣯⣀⣿⣌
⠀⠀⠘⢷⣤⣿⣦⣾⠏⠀⠀⠀⠀⠀⠀⡞⠛⡇⠀⢸⠀⢠⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⣿⣿⠀⠀⠀⠀⢀⣈⣛⣁⣉⣛⣁⣈⣓⡀
⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠐⠓⠒⠓⠒⠛⠒⠚⠂⠀⠀⠀⠀⠈⠉⠁⠘⠙⠁⠉⠉

⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⢀⡀
⠀⠘⣿⣿⡉⣩⣿⡿⠁⠀⠀⠀⠀⠀⣄⢰⣶⢀⡟⠑⠚⠛⠀⠀⠀⠀⠀⠤⠀⢁⣠⣀⡀⠁⠤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣽⣷⣾⣍⠀⠀⠀⠀⠀⠀⠀⠈⢳⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠘⣧⣼⠃⠀⢠⠄⠀⠀⠀⢰⣶⣾⢷⡆⢠⡾⣷⣶⡆
⠀⠀⣿⣿⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⣧⠀⠀⡄⠀⠀⠀⠀⠈⠉⠙⠛⠁⠈⠙⠋⠉⠁
⠀⠀⠘⠿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠐⠂

⠀⠀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣿⢋⢁⣉⢻⠇⢀⠀⠀⠀⠀⠀⠰⡄⢸⡿⠘⡿⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⡆⠐⢼⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠂⢸⣌⣛⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣲⠟⠁⠀⠀⠀⠀⠀⠀⣠⣧⡄⢾⣿⠂⢸⡇⠀⠀⠀⠀⠀⠠⠖⢛⣿⣶⣜⠿⠟
⠀⠀⠀⠈⠙⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⣸⣿⠀⠞⠓⠀⠀⠀⠀⠀⠀⡉⠉⣉⢉⡉⠁
⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⡀⡇⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠅⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣜⣛⠁⠀⣀⣀⣀⡀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢿⣷⠀⢻⠿⣿⠅⠀⠀⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢀⡟⠀⠀⠀⠀⠀⠀⠀⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⣿⣧⣶⣶⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⠦⠤⠛⠟⠀⢀⣾⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠉⠉⠁⠀⣰⣷⣿⠏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣶⣤⣾⡿⣯⡝⠀⠀⠈⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿⣿⣿⣿⣿⡟⣹⣿⠁⠀⠀⢀⣠⣶⠊⣡⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠇⣿⣋⣩⣽⣿⣿⣇⣿⣿⡶⠤⠴⠟⢻⠃⢰⠇⠀⠀⠀⠙⠓⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠀⠉⠩⠀⢸⠀⠀⠈⠉⠻⣿⣿⠁⠀⠀⠀⢀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠑⡯⠀⠀⠀⠀⠀⡸⠀⢰⠀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡆⠸⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠃⠀⢼⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣾⡷⠀⠀⠁⠘⢿⣷⣀⡅⠀⠀⢣⡀⠀⠀⢠⣷⡀⠀⠀⠀⡜⠀⠀⣿⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠩⣿⣿⣿⡄⠀⠀⠀⠱⢤⣀⣼⣿⡃⠀⣠⠞⠀⠀⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⣀⣀⣤⣿⠟⠉⠛⠋⠁⣀⣀⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠛⠉⠙⠛⢧⣄⡀⠀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⣿⡏⠀⠀⣠⣾⣿⣿⣿⣿⣵⣦⣤⣤⣤⣄⡤⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣍⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠀⠀⠀⠀⢀⠠⠃⡸⠁
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡅⡼⠁
⠀⠀⠀⢿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡾⠋⡾
⠀⠀⠀⢸⣇⢰⣶⣶⣄⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣉⣱⣒⣛⣳⣾⠃
⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠚⠉⠉⠉⠀⣿⣿⡿⠟⠛⠉⠁⢠⠉⠻⠟⠻⢿⣿⣿⣿⣿⣿⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠶⠓⠒⠛⠚⠚⠓⠒⠒⠒⠒⠢⠤⠅⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢹⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⠞⣿⡇⠀⠀⢀
⣀⣠⣤⣤⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⠟⠁⢀⣾⡏⠀⣠⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⢸⣿⠃⠀⠸⣿⡇
⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⣿⣿⣷⣯⣝⣛⣻⣿⡿⠿⠿⣿⣛⣻⣿⣿⣿⣿⣿⡿⠗⠘⢷⣦⣄⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠻⢿⣤⣄⡀⠀⢩⡿⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣿⣥⡾⢠⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠻⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢣⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣶⣶⣦⣤⣤⣄⡠⢄⡬⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⡀⠀⠀⢇
⠀⢠⣦⢶⠒⣀⣤⡀⢐⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡯⣶⡵⣂⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣶⣬⣓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠁⠀⠀⠀⠀⢀⣤⣀⡀⠄
⠀⠀⠀⠀⠀⡐⡰⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⠿⣻⠂
⠀⠀⠀⢀⢠⣷⣻⣿⡿⢿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⢷⣶⡔
⠀⠀⠀⠶⠿⠿⠛⣧⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⠻⣿⣿⣿⣿⣯⣟⣿⡿⠻⠛⠛⢉⣥⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡹⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠈⠙⢻⣿⣿⡅⠀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⣿⣿⣿⣿⡿⣿⠏⠀⠀⠀⠀⣽⣿⡷⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⢿⡯⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠭⣽⣿⣿⣿⣿⣟⠭⠊⠁⠀⠀⠀⠀⠀⣽⣿⡗⠀⠀⠀⠀⠀⠀⠀⠉⠚⠩⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⣞⡽⣻⠽⡫⠅⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠑⠩⠛⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣴⣶⣶⣿⣿⣶⠄⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣻⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡝⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⢎⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡷⡳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⠫⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢷⣦⣤⠀⢠⣾⠟⠁⠀⠀⠘⠿⠿⠿⢿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠛⠉⠉⠛⠛⠻⢷⣦⡄⠀⣠⣾⡿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⠟⠋⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⢠⣼⡿⠉⠠⣶⡀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣠⣾⠟⠛⠉⠉⠉⣀⣴⠿⠋⠀⠀⠀⠹⣷⡀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣠⣾⡿⠉⢠⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⠟⠋⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⣤⣴⡿⠋⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣤⣀⣀⣠⣤⣴⡾⠟⠋⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⡾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣶⣿⣾⡿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣿⣿⣿⠿⠿⠿⠟⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠰⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⡄⠀⡘⠀⠀⠀⠀⠀⣀⣀⡀⠄⠒⠀⣙⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣰⣿⠟⣻⣿⣍⠙⣿⣿⣿⣿⣿⣃⡄⢀⣀⠴⠒⠉⠁⣀⢨⣷⣾⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠾⣿⡏⠸⣿⣿⣿⡇⢸⣿⣿⣿⣶⠚⢡⣿⠀⢰⣶⣧⣾⣿⣿⣿⣎⡻⠿⠋
⠀⠀⠀⠀⠀⠀⡈⠀⠀⣉⣛⣛⣿⣮⡛⣿⣿⣁⠀⢨⡟⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢀⠄⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠓⠲⠞⠛⠋⠀⠀⠀⢹⣿⣿⢿⠁
⠀⣠⡞⠁⠀⠀⢀⠸⣿⣿⣿⡿⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⣿⢿⡌
⢰⠏⠀⠀⠀⣠⠟⢹⣾⣿⣿⠁⠀⣠⣾⣶⣿⡇⠀⠀⠀⠀⣾⣿⣿⢿⡇
⣏⠀⠀⠀⠞⠋⠀⢸⡿⠛⣿⣤⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⢧⢺⡅
⠙⠷⠶⠤⣤⠔⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⡀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⡀⠀⠛⢿⣿⡇⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣿⣿⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣧⣀⡴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣿⣿⣻⣻⣛⣛⣛⣫⣭⣥⡀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⠋⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠷⠈⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠁⠀⠀⠀⠀⢀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠻⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⣀⣠⣬⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⡟⠁⠿⢿⣿⣻⢿⣿⣿⣿⡿⣫⡶⠟⠉⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢹⣿⣧⢻⡿⠿⢟⣩⣦⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡋⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⠟⣫⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣛⣥⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⡉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⡶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢛⣻⣿⣦⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⣤⣀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠓⠿⠛⠻⠟⣉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⣛⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⠿⠷⠶⠞⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⡿⢿⠟⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠷⣤⣤⣤⣤⣶⠯⠓
⣤⣤⣤⣄⣠⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣜⣷⣶⣿⣛⣩⣄⣠⣄⣠⣄⣤⣤⣤⣤
⣿⠿⡿⠿⡿⢻⠿⢏⠻⠿⣿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣛⣛⣛⣛⣛⣿⣿⣛⣛⣛⣛⣛⣿

⠀⠀⠀⢀⡠⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⡔⠁⢧⠒⠊⠉⠉⠣⡀⠀⠀⣴⣿⣩⣽⣶⣾⣿⣦⠀⠀⢀⠾⡀⠀⣠⠤⠠⢝⢆⠀⢀⣜⢿⡿⢟⣯⣭⣛⢆
⠀⢸⢆⠀⠈⠢⡤⠄⣤⠤⡇⠀⢈⢿⣿⣷⣝⣻⣿⡟⣟⡃⠀⡌⠀⠈⠁⠀⠀⠀⠈⡞⠀⣼⣿⣿⣿⣿⣿⣿⣿⣞⡆
⠀⠘⡄⠑⢄⡼⠀⠀⡏⢠⠇⠀⠘⣷⣝⡿⢧⣿⣿⢷⣿⠃⠀⠰⣀⠤⠤⢤⣀⢀⡴⡹⠀⠸⡿⣛⣛⡿⢿⣿⡿⡽
⠀⠀⠈⠲⢎⣀⣀⡼⠕⠁⠀⠀⠀⠈⠛⢵⣿⣿⠟⠞⠁⠀⠀⠀⠙⠢⢄⣀⣀⠤⠚⠁⠀⠀⠘⠻⢿⣿⣷⠶⠛⠁
⠀⠀⠀⢀⣀⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⡀
⠀⠀⠰⠛⢁⣀⡀⠛⠻⠂⠀⠀⠀⣠⣤⡿⣿⢿⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⢈⡛⢦⡀⠀⠀⠀⢠⣾⣿⡿⢦⣍⠓
⠀⢠⡀⠀⣼⣿⣷⠀⠀⣠⡀⠀⠐⢿⣿⠁⠀⠘⣿⣿⠟⠆⠀⠀⠀⠀⠀⣰⡟⠁⠀⠉⠀⠀⣰⣿⣿⠏⢠⣾⣿⡇
⠀⠘⣿⠀⠀⠉⠁⠀⢸⣿⠇⠀⠀⢰⣿⣿⣶⣿⣿⡇⠀⠀⠀⠰⣄⡀⠾⠋⠀⠀⠀⠀⠀⠀⠿⣿⣃⣴⣿⣿⠏
⠀⠀⠀⠀⢰⣾⣶⡄⠀⠀⠀⠀⠀⠈⠻⠟⠉⠙⡿⠟⠁⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⠈⢷⣌⡛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⢀⡤⠂⠀⠀⠂⣀⠀⠀⠀⢀⢠⣶⣶⣶⣶⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⣿⣿⣿⣷⡀⠀⠠⢁⠇⠀⢀⠔⠋⠉⢁⠀⢠⡟⣸⣿⡿⣣⣶⣿⣧
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⢠⠎⠀⠀⣿⠀⠀⠀⢀⠀⠘⣰⣿⣿⡃⣿⣿⣿⣿
⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⢄⠀⠀⠹⣄⠀⢀⠀⠀⠈⢿⣿⣿⣇⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⢁⡒⠀⠘⠋⠀⠀⠀⠀⠀⢉⡛⠛⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟
⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⠀⠀⠀⠀⠀⠀⠀⠀⣨⡅
⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⢂⡉⠉⠑⢤⠀⠀⢠⣿⣿⣴⢾⣿⣶⣄
⠀⠀⠀⠩⠑⠀⠄⠐⠈⠀⠲⠀⡀⢻⣦⣄⣤⣶⣞⣿⣧⣤⣄⠀⠀⢘⠀⠠⠐⠂⠀⠀⠥⠀⢻⣷⣿⣟⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠉⢠⡀⠀⠁⠀⠹⣿⣿⣿⣷⡿⠿⠿⠛⠀⠀⣘⡀⠀⠀⠀⠀⢀⠎⠀⠘⣯⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⠠⠐⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣛⣻⣟⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣤⡄⠀⣤⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⣿⡇⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠷⠶⠿⠷⠶⠿⠷⠶⠿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠛⠿⠿⠟⠉⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠀⠀⠀⠒⢷⣄⠀⣿⡁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠿⠛⢀⣄⡀⠀⠀⠀⣴⡶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇⠀⠀⠈⣿⠀⣿⡇⠀⣼⡇⠀⢀⣀⡀⠀⠀⣴⡗⠀⠀⠀⠀⠀⠙⣿⡄⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣤⣴⣶⡿⠶⢿⣇⣀⣿⠃⢼⡟⠛⠛⠛⠻⠿⠷⠶⣶⠆⠀⠀⠀⢸⡇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⡀⢀⣈⣀⣀⣠⣤⣤⣬⣿⣿⠿⠀⠈⠛⠿⠿⠶⢶⣶⣦⣤⣤⣤⡀⠀⠀⢸⡇⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⠛⠛⠛⠋⠉⠉⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠁⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣄⣀⣀⣀⣀⣀⣀⣸⣇⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⢿⣿⠿⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣧⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⣼⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠛⣷⡄⠀⠈⢿⡆⠀⠀⠀⠀⣸⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢰⡿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⡇⠀⢸⡇⠀⠀⣼⡇⠀⠀⠀⣿⣇⠀⣰⡿⠛⢿⡟⠛⢿⡿⠛⠛⠛⠛⠻⣿⠟⠻⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠛⠁⠀⠘⠟⠀⠀⠻⠃⠀⠀⠀⠈⠛⠻⠛⠁⠀⠈⠻⠿⠛⠁⠀⠀⠀⠀⠀⠙⠻⠟⠋





⣿⣿⣶⣾⣷⡿⢾⣿⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⢷⠶⠶⠶⠶⠶⣶⠾⠶⠶⠶⠶⣶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣠⠖⠛⠛⠛⠓⢦⡀
⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⠀⠀⠀⣴⡛⠓⠈⠳⢦⣀⣰⠃⠀⣠⠔⠒⢤⠀⠙⡆
⢠⡞⠉⠀⣀⣀⠀⠀⠈⢧⣠⠶⠋⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⢧⣀⣠⠆⠀⠀⡿
⣿⠀⢰⠋⠀⠈⢱⡀⠀⠈⠁⢀⣀⣀⠀⠀⠀⠀⠀⠲⢿⣿⣶⡄⠀⠀⠀⣀⠼⠁
⢻⡀⠀⠳⠤⠤⠞⠁⠀⠀⣴⣿⠿⠋⠀⠀⠀⠀⠀⢀⡤⠦⣄⠀⠀⠀⠈⠛⠶⣤
⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢦⣄⠀⠀⠀⠀⢸⣋⣦⠈⢧⠀⠀⠀⠀⠀⠺⣄
⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⡏⠀⣤⣿⣧⠀⠀⠀⠸⣿⣿⠃⣸⠀⠀⠀⠀⠀⠐⢿
⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⢧⠀⠻⣿⣿⠀⡠⠤⠀⠘⠳⠖⠛⠋⠀⠀⠀⠀⠀⣈⡷⠶⠶⠚⠓⢦⣀⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠴⠞⠓⠤⠞⢁⣤⠒⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠠⣼⠀⠀⢀⡤⢄⠀⠀⢹
⠀⠀⠀⠈⢧⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣠⡶⠋⡧⠀⢫⣀⡸⠀⢀⡼
⠀⠀⠀⠀⠀⠳⠶⢦⡀⠀⣀⠤⠄⠠⢀⠀⠀⠀⠉⢻⠀⣄⠀⠀⠀⠠⣀⣼⢋⣠⠞⠁⠀⠀⠀⠀⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠁⠀⠀⠀⠀⠱⣄⡀⠐⠾⠟⢀⡀⠄⠀⠀⠈⢻⠉⠁⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠄⠀⢀⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠎⠀⢀⠔⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⡆⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢰⠇⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⢽⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣮⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⢀⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠂⢸⡿⠛⢳⡖⠂⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠠⠄⠘⠷⢤⡀⢀⡼⠇⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡀⢀⣽⣏⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⢴⠧⠞⠁⠈⠳⠤⠴⣤⣠⡤⠞⠁

⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠈⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠛⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⠛⠛⢿⣿⣿
⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣦⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴

⠀⠀⠀⠀⣀⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢲⠰⢂⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡀⣀⡀⠀⢀⣾⠫⠇⡀⠀⠀⠂⢺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠘⡏⢼⡏⢠⡿⢖⣻⠠⢄⠃⠄⠐⡘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⢀⡴⣤⠀⢡⢼⡇⣼⠃⣄⠃⠠⠌⠀⠀⠨⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠸⢦⠈⠆⢸⢸⡇⣿⠍⣔⠃⠥⠀⡀⠀⠅⢠⣿
⠀⠀⠘⢧⠘⣼⡎⡇⢹⣆⠣⠀⢀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⢣⠘⢧⡇⠈⢷⣞⡈⠦⠂⡄⠆⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢣⡸⣿⡀⠈⢟⣦⣬⣐⡘⣾⠋
⠀⠀⠀⠀⠀⢸⢳⡄⠱⡀⠀⡆⠉⡵⠋
⠀⠀⠀⠀⠀⢸⠀⢳⡀⠙⣆⡇⢰
⠀⠀⠀⠀⠀⢸⠀⠈⢳⠀⠈⠳⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠘⣆⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢀⠴⠎⠉⠀⠀⠀⠁⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠸⠀⠀⠀⡈⣄⠀⠀⠈⢢⠀⠀⠀⠀⡰⠋⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⣿⡆⠀⠀⠀⢣⠀⠀⢰⠁⠀⢀⠠⠊⠀⠀⠀⢀⠄⠂⠀⠀⢀⣠⠧⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡆⠀⠀⠀⠳⡤⠒⠲⡈⠀⠀⠀⠀⠀⠐⢇⠀⠀⢠⠖⠙⡀⠀⠀⠀⠐⠓⢌⠐⣬
⠀⠀⠀⠀⠀⠀⡆⠀⠀⣿⡏⠉⠻⣦⠀⠀⠀⠱⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠑⡴⠁⠀⣰⣿⣿⣶⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⡇⠀⡔⠛⠑⢦⡀⠈⠣⡀⠀⠀⠘⡄⠀⢫⠀⠀⣐⠀⠀⠀⢀⣦⡠⠐⠙⢿⡿⠟⠀⡀⠀⡀⠐⠻⢿
⠀⠀⡜⠋⠉⠈⣧⠠⠷⠀⡀⠀⠉⠲⠄⠑⡄⠀⠀⠘⢄⠘⠹⡁⠀⠐⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡁⠀⠀⠀⢹⣄⡀⠀⠈⠑⠒⠀⠀⠀⢻⣄⠀⠀⠈⢢⣄⡑⢄⣀⣀⡀⠀⠓⠤⣀⣠⣴⣄⠀⠀⠀⡄⠀⠀⠀⢰
⠀⠀⠣⡄⠀⠀⢘⡈⢯⡢⣀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠱⠱⡄⠀⡠⠒⠂⠑⡄⠘⣿⣿⣿⠗⠀⠀⠀⠀⢠⣤⠂
⠀⠀⠀⠀⠀⠉⠀⠑⠆⠷⠏⡀⠀⠀⠀⠄⠀⠀⠐⡳⢄⣤⣨⠗⠃⠀⠁⠀⠀⠈⠉⠲⢉⠉⠙⢄⠀⠀⠀⡀⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢠⣤⠴⠞⣛⣉⡙⣦⡀
⠀⠀⠀⠀⠀⣾⡟⠛⠉⣉⣉⣻⣾⠹⡆
⠀⠀⠀⠀⢀⡟⠴⠂⠀⣀⣀⣈⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠄⠀⠀⣀
⠀⠀⠀⠀⢸⡇⠐⠋⠡⣤⣀⡈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠀⠠⣤⣤⣤⣤⡴⠞⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠈⠙⣯⣴⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢸⠀⣰⠀⠀⠀⣸⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠸⣇⠘⠓⢶⣚⣫⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠞⣳⣒⡫⠍⠂
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠙⠽⣄⠻⣄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠖⠺⠿⢶⣤⣾⣤⣄
⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠀⠘⢦⠙⣦⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣌⢳⡄⠙⢶⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆⠀⠀⠀⠀⠈⢷⣄⠀⣸⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢻⣄⠀⠻⣦⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠻⣿⢠⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠳⢦⣈⠻⢶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠘⣧⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢰⠀⢀⠈⢷⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣿⠰⣄⠈⣿⡷⣄⢀⣀⠀⠀⠀⠀⠸⣇⠹⡆⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠈⡇⣸⠀⠘
⠀⠀⠀⠀⠀⠀⠸⣇⠚⠀⣿⠈⠚⠛⠒⠂⠀⠀⠀⠀⣿⡿⡅⠦⣤⣤⣤⣴⠾⠋⢀⣴⡣⠀⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠸⣦⡀⠀⠀⠀⠀⠤⠤⠞⠁⣧⠀⠀⠀⠀⠀⣀⢄⣀⢯⠏⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⡛⠛⠶⠶⠶⠖⠂⠀⠀⠏⢀⡆⠀⠀⠀⠈⠳⠥⠬⡇⠀⠀⣾⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢦⡀⠀⠀⠀⠀⢠⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠀⠈⠻⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣙⠓⠒⠒⠀⢀⣠⣤⣤⣤⣤⣤⣤⣶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠁⠀⠁⠀⠀⠀⢰⣠⣄⠖⣀⣀⣴⠀⠒⠀⢠⢂⡠⠒⣶⡂⢆⡀⠀⠒⢀⠐⠀⠀⣲⠀⣆⠐⠂⣲⡐⢀⡆⢰⠀⡆⠀⡴⠀⡰
⠀⠠⣄⠘⣃⡄⠀⠀⠀⠁⠈⠀⠀⠈⠉⠁⠁⠀⠈⠂⠈⠂⠁⠂⠀⠁⠀⠀⠈⠐⠁⠀⠊⠁⠉⠈⠂⠉⠈⠀⠀⠉⠀⠑⠀⠉⠀⠀⠀⠀⠀⠀⠋⠀⠶
⠤⠤⠤⠿⠴⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠶⠤⠦⠤⠤⠴⠤⠤⠤⠤
⠀⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⣠⠤⣀⠀⠀⠀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⣄
⠀⠀⢀⡄⠉⠀⠀⠀⠀⠀⠁⢆⠀⠀⢀⠤⠀⢄⠀⢠⣏⠀⠀⠀⠱⠀⠀⠸⠿⠀⠈⠑⠂⠒⠁⠀⠀⠁⠀⠀⠀⠀⢠⠂⠁⠀⠂⠀⠈⠀⠀⠀⠀⠑⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⠀⠀⠀⠀⠈⠉⡠⠀⠒⠁⠀⢬⡷⠀⠀⢼⣦⠄⠀⠀⢀⡠⠂⠠⠤⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⢂⡀⡰⠃⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠁⠀⠸⠀⠀⠇⠰⢀⡀⠀⠀⣀⠐⠀⢀⠂
⠀⠀⠑⡄⠀⠘⠃⠰⠇⠀⠀⢂⡀⠀⠀⣀⠜⢣⡀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠑⠆⠑⠀⡼⠒⠋⠀⠀⠉⠀⠰⠀⠉
⠀⠀⠀⠘⡀⠀⠀⠀⠀⣶⡦⢄⠈⠀⠈⠀⢀⡰⠃⠔⠀⠀⠀⠀⠀⠄⠀⣀⣠⣄⣐⣀⠀⠄⠀⠀⢀⠔⠀⡰⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠜⠀⡤⠊⢉⠠⠀⢸⠀⠀⠀⡄⠑⡄⠀⠀⠀⠀⡀⠠⠄⣀⠴⠂⠉⡤⠒⠉⠰⠁⠀⠈⠒⠻⠟⣀⠐⠀⠐⢦⡀⢀⠄
⠀⠠⠚⠂⣆⠀⠀⢀⠀⠀⡈⠀⢘⠀⠀⠃⠀⠈⠁⠢⣀⢀⡀⠀⠱⢄⣀⡠⠊⠀⠀⢠⠉⠲⠄⢸⠀⠀⠀⠐⣄⠀⠀⡀⠔⠘⠋⠒⡄⠀⠀⠁⠁
⠀⠁⠤⠔⢸⠀⠀⠀⠀⠀⠡⣀⠘⢄⠀⢣⣀⡔⠁⠀⠀⢀⠀⢀⡴⠖⠒⠂⡄⠀⠀⢀⠀⠀⠸⠀⠉⠐⠀⠀⢢⠉⠁⠀⠀⠀⠢⠤⠂⣠⡄⡏⠉⠓⡄
⠀⠀⠀⠀⢨⠀⢠⠖⠀⠑⠀⠈⢣⠀⠀⣀⡉⠀⠀⡀⢀⠉⠀⡎⠀⠀⢱⠀⠈⢦⡀⠈⠓⠚⣁⠔⠂⠒⠒⢄⠀⠄⠀⠀⡔⠀⠂⠀⢏⣙⣁⠈⢢⠀⠘
⠀⡠⠂⠒⡄⢉⠖⠉⠑⠄⠘⠀⠎⠀⠊⠀⡀⠀⡰⠀⠀⡷⠀⠐⣀⡰⠂⠠⠒⠒⢏⠐⠒⠊⠁⡠⠈⠉⠢⡀⠱⠈⠢⠤⠃⠀⡈⠀⠀⠀⠀⠉⠁⠀⠀⡆
⠀⠑⢄⣀⡟⠁⢀⠀⢀⠈⠢⡀⠀⠈⣥⠔⠁⡠⠃⠀⢀⠓⡐⠀⠉⠀⠁⠀⠀⠀⠀⠁⢤⡀⣠⠁⠀⠀⢀⠇⠀⠗⠀⢀⡀⠚⣁⠀⠀⠀⠀⠁⠀⠀⢠⠁
⠀⠀⠀⡰⠁⠀⠀⠀⣌⠉⠂⠀⢈⡡⠤⣌⠉⠀⠀⡠⠎⡀⠃⠀⠀⠀⠐⠂⠐⠂⠀⠄⡈⠁⢹⠀⠒⠈⠁⠀⡴⠂⡔⢁⠄⠉⠻⠁⠀⠄⠀⠀⠀⠔⠁
⠀⠀⡜⠁⠀⠀⠀⠀⠿⠁⠙⠀⡏⠠⣶⠄⠀⠒⠈⢡⠊⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠠⠀⠚⡀⠀⢀⠊⠁⠀⠀⠀⡄⠀⠀⠀⠀⠘⠦⠀⣀⣀⠈⠂
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠃⡀⠈⠂⡀⠀⠀⠀⢱⠀⠀⠆⠀⠀⠙⠋⠘⠛⠀⠀⠠⠀⠀⠈⠑⠢⡕⠢⡀⠀⢣⠈⠒⠀⡄⠀⠀⠁⠐⠄⠀⠽⠆
⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠆⠀⢰⠀⢀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠤⠄⠠⠌
⠀⠀⠀⢱⠀⠠⠤⠒⠂⠀⠀⢠⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠛⠀⠀⢀⠀⠀⠀⠛⠀⠀⠀⠰⠿⠗⠈⢠⠃⠀⠀⢰⠀⠨⡁⢀⠄⠴⠓⠂⢄
⠀⠀⠀⠈⡄⠀⠀⠀⠀⣀⢤⡠⠤⠄⣀⠠⠃⢀⡀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣀⣀⠔⢋⠁⠐⠂⠸⠀⣀⠤⠤⠤⢀⢣⠀⠀⠡
⠀⠀⠀⠀⠈⠁⠒⠀⠉⠀⢈⠀⠀⡠⠃⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢰⠀⡃⡁⠘⠢⠀⠀⠀⠀⠈⠛⠁⠀⠈⠒⠒⠰⠁⠰⠀⠀⠀⠀⠀⢰⠉⠈⠁
⠀⠀⢠⠔⠂⠀⢈⡈⣀⢀⡠⢖⠋⠀⠎⠀⠲⣀⠜⢀⠀⠀⠀⠀⠀⢸⠀⡥⡄⢘⡁⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠀⡖⠢⡄⠓⠀⡁⠀⠁⠀⢄⣀⣀
⠀⠀⠈⢄⠀⠀⠸⠀⠠⠀⠥⠈⠤⡀⠈⠉⠉⡃⠠⠿⠃⠀⠠⠀⠀⢨⠀⡆⠀⢨⣁⠀⠀⠄⠀⡰⠃⢀⠆⠉⠁⠀⣡⣤⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠰⠀⠀⠀⠀⣰⣦⠀⠀⢀⡀⢰⣦⠀⡠⠄⠶⢄⡀⡇⠀⠀⠀⠀⢉⠉⠀⠀⠀⣀⣤⡀
⠀⠀⢀⠚⠀⠈⠀⠀⠀⠀⠀⠀⢰⣶⠔⠀⡸⠀⠀⡇⠀⡤⠂⠉⠀⠀⠀⠹⠏⠀⡹⠸⠀⢠⡄⠀⠐⢵⢄⡀⠀⠀⢸⠀⠀⠀⠘⠈⠡⠠⠄⠀⠀⠀⠸
⠀⠠⠁⠀⠀⠀⠀⠙⠃⠚⠁⠀⠀⠀⡠⠘⢀⡠⠖⠀⠘⠀⠀⠀⡠⠄⠊⠁⢀⠜⠁⠀⠇⠈⡇⠀⠀⠀⡆⠙⠄⠀⠸⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡰⠁
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡜⠀⠀⡤⠀⠀⢯⡀⠀⡁⠀⠀⠀⠘⣄⠀⠀⡀⠀⠱⡀⠀⢠⡅⠀⡀⠀⠀⠣⡀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⣎⠀⠀⢀⡴⠉⡆⠱⣄⠀⠀⠀⠀⠑⠀⣀⠀⢀⣉⠐⠁⠀⡐⠀⠀⢀⣀⣈⠒⠠⠤⠄⠒⣀⠄⠒⠠⡀
⠀⠀⠑⠒⠒⠒⠂⠠⣀⠀⠀⠀⠀⡆⠀⠐⢄⡈⠁⠈⠉⠠⢀⢃⠀⠈⠑⠒⠒⠒⠈⣡⠐⢠⡀⠀⢣⠀⢰⠀⠀⡐⠁⠀⠈⡆⠀⠔⠉⠙⠋⠰⡀⠀⢰
⠀⠀⢀⠒⠉⠈⠁⠢⡈⠑⠠⠄⠰⢁⣀⡀⠀⠈⠢⠀⠇⠀⠈⢋⠃⣰⣆⠐⠆⠀⢰⠁⠀⢀⡅⠀⡘⠀⢠⠀⢠⠁⠀⠀⢀⠇⠠⡀⠀⠠⡀⠀⡠⠀⡘
⠀⠀⣄⡄⠠⡀⠀⠀⠈⠑⠒⠂⡉⢀⡀⠈⠢⡀⠀⡇⠈⠑⠢⡈⢆⠉⣹⠀⠐⠄⠀⣦⡄⠋⠀⢠⠁⠀⠈⠦⢘⣀⢀⠔⠃⠀⠀⠿⠃⠀⠈⠉⠀⡐⠁
⠀⠀⠛⣄⠀⣨⠀⠀⠀⠀⣶⠎⠀⠀⠈⠰⡀⠂⠀⡇⢀⠤⠀⢾⢄⠁⠀⠀⠀⠀⠀⠀⠀⢢⡀⢸⠀⢀⠤⠤⡀⠋⡀⠀⢀⣲⡖⣖⣲⣒⣖⠀⡐
⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠰⠠⠄⠠⠌⠀⡗⠀⠀⣤⠀⣤⠀⠀⠀⠈⠆⠱⣇⠀⢀⡐⠀⢠⠀⠀⠉⠁⠉⠉⠉⠉⠀⠇
⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠶⣦⠀⠀⠀⠸⠀⡇⠀⠑⣄⠀⡤⠊⠀⠀⡀⢉⠁⡉⠀⠀⡀⠀⠘⠀⠩⡈⠁⠀⢀⡘⠀⠀⠀⠓⠛⠒⠺⠀⠀⠰
⠀⠀⡠⠃⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠈⢂⠑⠀⠒⢂⠀⠈⠁⠁⢠⣤⠀⠠⠚⠀⠀⠈⠉⣉⡁⠀⠀⠀⠀⠘⠗⠺⠂⠀⠀⠀⠦
⠀⠘⡁⠀⠒⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⡰⠀⠀⠠⠀⠀⠀⠸⠀⠀⡴⠃⠀⠀⠀⠀⠈⠹⠀⠣⠀⠀⠤⠐⠉⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠈⠒⠈⠉⠉⠒⠤⠄⠀⠀⠀⠴⠊⠀⠀⠀⠀⠁⠒⠊⠀⠀⠀⠑⠂⠤⠤⠤⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠿⠿⢿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣴⣶⡿⠿⠆⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠰⠿⢿⣶⣦⣤⡀
⠀⠀⠀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⣼⡿⣿⣿⢿⣧⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠉⠙⢿⣷⣄
⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⣼⡿⠁⣿⣿⠈⢿⣧⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⢀⣾⡿⠁⠀⣿⣿⠀⠈⢿⣷⡀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⣿⣿⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠁⠈⣿⣇⠀⠀⢀⣴⡦⠀⠀⠀⠀⢴⣦⡀⠀⠀⣸⣿⠁⠈⠛⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠸⠿⠋⠁⠀⠀⠀⠀⠘⣿⣦⣴⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⣴⣿⠃⠀⠀⠀⠀⠈⠙⠿⠇⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣴⣤⣄⠀⠀⠀⠀⠀⠀⠼⡿⠋⠻⠿⣿⣿⣧⠀⠀⠀⣀⠀⢀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⣿⣿⠀⠀⠀⣱⣘⣙⣋⣜⠛⣟⣋⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠁⠉⠁⠉⠉⠁⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣁⡐⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⠋⠛⣭⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣀⡀⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⢀⣴⣀⣀⡄⠀⠀⠻⢿⠁⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⡀⠛⠀⠀⠀⢶⣾⣿⡶⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣄⠈⠀⠀⠓
⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣄⡀⠀⠉⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀
⠀⠀⠀⢸⣿⣟⣿⠹⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⡇⡁⢁⠄
⠀⠀⠀⠀⢻⣿⣴⣦⣿⣿⣿⣿⣿⣿⡟⢩⣿⢿⢿⡿⢱⣻⣹⣷⡧⣤⡈⠻⣿⣿⡿⢿⣿⠿⠿⢿⣷⡇
⠀⠀⠀⠀⠸⣯⣭⣤⣤⣬⣿⣿⣿⣻⠖⢬⠛⠛⠷⠉⠀⠻⠏⠫⡱⢏⣴⣤⣬⣥⣤⣿⣷⣶⣦⣤⣴⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣤⠀⠀⠈⠀⠈⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣉⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠐⣊⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠒⠉⠉⠁⢇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢍⡑⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣭⠭⠭⠙⠀⠀⠀⠀⠀⠀⣀⢤⣒⠬⣛⡏⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢀⣀⣣⠃⠀⠀⠀⠀⣀⡠⣔⡪⠝⠊⠁⣠⣾⠗⢹⣃⣀⣀⡀
⠀⠀⠀⠀⡠⢒⠭⢒⠈⠉⠉⢑⣶⠭⡲⢄⢤⡲⠍⠒⠉⣿⠀⠀⡠⡪⢚⠥⣒⠭⡵⡖⠒⠒⢭⣕⠦⡀
⠀⠀⢀⢎⠜⠁⡀⠀⠀⠀⢀⣾⠏⠀⠈⠢⡣⡀⠀⣀⠤⢿⡠⡪⠊⡴⡡⠊⠀⠀⢧⢣⠀⠀⠂⠀⠙⢮⢢
⠀⠀⡎⠞⠀⠀⡈⠢⠀⢀⣾⡏⠀⠀⠀⠄⢳⢡⠎⠀⣀⡀⠈⠆⡘⡼⠀⠀⠁⢄⠘⡾⡀⠀⠀⠈⠀⡀⢧⢡
⠀⢸⢸⠄⠀⠀⠀⠁⢰⡞⢻⣴⣾⠶⠦⠬⢽⣼⠓⢴⡷⠃⠀⡼⡃⡁⠀⠀⠁⠀⠀⡶⢷⡀⠐⠀⠁⠀⢀⡎⡆
⠀⠈⡜⣄⠀⠀⠀⠀⠀⠉⠋⠠⡀⠀⠀⠀⢰⢰⠉⠢⡸⠖⠊⠀⡇⡅⠀⠀⠀⠀⡈⠛⠚⢃⠂⠀⠀⠀⢀⢇⠃
⠀⠀⠱⡱⡀⠀⠀⠀⠈⠀⠀⠂⠈⠢⠀⣠⢣⠃⠀⠀⠀⠀⠀⠀⠱⡹⡀⠀⡀⠈⠐⠀⠀⠀⠁⠀⠀⢀⠞⡜
⠀⠀⠀⠘⢮⡣⢄⡈⠀⠀⠀⠀⣀⡠⢞⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⠦⡀⠠⠀⠀⠀⠀⠀⢀⡱⣪⠎
⠀⠀⠀⠀⠀⠈⠐⠪⠭⠬⠥⠭⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠕⣒⣒⣒⣒⡪⠕⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡾⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠙⣧⠀⠀⠀⠀⢻⡄⣴⠏⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣴⠋⠀⠀⠀⡶⠛⢷⡞⠛⣦⠀⠀⢰⡏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⣷⠀⠀⢸⣇⡀⠘⠁⢀⣿⠀⠀⠀⣹⠆⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠸⣏⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⢸⡇⢀⡀⢸⠀⠀⠀⢠⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣇⣿⠀⠀⠀⢸⣗⣏⣿⣸⠀⠀⠀⢸⣇⣞⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠹⠏⣿⠀⠀⠀⢸⡿⠿⠿⢹⠀⠀⠀⢸⡯⣭⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⣤⣿⣄⠀⢀⣼⣧⣤⣤⣼⣄⠀⢀⣼⣧⣤⣤⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣼⠀⢸⣇⣀⣀⣀⣀⣸⠇⢸⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠛⠛⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠛⢁⣀⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡄⠀⠀⠈⠉⠉⠈⠉⠄⡰⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⢀⣷⡀⠀⠀⡀⣴⢶⣴⣿⣶⣄⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢸⣿⡿⠂⣤⣄⢀⣼⣿⣿⣿⣿⣷⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⢈⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⣿⣿⣿⣿⣿⣯⠀⠈⠉⠛⠉⣿⣹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡼⣾⣿⣿⣏⣿⣿⣿⠟⠀⠀⠀⢠⣇⠘⠇⠑⠁⠂⠠
⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣽⣿⢣⣾⣿⣿⣿⠏⠉⠁⠀⠀⠀⢀⠜⣿⣦⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠸⢃⣿⣿⣿⢹⡧⢀⣠⡤⣶⣶⡾⠃⠀⠈⠻⣿⡀⠀⠀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠠⠂⠀⠀⠈⢘⡟⣻⣿⡿⠟⠋⠀⠀⠀⡀⠀⠀⠀⠀⠈⠳⡀⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠙⠀⠀⠀⠀⠠⠞⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⢠⡖⠀⣀⣴⡟⢠⡾⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠐⠿⠛⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣾⣷⣶⣶⣴⣴⣶⣾⣷⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⣿⣿⣛⣿⣿⣿⣿⣿⣋⣽⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢋⣙⠉⢿⠿⠹⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⣀⢾⣿⣧⣇⢰⣷⣿⣿⣿⣯⢿⡗⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⢿⣿⣿⣿⣿⣾⣿⣿⣿⡏⠛⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠛⢷⣝⣿⣿⣿⡿⠻⠿⠎⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⠀⠀⡠⠐⠒⠀⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⣄⡘⠃⣨⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠳⢴⣾⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠄⠁⠈⠉⠁⠀⠉⠀⠄
⠀⠀⠀⠀⠀⣀⠤⠐⠁⠀⠀⣠⣀⡀⣮⡷⠀⠀⢧⣐⡠⡁⢠⣠⣤⡀⢀⣤⣔⡜⡁⠀⢈⠀⠀⠀⠀⠀⠀⢀⡘⠋⠑⠠
⠀⠀⠀⠀⠀⡇⠚⣷⣆⢠⢤⡌⣋⣵⣨⡻⡞⢠⣿⣅⡁⢳⡄⠉⠱⣤⣤⡍⠹⢼⡾⠀⣼⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⣀⣨⣟⡎⢛⣵⠳⢶⣿⣀⣢⠎⠈⠏⠀⠀⣹⠓⣶⣔⣛⣲⡶⠞⠛⠲⠏⠐⠀⢀⡀⠀⠀⡜⠃⡁⠐⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣬⣭⣤⣠⣡⠞⠉⠀⢀⡏⠠⠀⡏⠀⢌⢠⠉⣡⣈⠠⢀⠁⡸⣦⢴⡆⢣⣾⣥⣤⡶⠁⠀⡄⠄⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠶⠤⢒⣘⠾⢈⠀⢀⠔⠀⠠⠋⡨⠢⢼⡀⠀⠾⡐⠀⠈⡓⣶⣦⣶⠖⠋⡂⠀⠠⠀⠲⠀⠄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠚⠒⠈⠉⠉⠉⠉⠉⠉⠃⡠⢀⡄⠀⠠⠔⢤⡒⢠⡔⠀⠀⡠⠼⢋⣀⣀⣒⣐⣿⠀⠀⠀⠀⣇⠢⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢼⠀⠀⠀⠀⠀⢁⠴⠀⢀⠔⠁⢀⠀⠀⠀⠈⠉⡻⠀⠀⢀⢎⠀⢠⠄⡏
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠠⠆⢈⡁⠀⡠⠆⠀⠀⣤⢀⢜⠠⠄⠀⠂⠀⠀⢀⡜⠀⠀⢠⠀⠀⠁⡈⠔⢃
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠀⡀⢀⡇⠀⢀⠔⡡⢘⣹
⠀⢀⣀⣀⡀⠀⣀⠀⢤⣤⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⣠⢚⠝⡩⠞⢡⠟
⠀⣀⠄⠀⣀⣀⠀⠀⣤⣤⡤⠠⠌⢀⣈⣛⣿⠦⣤⡀⠌⠀⢀⡴⡄⠲⠤⣤⣤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⢤⣡⣪⠤⠊
⢰⠕⠊⠉⠁⠀⠀⠀⠀⠀⠁⠉⠃⠈⠀⠒⠛⠶⢢⣥⣦⡙⠖⠇⠤⠑⠂⠀⠈⠀⠉⠉⠉⠁⣀⠀⠀⠠⠔⢁⠀⠈⠾⠈⠁
⢨⣮⣐⣒⣂⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄⣀⡀⠀⠀⢫⣀⠤⡔⠁
⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣙⣛⣒⣒⣂⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⢉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣠⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⢶⣤⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠀⢀⣈⣉⣻⣿⢶⣦⣤⠀⠀⠀⠀⢠⣴⡾⣟⣛⣭⣄⣀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⡟⣿⣿⡿⢷⣆⠉⠀⠀⠀⠀⠀⢠⣾⠻⣿⣿⣉⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠷⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠋⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠻⣿⣿⣿⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⣿⣿⡏⠸⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣆⢻⣿⣿⠀⠀⡄⠰⠓⠐⠚⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠘⢷⠰⡀
⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠮⠭⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⠀⡜⠀⠀⡆⠀⠀⠀⢀⣀⢀⣀⣠⠳⠤⠴⢇⣀⣀⠀⠀⠀⠀⠀⠀⡎⠀⠑
⣿⠀⠀⠀⠙⠉⠉⠙⠁⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁⠀⠀⢈⠉⠉⠉⠻⠀⠀⠀⣿⢠⠀⠀⠀⠋⠉⠉⠙⠁⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⡉⠉⠉⠙⠄⠀⠀⢁
⣿⣄⣀⣀⡀⠒⠒⠚⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠒⠒⠀⠀⣀⣠⣿⠘⢤⣀⣀⡀⠒⠒⠚⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠓⠒⠂⢀⣀⣠⠄
⣿⣿⣿⣿⣷⣶⣶⣿⣿⠉⡱⢤⣤⣴⡂⠘⣦⣤⣤⠶⠋⢹⣷⣶⣶⣶⣿⣿⣿⣿⠀⠀⠈⠉⠓⠒⠚⠙⣏⢈⠳⠤⣤⣶⡁⢑⣦⣤⠴⢚⣉⡿⠓⠒⠒⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡦⠋⠀⠀⡀⠀⠙⡇⣰⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⡜⡉⠀⠀⠀⠀⢙⢆⣦⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠛⠀⠀⠄⠀⠘⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠋⠁⠀⠀⠈⠛⢸⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠸⠂⠀⠀⠐⠺⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢛⠁⠀⠀⠘⠏⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣷⣦⣤⣦⣴⣷⡞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣿⣷⣴⣶⣾⣿⠛⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠈⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡿⣿⡿⣿⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇⠘⡏⠸⡇⠀⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡏⠀⢸⠁⢸⠀⢹⠀⠘⡟⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠁⢀⡇⠀⠁⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢱⠀⠀⠀⡸⡀⠀⠀⠀⠁⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣦⠀⢠⣾⣿⣄⠀⢠⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡆⠀⣼⠁⢹⡄⠰⡞⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠀⢸⣿⣿⣏⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⢸⡇⠀⠀⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣸⣿⣿⣿⡀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⢠⡇⠀⠀⣧⠰⢾⡅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠠⣿⣿⣿⣿⠇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠘⣷⠀⢰⡟⠀⠈⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠀⠸⡀⠀⢠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣸⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣤⠁⠀⠀⢣⡄⠸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠲⢦⣝⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⡿⠛⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠒⢽⣧⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⡳⣽⣷⣌⢻⢦⣀⣨⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢠⡾⣱⣿⣷⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢭⣿⣿⣿⣿⠿⠛⢻⣿⣶⣤⣦⣤⣄⣤⣤⣴⡷⠿⣿⣴⣿⣿⣧⡴⠆⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠿⣿⣿⣿⣿⠋⢀⣦⣽⡿⠀⠉⠹⠏⡿⠋⠋⠈⣷⡀⠀⠙⠿⣿⢿⣷⣶⡦⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢰⣶⣾⡟⠉⠁⠀⠙⠻⢿⠠⡄⠀⠀⠀⠀⠀⠀⠀⣿⡷⠊⠰⠶⣦⡀⠉⠛⠛⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⠍⠀⠀⣀⣤⡴⠞⠳⢦⡀⠹⡆⠀⠀⠀⢠⡔⢀⡥⠶⠶⣦⣄⡀⠈⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠀⠉⠙⠻⣶⣦⢤⣾⡏⠀⣾⣷⠀⣿⣀⣿⠃⠀⠀⣾⡇⡜⢠⣶⡄⠈⣿⣿⣷⡆⠀⣐⣾⣿⣿⡷⠠⠤⠦⠤⠤⣄⣀
⠀⠀⠀⢠⢾⣾⣿⠏⠻⠷⣴⣦⠘⢾⣿⣿⣷⣌⡙⠦⠿⠿⢐⣿⣿⡏⠀⠀⠀⢺⣿⡿⢼⣿⡯⠴⢛⣥⣶⣿⣿⣶⣿⡿⠁⠀⣶⡀⠐⠶⠶⠄⠉⠷⣄
⠀⠀⢰⡇⠉⠙⣏⠀⠀⡀⢹⣄⠀⠀⠻⣿⣿⣿⣷⣾⣷⣾⠟⠛⢻⣉⡉⠉⣉⣻⠿⠻⢦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡄⠈⣷⢠⡄⢀⠀⡄⢣⢸⡆
⠀⠀⠘⣷⣤⣠⣿⣶⣼⣧⣴⣿⣤⣦⣸⣿⣿⣿⣿⣿⣟⣫⣡⣤⣄⣈⣥⣯⣍⣀⣀⣠⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣷⣴⣿⣬⣷⣿⣶⣿⣾⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣒⠀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⢟⢷⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠳⠞⢿⡟⠫⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣦⢺⣿⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣏⡡⠄⢺⣿⣿⣿⣿⣷⠹⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⡀⣀⡀⠀⢀⡾⠿⣿⣷⠀⡆
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠈⠉⠐⢴⣦⣿⣿⣿⢟⣋⠑⠢⠒⠋⠉⢐⣢⣤⡤⠶⠒⠒⠶⣖⣉⡀⠀⠀⣤⣶⣾⣷⣿⠿⢶⣶⠮⣵⣿⣯⡼⠁
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⣿⢇⣼⣿⣶⡦⠀⢰⣶⣎⠉⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢸⣿⡃⠀⠀⣠⣾⣧⡀⠀⠀⠀⣠⠟⡿⢿⣿⡿⣰⠓⣸⣿⣿⡷⠦⢴⣶⡿⠟⠋⠀⠉⠉⠁
⠀⠀⠀⠀⠈⣿⡇⠀⠰⠟⠀⠘⣿⣶⣄⣼⣵⣷⣿⡿⠿⢷⣡⣾⠟⠉
⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⠀⠀⣿⠿⠋⠀⣨⡝⠉⠀⠀⢠⣿⠏
⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠰⠋⠀⠀⠀⣸⡿⢳⣶⣦⠴⠋⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⡔⠀⠀⣼⡿⠁⠈⣿⠃⡜
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣤⣤⣀⣴⠿⠚⠂⢀⣿⡜
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠋⢉⡴⠶⠒⠀⣾⠁
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣯⠀⠀⡰⠶⠦⢤⣏⡟
⠀⠀⠀⠀⢀⣾⣭⣽⣛⣛⣿⠿⢗⠒⣒⣻⡋
⠀⠀⠀⠀⠋⠀⠀⠈⠈⠃⠛⠙⠛⠙⠙⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀
⠀⠀⠀⡇⠄⠀⠀⣾⣿⣿⣆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠘⠄⠀⢀
⠀⠀⠀⡇⠂⠀⠀⢻⠃⢹⣿⡀⠀⠤⠀⢘⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⡤⠀⠀⠀⠙⠁⠀⢰
⠀⠀⠀⡏⠀⠀⠀⠸⠓⢼⠿⠃⠀⠀⢰⠿⢻⡄⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠳⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠂⠑⣀⠀⠀⢰⣃⢎⠀⢄⠀⣨⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠧⠉⠱⠮⠀⣀⢈
⠀⠀⠀⡗⢀⠠⢀⡤⠈⠀⣟⡅⠋⠑⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢨
⠀⠀⠀⡗⠀⠀⠀⡀⠀⠈⠐⠀⠀⠀⠀⠈⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠈
⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⢁⠠⠔⠠⣀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒⠒⠒⠀⠈⠂⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢤⣄⠀⠀⠀⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢀⠀⠀⢀⡀⠀⠀⠀⠄⠂⠈⠁⠀⠀⠁⠐⢂⣀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠴⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⡾⡴⠀⠘⢵⡆⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠸⠨⠨
⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠓⠀⠀⠀⠀⠈⠉⠁⢀
⠀⠀⠀⠁⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠄⠅⠀⠀⠀⠀⠀⠨⠅⠀⠀⠠⠀⠠⠤⠄⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠛⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠛⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠉⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠂
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣘⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣙⣃⣀⣀⣀⣀⣀⣀⣀⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠋

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




⣄⣀⣀⣀⣀⣄⣠⣀⣀⣠⣤⣠⣀⣀⣀⣤⣤⣤⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣀⣠⣤⣤⣤⣤⣤⣤⣀⣠⣀⣀⣀⣠⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠔⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⢦⣤⠶⠶⠛⠿⠿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⣧⠀⠐⠿⣿⣦⡀⠀⠀⠀⠈⡹⣿⣿⣶⣄⡀⠀⠀⣀⡴⣊⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠸⡄⠈⠳⣿⣿⡹⣞⠛⠛⠉⠛⠛⢛⣿⣿⣿⣶⣾⣫⣾⠅⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁⣠⠞⠁⢠⣾⣿⡀⢙⣷⣿⣷⠙⠀⠀⠀⠀⠀⠈⠀⢡⣾⡿⣽⣿⣿⠷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠃⠀⣼⠃⠀⣰⡿⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠠⢀⡄⠀⠐⠋⠁⠘⠫⣿⡷⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢠⢏⠀⣰⣿⠁⠀⠀⣀⡤⠶⢷⣽⣶⡀⠀⠰⠋⠃⢀⣴⣶⣤⣤⠤⠜⠛⢿⡿
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⢀⣿⠏⠀⣿⣏⢀⠀⠀⣠⡦⢀⣀⣀⠻⠇⠀⠀⡀⠀⢸⣍⣀⡀⠈⠁⠀⠤⡌⢳⡄
⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⢾⣿⠄⠀⢹⣿⡁⠀⠚⡫⠿⡟⢱⣿⡷⡄⠈⠛⠁⠀⣽⢻⣿⡏⠳⠀⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⣾⡿⠀⠀⢉⣿⣿⣦⣶⣖⡀⠙⠢⠭⠾⣧⠀⠀⠀⠀⠟⠦⠭⠴⢃⡀⠀⠠⡀⢴⡿
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⡀⣿⡇⠀⠀⠁⠀⠉⠉⠙⠛⠓⠒⠶⠦⣼⣿⡀⠀⠀⢸⠀⠈⠐⠊⢉⡉⢀⠀⣿⣦⠇
⠀⠀⠀⠀⠀⣀⣈⣿⣿⣷⣼⣿⡇⢀⠀⠉⢻⡦⠤⣤⣄⣀⣀⡀⢀⣈⠉⢉⢑⠒⢿⣄⠀⣢⣶⣿⣤⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⢧⣤⣶⣤⣤⣀⠉⡿⠟⠁⠀⠀⡄⠀⠈⢢⢉⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢳⣅⢀⣷⡀⣄⣤⣄⢂⣼⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠆⣀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⣹⣇⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⢻⡆⣤⠶⠶⣤⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣸⣇⣿⠀⠀⣿⢸⡇⠀⠀⣿⢠⡶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⢹⡇⠀⣿⢸⡇⠀⠀⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⡴⣿⠀⠀⣿⢸⡇⠀⠀⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠁⢀⣠⣿⣀⣀⣿⢸⡇⠀⢀⡿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠋⠁⠈⠉⠉⠁⠀⠙⠛⠋⠁⠙⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠂⠘⠀⠀⠂⠂⠀⠂⠂⠀⠀⠐⠀⠀⡀⢠⢘⠀⠀⠀⠀⠐⠀⡄



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⡀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢹⡧⡷⢿⢿⡇⠀⡇⣿⠄⠀⠀⠀⠐⠒⠒⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣷⡀⢰⡇⠀⢰⣴⢿⣧⢰⡶⣦⠀⢶⡆⣴⣶⡄⢠⡾⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠛⢻⡿⠛⢿⡿⢸⡿⣿⡄⢹⡇⢸⣿⡏⢸⡇⣿⠃⢻⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠁⠀⢸⡇⠀⣸⡇⣼⠇⢹⡇⢸⡇⢸⣿⠁⢸⡇⣿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⡆⠀⢸⡇⠀⣿⡿⠋⠀⢿⡿⣾⡇⢸⡟⠀⣾⡇⣿⡐⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣾⡟⠀⠘⣧⡀⢹⡟⠲⠀⠘⢧⡿⠉⢸⡇⠀⠿⠇⠸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠆

⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⣦⣦⠀⠀⠀⠀⣀⢠⣤⢀⡀⠀⠀⠀⠀⣤⣠⠆⠀⠀⠀⢤⣠⣄⡤
⠀⠀⣼⣿⣷⠀⠀⠀⠀⠰⣿⣿⠆⠀⠀⠀⠐⣾⣿⡷⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠉⢻⣿⠉⠀⠀⠀⢀⡴⣾⡏⠀⠀⠀⠀⠀⣿⡟
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⢿⡀⠀⠀⠀⠀⢠⠏⢧⠀⠀⠀⠀⠀⡾⠹⡄⠀⠀⠀⠀⢰⠟⢧⠀⠀⠀⠀⢀⡟⢻⡀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠈⠀⠈⠁
⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⢠⡄⠀⠀⠀⢀⣀⣰⠆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣀⣶⢀⡀
⠀⠀⢛⣿⠑⠀⠀⠀⠀⠐⣿⡛⠆⠀⠀⠀⠀⣼⣿⡶⠇⠀⠀⠀⢨⣿⠿⠖⠀⠀⠀⠘⢿⡟⠋⠀⠀⠀⠐⢻⣿⠳⠂⠀⠀⢀⠚⣹⣟⠋
⠀⠀⠞⠙⠧⠀⠀⠀⠀⠠⠟⠹⠄⠀⠀⠀⠴⠻⠏⠙⠂⠀⠀⠠⠞⠽⠁⠀⠀⠀⠀⠴⠋⠹⠆⠀⠀⠀⠠⠞⠸⠃⠀⠀⠀⠈⠙⠋⠉⠧
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⣿⣄⠀⠀⠀⠀⢀⣼⣧⡴⠀⠀⠀⠀⠀⣰⣦⡖⠀⠀⢠⣄⣠⣿⣀⡄⠀⠀⠈⢷⣷⠞⠀⠀⠀⠀⣠⣿⠞⠁⠀⠀⠀⠀⣼⣥⠆
⠀⠐⢫⠿⡟⠂⠀⠀⠀⢋⡟⢷⠀⠀⠀⠀⠀⢋⣿⣧⡀⠀⢀⣠⠴⠿⣇⠀⠀⠀⠀⠀⣸⢿⣄⠀⠀⠀⠈⢹⣷⡄⠀⠀⠀⠀⠸⡿⣦
⠀⠀⠛⠀⠙⠀⠀⠀⠀⠘⠁⠋⠀⠀⠀⠀⠚⠋⠀⠚⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠐⠃⠘⠁⠀⠀⠀⠀⠚⠘⠁⠀⠀⠀⠀⠘⠃⠁
⠀⠀⠀⣤⠀⠀⠀⠀⠀⢰⣠⣄⡆⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢦⣴⣤⠆⠀⠀⠀⢰⣠⣦⡰⠀⠀⠀⠀⠠⣦⡴⠀⠀⠀⠀⢢⣰⣆⡖
⠀⠠⣴⣿⡦⠄⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣹⣾⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢾⣿⡁⠀⠀⠀⠀⣀⣻⡏
⠀⠀⢰⠟⡇⠀⠀⠀⠀⠸⠏⡽⠃⠀⠀⠀⢀⡼⠻⣿⠇⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⢠⠇⠟⠀⠀⠀⠀⠉⠛⠃
⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⣀⣰⠆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡦⠀⠀⠀⠀⢀⣀⣴⠀⠀⠀⠀⠀⣀⡶⠀⠀⠀⠀⠀⣀⣀⡶⠀⠀⠀⠀⢀⣀⢀⣄
⠀⠀⢡⣿⡙⠁⠀⠀⠀⢈⣿⢷⣺⠂⠀⠀⠘⢹⣟⠷⠂⠀⠀⠀⢫⣿⡛⠃⠀⠀⠀⠟⣻⣛⠛⠀⠀⠀⠘⢫⣿⡷⠆⠀⠀⠀⢻⣿⡿⠿⠃
⠀⠰⠋⠸⠇⠀⠀⠀⠠⠞⠽⠉⠉⠀⠀⠀⠤⠞⠽⠀⠀⠀⠀⠀⠾⠁⠻⠀⠀⠀⠀⠀⡝⡍⠀⠀⠀⠀⢠⠟⠽⠃⠀⠀⠀⠰⠾⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⣤⢀⡄⠀⠀⠀⠀⢠⡄
⠀⡤⢤⣼⡧⠤⠀⠀⠀⣤⣿⣶⡦⠀⠀⠀⠀⣤⣿⠃⠀⠀⠀⠀⠤⣾⡷⠆⠀⠀⠀⠀⣨⣿⠃⠀⠀⠀⢠⢾⣿⠉⠀⠀⠀⠀⠠⣾⣷⡄
⠀⠙⢻⡏⠀⠀⠀⠀⠀⠙⡟⠁⠀⠀⠀⠀⠀⢹⣟⡦⠀⠀⠀⠀⠐⠛⡿⠀⠀⠀⠀⠘⣹⢛⡦⠀⠀⠀⠀⢈⣿⠆⠀⠀⠀⠀⠘⠛⠿⠃
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⡄⣠⠀⠀⠀⣠⣀⢠⡄⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢶⠀⡀
⠀⠠⢴⣾⠧⠆⠀⠀⠀⡶⣾⠏⠁⠀⠀⠀⢷⣾⠟⠛⠋⠀⠀⠀⣴⡟⠻⠓⠀⠀⠀⢀⣤⣯⣤⠆⠀⠀⠀⡴⣿⣆⡀⠀⠀⠀⠺⣿⣏⠁
⠀⠘⠻⠛⡆⠀⠀⠀⠀⢠⣟⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡿⢻⡄⠀⠀⠀⠀⣨⡼⠻⢦⡀⠀⠀⠀⣀⡿⣄⠀⠀⠀⠀⠀⣿⢸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠡⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦
⠀⠀⠀⠀⠀⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠬⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⢀⣈⡁⠈⠀⠀⠂⠀⠀⠀⠀⠘⠀⠀⠁⠸⠁⠀⠀⠀⠀⢀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣶⡿⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠟⠛⠣⡀⠀⠀⠀⢀⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢨⣶⣤⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⣀⡠⣿⣿⣿⣿⡆⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡆⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠈⢻⠛⠁⠀⠑⢴⡿⠀⠁⢄⠢⠒⠀⠀⠀⠂⠈⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⣀⣀⣘⠀⠀⠀⡠⠎⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⠛⢋⠉⠁⠙⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⣀⣴⣶⣟⢻⡿⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⢿⢶⡶⠟⠿⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠢⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣤⠀⢘⣇⠀⠀⠀⠀⢠⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠹⣧⣩⣿⡀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣶⣀⡀⠀⠹⣿⣿⡇⠀⠀⠀⢸⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠠⠀⢹⣿⣿⠀⠀⠀⢸⡇⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⣀⡀⠀⠀⢀⠀⠀⠀⣿⣿⣧⠞⢿⣷⣵⡀⢻⣿⣇⠀⠀⢸⡇⣿⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣞⣛⣿⣿⣦⡷⣿⣿⣿⡷⠟⠛⣿⣿⡄⢿⣿⣧⡀⢸⣿⣿⠀⠀⢀⡟⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣏⣘⣿⣿⣿⣷⠀⠻⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣇⣼⣿⠏⡀⠖⢉⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡇⠈⠉⠋⠙⢻⣿⡿⣂⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡿⣿⣦⡄⠀⠀⢰⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⠿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⠀⠙⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠟⢫⣾⢿⣷⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠹⠛⠉⣕⣿⣿⣷⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠋⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣦⣄⡀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣶⣦⣀⣴⣾⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⢩⠽⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠋⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠉⡿⣿⣿⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠏⢛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢿⣿⣷⣿⣴⡄⣤⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣠⣶⣾⣶⣦⡀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠈⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣠⢿⠴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢼⢇⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⢻⣿⣿⣿⣿⣿⡿⣿⣿⢃⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢿⣿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⡀⠀⢰⡖⠒⠶⠒⠲⡆⠀⠀⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⠀⢿⣿⠂⠀⠀⠀⠀⠀⢰⣶⡆⠘⢿⣿⣃
⠀⠈⢦⣿⣿⠀⢸⡗⠒⠶⠒⢲⡇⠀⠀⠀⠀⢠⣾⣧⠀⠀⢰⣶⡄⠀⠀⢰⣿⣧⠀⠀⠀⠀⠈⠉⣵⣾⠓⠛⣿⣇
⠀⠀⢿⣿⣿⣦⠈⡷⠶⠶⠶⢾⠇⠀⠀⠀⢠⣿⣿⣿⠀⠀⢈⣿⡅⢀⣴⠟⣽⣿⠄⠀⠀⠀⠀⠀⣹⣿⡇⠀⣿⠏
⠀⠀⢸⣿⣿⠻⣄⣁⠀⠀⠀⠈⠁⠀⠀⠀⣸⣿⣿⣿⡗⠀⣾⣿⠉⠉⠀⠘⣿⡏⠀⠀⠀⠀⢰⣾⣿⣿⠇⢸⣿
⠀⠀⢸⣿⣿⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡟⠋⠀⠈⣿⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⢣⣿⣿⣿⢠⣯⣤⣤
⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⢿⠃⠀⠀⠀⠸⠷⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿
⠀⢠⣶⡄⠀⠀⠀⠀⢀⣤⣤⠀⠀⢀⣤⣄⠀⠀⠀⢠⣴⡄⠀⠀⣤⠈⢰⣿⣆⠀⠀⠀⢠⣤⡄⠀⣤⣤
⢠⣬⠛⠁⠀⠀⠀⠀⠀⠛⢛⣤⠀⢸⣿⣿⠀⠀⠀⢈⣻⣁⣤⠟⢻⣶⠟⣿⣿⠀⠀⢀⣬⠛⠁⢀⣽⣯⡀
⣿⣿⠓⠶⠐⠂⠀⠙⣛⣛⣻⣿⣇⣿⣿⡏⠀⠀⠀⢸⣿⠁⠀⠀⠀⠁⠀⣿⡏⠀⠀⣾⣿⡀⠀⠹⣿⣿⡏⠓⠒
⠙⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⣿⠉⠀⠀⣿⣿⡇⢰⣄⡀⣀⣶⡂
⠀⣿⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⠀⣿⢿⠇⢼⣿⡏⠋⠈⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠⠀⠀⠀⢠⠀⣀⡀
⠀⠀⠀⠀⠀⢀⠀⢀⣿⣧⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣀⣄⢠⡌⢧⣽⣥⠀⠀⣠⠤⠤⠤⣄
⠀⠀⠀⣿⡷⣸⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣰⠇⣻⣟⣼⠁⠐⣿⣿⡇⢠⢧⣤⣤⣤⡼⡄
⠀⠀⣴⣶⣾⠋⠛⢻⡿⢿⡟⣻⡆⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⣴⣿⣿⡁⣼⣿⣿⠁⠀⠠⣿⣿⡇⢸⡾⠿⠿⠿⢷⡇
⠀⠀⣿⣿⣿⠀⠀⠀⠃⠙⠀⠘⠁⠀⠀⠀⠀⠀⠈⠉⢺⣷⣄⠀⠐⢻⣿⣿⡇⠟⣿⣿⠂⠀⠘⠟⠏⠁⠈⠁⠂⠀⠀⠈⠑
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠠⣄⢀⠀⢠⣶⣄⠀⠶⠶⠋⣹⡟⠀⠀⠀⣿⣿⠀⠀⣿⣿
⠀⠀⠈⠟⠛⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠉⠀⠀⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣤⣤⣤⣷⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠉⠢⡀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⢸⢀⡀⢀⣀⠜⢹⡀⠀⠀⠀⠀⠀⠀⠀⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⢆⠸⡀⠀⠀⠀⠀⢨⠇⠀⠀⠈⠁⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⠤⠓⠒⠒⠻⢤⣱⡀⠀⠀⠀⡎⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡠⠊⣁⡀⠀⡠⠔⠒⠒⠲⣌⠳⡄⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡠⠴⡶⠦⢄
⠀⠀⠀⠀⢠⠎⠀⠀⡠⠤⡊⠀⠀⠀⠀⠀⠈⣆⠹⡄⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⢀⠏⢀⠀⡜⠀⣠⠃⠀⠀⠀⠀⠘⡀⢸⠀⢻⠈⠀⠈⠓⠦⡤⠤⠤⣖⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢣⠀⠀⠀⠸
⠀⣀⠤⣸⠀⠁⠀⢙⠋⠁⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠀⠀⠀⠀⠀⡱⠂⢰⣉⣄⣀⣀⣀⠀⠀⠀⡰⠃⠀⠀⠀⠣⡀
⡞⠀⠤⣸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⢁⡟⢀⡟⠀⠀⠀⠀⡈⢀⡴⠋⠀⠀⠀⠀⠀⠉⠲⣜⠁⠀⠀⠀⠀⠀⠈⠒⡺
⢧⠀⠀⠈⢧⠀⠀⠈⢧⠀⠈⠲⠤⠤⠖⢡⠞⢀⠞⡠⠂⠀⠀⠂⡼⣉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⣀⡴⠊⠁
⠈⠳⠤⠤⠞⠳⣄⠀⠀⠑⠢⠤⠤⠴⢚⣡⠖⠉⠌⠀⠀⠠⢀⠜⡁⠁⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⢳⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⡶⠒⠛⠉⠀⠀⢠⠀⠀⡐⠠⠠⠊⠠⠂⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠓⢄⡀⠀⠀⠀⠘⣀⠔⡐⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢀⡤⠒⠋⠁⠀⠀⠀⠈⡏⠑⠚⠀⠁⠴⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⢰⠋⠀⠀⠒⠠⢄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢡⣰⠋⠀⠀⠀⠀⠀⠀⠀⢙⣤⡀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠔⠋
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠓⠶⣤⠶⠿⠖⠚⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠐⠚⠉⠀⠀⠀⠀⠀⠀⣿⠈⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⠉⠉⠐⠢⣀⠀⠀⠀⠀⠀⡼⠡⠆⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠱⡄⢀⣠⠞⠀⠀⠐⡀⠀⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠞⠛⠉⠀⠀⠀⣀⠖⠁⠀⠙⠓⠒⠲⠤⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢠⣤⣼⣧⡀⠀⠀⠀⠀⠀⠒⢦⣤⡶⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣀⣼⣆⣠⠀⠀⠀⢈⣧⣤⡀⠀⠀⠀⠀⢀⠐⠶⣤⣴⡆⠀⠀⠀⣴⣧
⠀⠀⠀⢠⣿⡏⠙⠢⠀⠀⠀⠀⠀⣼⣿⠛⠒⠓⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠉⠀⣿⣧⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⠀⠀⣸⣿⡇⠀⠀⢀⣿⡏
⠀⠀⠀⣼⠛⠻⡄⠀⠀⠀⠀⢠⠾⠋⠻⣄⠀⠀⠀⠀⠀⠀⡾⢿⠀⠀⠀⠀⠀⢰⡏⠹⡆⠀⠀⠀⠀⢙⡿⣷⠀⠀⠀⠀⠀⠀⣾⣿⠟⠁⠀⠀⠘⣿⣇
⠀⠀⠋⠁⠀⠀⠹⡄⠀⠀⠴⠋⠀⠀⠀⠈⠳⠄⠀⠀⠀⢠⠃⠘⡅⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⢼⠀⠸⠆⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⢀⡀⢀⣠⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄⣀⣀⡀⠀⡄⢀⡀
⠀⠴⠒⠒⣶⣿⣅⡀⠀⠀⢀⣼⣷⠒⠋⠁⢀⡴⢿⣿⡟⠋⠛⠀⠒⠒⢾⣷⠚⠉⠀⠀⣼⣿⣏⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⣿⣿⡏⠀⠀⠘⢳⣿⡶⠤⠄
⠀⠀⠀⢠⣿⡁⠀⠉⠀⠀⢉⣿⣧⡀⠀⠀⠈⠀⢸⣿⠇⠀⠀⠀⠀⠀⢿⣯⠀⠀⠀⠀⢩⣿⣿⠀⠀⠀⠀⢰⣿⡟⠉⠁⠀⠀⢠⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⠀⣠⠏⢹⠀⠀⠀⠀⣼⠁⠈⢻⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⡾⢹⠃⠀⠀⠀⡟⠁⠙⣧⠀⠀⠀⡾⣹⠇⠀⠀⠀⠀⢸⠙⡆⠀⠀⠀⠠⡏⡇
⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠃⠀⠀⠘⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠓⠘⠂⠀⠀⠐⠃⠀⠀⠘⠂⠀⠀⠃⠉⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣤⣴⡆⠀⠀⢠⣶⣶⡶⣶⠀⠀⠀⣰⠆⠀⡀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⢣⡀⠀⡇⠀⠀⠀⠀⠀⠂⠀⠀⢹⡿⠯⠿⠀⠀⠙⠃⠈⡾⠁⠀⣠⣴⣿⠄⠀⠈⣾⣿⣹⣥⡏⠀⠀⠀⠀⢺⣴⠔⠁⠀⠀⢶⣵⠀⠀⣠⣤⣽⡿⠿⡇
⠀⠀⠀⢿⣾⣁⣤⣠⣤⠤⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⣯⣼⡄⠀⠀⠉⠀⠀⠋⠂⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠈⣿⣦⠀⢻⠈⢿
⠀⠀⠀⠀⠙⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⢺⠛⢿⠀⠀⠀⠀⠀⠀⠭⢹⡄⠛⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠀⠀⠀⠀⠀⣰⣆⠀⠸⠂⠀⠙⢦⠀⢠⡄⠀⠀⠘⡇
⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⠀⡠⣾⡷⢆⠀⠀⠀⠀⠂⣾⣏⣉⠢⠀⠀⠀⢸⣿⡿⣄⣀⠀⠀⠀⠀⣰⡿⠇⠀⠀⠀⠁⠀⠠⢶⣷⡦⡄
⢀⣀⠀⣿⡿⠷⣯⡀⠀⢀⠴⢻⡇⠉⠄⠀⠀⠀⠸⠴⠛⣷⠀⠀⠀⠀⢠⣤⣈⣹⣏⡀⠀⢀⡴⠟⠉⠀⠈⢡⠀⠀⠐⠓⠿⢛⠒⡦⢤⠆⠀⣀⣠⣾⣛⣁
⠈⠉⠙⣿⣤⣄⡀⠙⠁⠀⣠⢾⡿⠴⠀⠀⠀⠀⠛⠉⠉⢹⠉⠁⠀⠀⢰⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠨⠉⠁⠀⠀⠀⠀⠨⠆⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡿⠈⠀⠤⠄⠀⠀⠀⣆⠀⢀⣘⡥⠀⠀⡀⢸⠀⢀⣠⡤⠀⠀⠀⣀⣀⣀⡀⠤⠤⠀⠀⠀⠀⠀⣘⣀⡀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⣠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠉⠈⠉⠈⠉
⠀⣷⣶⠀⠀⠀⠀⣏⣰⡄⠀⠀⢼⢀⡄⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠤⠄
⠀⣿⡟⢆⠀⠀⠀⠘⣿⡟⠒⠀⠀⢿⣷⠃⠀⠀⢠⢿⣿⡟⠀⠀⣠⣿⣇⠀⠀⠀⢿⣿⠛⠦⠀⠀⠀⠀⢀⣀⣀⡀⠈⣻⠿⣷⣄⠀⠀⠀⠀⢀⣤⣄⡀
⢸⡟⣻⡆⠉⠀⢀⡼⣿⡇⠀⠀⠀⢸⡿⢧⡀⠀⠁⢸⡿⣧⠀⠈⢠⣿⣷⠄⠀⠠⡴⢿⡀⠃⠀⠀⢀⣾⣟⢻⠉⠁⠀⠁⠀⣾⣧⡀⠀⠀⠀⢠⣫⣿⣿⣀
⠀⡇⠀⠀⠀⠀⠋⠀⠹⠖⠂⠀⠐⠾⠃⢘⠁⠀⠀⠈⡇⠉⠀⠀⢸⠀⠋⠀⠀⠀⠙⡎⠳⣄⠐⠛⠛⠋⠉⠰⠀⠀⠀⠀⠀⠀⠈⠛⠷⠠⠆⠘⠈⠈⠟⠙
⠀⠘⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢠⠶⣾⣧⠀⠀⠀⢀⣼⣇⠆⠀⠀⠀⢀⣼⡄⠀⠀⠀⣿⡀⠀⠀⠀⣤⣼⡇⠀⠀⠀⣺⡇⠀⠀⠀⣼⣧⡀⠀⢀⣼⣧⡀⠀⠀⢀⣀⣾⠀⠀⡄⣷⣀
⠀⠃⣼⣿⠃⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⢻⣿⡗⠀⠀⠠⣿⡟⠀⠀⠐⣼⡿⠃⠀⠀⠀⣿⠏⠀⠀⠘⣿⣏⡃⠀⠙⢾⣿⠁⠀⠀⠙⣿⡿⠀⠀⠘⣿⡏⡇
⠀⠠⣿⠏⠀⠀⠀⣀⣼⠟⠙⢷⠀⠀⠀⣸⡿⡇⠀⠀⢰⡟⡇⠀⠀⠠⣿⠃⠀⠀⠀⢸⡟⣷⡀⠀⠀⣿⡿⠀⠀⠀⢸⣟⠀⠀⠀⢠⡿⢧⠀⠰⡞⠛⢿⡉
⠀⠰⠁⠀⠀⠸⠋⠉⠀⠀⠀⠘⠆⠀⠈⠀⠀⣇⠀⠀⠀⠧⢹⠀⠀⠘⠃⠀⠀⠀⣰⠛⠎⠁⠀⠀⠀⠀⠇⠀⠀⠠⠏⢻⡀⠐⠊⠉⠀⢉⠀⠀⠷⠀⠀⠉⠲