Squiggly arrow Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⡄⠁⠀⣳⠄⠀⠀⠀⢀⣀⠄⠰⠀⠀⠀⠀⢠
⠀⠀⢠⣶⠿⠿⠿⠯⠿⣷⣶⡟⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⠃⢸⠇⠀⠀⠀⠀⠀⡠⢫⠌⠀⠀⠀⢀⣾⣷⠖
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⠬⠼⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢰⣶⣿⠋
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣰⠖⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁
⠀⠀⠐⠞⠂⠀⠁⣀⣤⠞⠃⠂⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠔⠦⡀⡀⠀⡀⠀⠀⠀⠀⠀⠴⣦⠄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠠⠁⠚⠑⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⡠⠀⠀⠀⣮⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠋⠀⠀⢠⠀⠀⠺⢶⡆⠀⠀⠀⠿⠿⠿⠿⠿⠿⣿⣿⠟⠁⠀⢀⡔⠀⠀⠀⠀⠤⡄⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⡎
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣀
⠀⠀⠀⠺⢿⣿⡷⠶⠶⠶⠶⢶⠄⠀⠀⠀⠀⠀⢾⣿⣿⣷⠀⠀⠀⠀⠀⠠⢿⠄⠀⠘⣆⠀⣸⠉⣨⠇⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⠊⠁⠀⠀⣠⠖⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠖⠋
⠀⠀⣲⣶⡤⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⡠⠀⣀⣀⠀⠀⠀⠀⣠⠈⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢿⡄⠀⠀⠀⠈⠧⠀⠀⠀⡔⢁⠔⠒⠢⡀⠑⡄⠀⠀⠀⣴⠥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡚⠛⢻⡆⠐⠳⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠄⠄⢁⠇⠀⡇⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⡘⢷⣤⠌⡸⠃⠀⠀⠀⠀⠀⣤⣤⡀⠀⠓⠂⠒⠂⠁⢀⡴⠁⠀⢠⣴⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⣿⠟⠧⠤⠤⠤⠖⠒⠊⠁⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⡤⠄⡀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡄⠀⠀⠀⡞⠁⠈⢂
⠀⠀⢀⡏⠀⣀⠞⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⣀⠰⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠃⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠸⡆⠈⠁⠀⠀⣀⠔⠁⠀⠀⠀⢀⡔⠉⠀⠀⡇⠀⠀⠈⠐⣸⠄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠘⠠⠤⠤⠚⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠤⢀⣶⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡞⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡠⠃⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠇⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠱⠔⠊⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⡔⠂⠂⡄⠈⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠃⢀⡇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠈⠀⠠⠴⠊⠀⠀⠀⠀⢣
⠀⠀⠀⣀⠤⠤⠀⡁⠀⠀⠢⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡇
⠀⠀⡼⠁⢀⡀⠀⡈⢆⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡀⠀⠀⠀⠀⠰⠇
⠀⠀⡇⠀⢇⠀⠰⠃⡸⢀⡼⠁⠀⠀⢠⠔⠒⠀⢸⡂⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠃
⠀⠀⠐⠄⠀⠁⠀⢉⡤⠊⠀⠀⠀⠀⠱⠀⠀⣀⠜⢳⠀⠀⠀⡏⠀⠰⣤⢒⠀⠀⠄⠀⠀⠀⢸⠁⠀⠀⡠⠤⠤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢇⠀⠀⠁⠀⠀⠀⡸⠀⠀⠀⡟⠀⠀⡎⠀⠀⠀⠀⢰
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠀⠀⠀⠀⢠⢀⡏⠀⠀⠀⠈⠂⠀⢀⡀⠤⠚⠁⠀⠀⠀⢻⠀⠀⠐⠀⠄⠀⠀⣸
⠀⠀⠀⠀⠀⠢⡀⢀⠴⠊⠁⠐⠃⠀⠀⠀⠀⠸⡾⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⣠⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋
⠀⠀⠀⢀⡞⠁⠀⢸⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⣀⡠⠤⠤⠤⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠸⡀⠀⠀⡸⠀⠀⢀⡠⠒⠉⠀⠀⠀⢀⡴⠊⠉⢢⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠐⠋⠀⠀⠀⠀⠀⠀⠺⢀⣀⡀⠜⠀⠀⠀⠀⠀⠑⠠⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠤⠄⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⢠⡶⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠙⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⡾⠀⠀⢻⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⡇⠀⠀⣼⠀⠀⠀⠀⠀⢰⡇⠀⠀⠒⢺⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡀⢀⡿
⠀⠀⠀⠀⠀⢿⠀⢠⡏⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢿⡘⠀⠀⢀⣼⠃⠀⠀⣠⠀⠀⠀⠀⡀⢹⡆⡀⠀⠀⠀⠀⣧⠀⠀⠠⣶⣿⠶⠛⠁
⠀⠀⠀⠀⠀⠘⣧⡾⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⠛⠶⠶⠛⠁⠀⠀⣠⠏⠀⠀⠀⠀⠙⣾⡿⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀
⠀⠀⠀⠀⢀⡾⠁⠹⣆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠛⠀⠀⢤⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢱⡟⠆⠀⠀⠀⠀⠀⣀⡤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣤⡀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⡈⣧
⠀⠀⠀⠀⣠⠖⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⣾⢁⣀⡀⠀⠀⠀⠀⠀⣠⠶⠋⢽⠋⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢳⣿⠶⠂
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⢹⣟⣁⣹⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣦⠀⠀⠀⠀⢻⣄⠀⠀⠀⠈⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣾⠈⠉⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠙⠷⢤⣄⡀
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣠⣤⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠙⢦⣽⡄⠀⠀⢀⡏⠀⠀⠀⠀⣼⢧⣀⡿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⠀⠖⠛⠓⠀⢀⡾⠁⠀⠀⠀⠀⢿⡀⣉⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⣳⣿⡄⠀⠀⠀⠀⠀⠀⠈⠛⠲⠆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⣀⣤⣴⣶⡷⠀⠀⠀⠀⠀⠤⢐⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡶
⠀⠀⠀⣀⡴⠚⡹⢃⣠⣶⠿⠟⢋⡽⠋⣀⣤⣦⣠⣤⣶⠿⠟⠋⠁⠀⠀⠠⠔⠚⢛⣻⢟⣉⣠⣤⣶⣶⠿⠿⡛⠻⠭⠍
⠀⠀⠀⠁⠀⣴⢷⣿⠯⠀⠀⠀⠟⠚⠉⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⢀⣀⣤⠴⢖⡿⠟⣁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⢀⢠⣢⣴⣶⣗⣠⣤⣶⠿⠟⠋⠀⠀⢀⡠⢴⣖⠚⢉⡵⢋⣤⠶⠞⠋⠉⣠⠖⣉⣤⣵⠶⠚⠋
⠀⠀⠀⣠⠴⠖⠛⠋⣽⢏⣠⡶⠟⠉⠐⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠐⠊⠁⢀⣴⡿⠚⠉⠀⠀⠀⣠⡾⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆⠀⠀⠀⠀⢀⣀⠤⣂⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⣾⡆⣾⣸⠃⠀⣠⡤⢠⠖⠁⣀
⠀⠀⠀⠀⢀⣠⠀⢀⣠⡶⢛⡿⢋⣤⣶⠀⢀⣰⣽⣶⡿⠛⠁⠀⢀⣀⠀⠀⣄⠈⡟⢷⡀⣿⡅⠃⣿⣠⣾⡟⢁⣡⣶⠿⠋
⠀⠀⠴⢚⡝⣡⠴⡿⠃⣴⡿⠟⢋⣼⣷⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⣬⣍⣒⡈⠳⣿⠈⠻⣿⠀⢸⡿⢫⣿⣶⠟⢋⣡⡴⠆
⠀⠀⠀⠾⠋⠁⠈⠀⠀⠈⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠈⠁⠀⠙⠀⠀⠀⠿⠋⠁⠚⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⢿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⣿⣿⣿⣿⣟⣵⣿⣯⣾⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣻⣿⠇
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠾⠿⠿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣛⣻⡿⣿⣟⣿⠿⣿⣿⡏
⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣷⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⡿⠶⠛⠋⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣍⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢿⣿⢿⣿⠛⠛⠶⢦⣄
⠀⠀⣠⣾⠟⢻⣧⡙⠀⠀⠀⠀⠀⠀⠀⣿⠙⠿⠟⠀⠀⠀⠀⠀⢠⡞⠁⣿⡇⠙⣷⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢸⣇⣠⣿⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠉⠁⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢿⣿⠟⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢰⢀⡟⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⣰⡿⠃⢀⣴⠿⠿⢷⣦⣄⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠸⣿⣤⣴⠆⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣀⣽⣧
⠀⠀⠀⠀⠀⣸⠏⠀⠀⢸⣿⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⢤⣤⣤⡄⠀⠀⠈⠙⠓⠂⠀⢠⡀⠀⢀⣀⠀⠀⠀⠀⣼⣿⣿⠙⠂⠀⠀⠀⠀⠀⠀⠈⠙⠋⢡⡿
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠹⢷⣤⣀⠀⠀⠀⠀⠀⣀⣀⣤⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣏⣹⡇⠀⠀⠀⠉⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠉⠙⠛⠛⠿⠟⠛⠛⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣰⣦⡀⠀⠀⠀⠘⠻⣶⣤⣄⣀⣀⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣠⣴⠶⠿⠶⢶⣤⡀⠀⠀⠀⠀⠼⠟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠈⢳⣄⣠⠴⢦⡀⠀⣠⡶⠛⣿⠃⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣨⣿⣿⠟⠛⠿⣶⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠠⣀⠀⣀⡉⠁⠀⠀⠀⠀⠸⣟⠛⠛⠀⢠⡟⠀⠘⠃⢀⣠⣴⣿⣤⣄⠀⠀⠀⠀⣼⡏⠀⣿⡇⠀⠀⠈⢿⡆⠀⠀⠀⢰⣿⣿⠿⢿⣶⡄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢀⠀⠙⠦⣤⣤⠞⠁⠀⠀⣰⡿⠋⠸⣿⡈⣹⡇⠀⠀⠀⠘⠿⠾⠛⠀⠀⠀⠀⣸⡇⠀⢠⡏⠸⠿⠿⠶⠀⠙⣿⡀⠀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⣀⠸⣿⣠⣿⠁⠀⠈⢳⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⡿⠁⠀⠈⢿⣤⣀⣀⣀⣠⡾⠋⢠⣆⣴⣿⣡⣤
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠃⠀⢠⣤⠶⣿⣄⡀⠀⠀⠀⠹⣧⠀⢰⡟⠉⠹⣧⠀⠀⠀⠀⠀⠀⢀⣿⣃⣴⡿⠁⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠘⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣅⣠⡿⠉⠛⢷⣄⣸⣆⠙⢷⣬⣿⣤⣼⠏⠀⠀⠀⠀⣠⠄⠿⣿⣿⡋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⡀⠉⠁
⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠈⠉⠉⠀⠀⠀⢠⣬⣿⣿⡀⠀⠈⠉⠙⠿⣶⣦⣴⠶⠟⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣨⣿⣿⡿⠀⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠶⣦⡀⠀⢀⡾⠋⠘⠿⠃⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⣿⣴⠶⠶⢶⣄⠀⠀⢤⡴⠶⣾⣿⠀⠀⠀⢀⡴⠖⠛⠋⠉⠉⠉⠉⠉⠛⣓⣠⣤⡤⠀⠀⠀⣠⡾⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⣠⡄⢠⡿
⠀⠀⠀⠀⣴⡟⠻⢶⣤⣴⠟⠀⠀⠀⢀⣾⢿⣏⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢷⣄⠀⠀⢰⣏⠠⣤⡀⠘⣧⡀⠀⠀⠀⠀⢼⣿⣴⡟⠁
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠘⠟⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⣿⡇⠀⠀⢹⣷⣿⡇⠀⠈⠙⠛⠶⠒⠀⠈⠙⠛⠋
⠀⠀⠀⠀⢘⣷⣾⠿⠿⢿⣶⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⡀⠀⠀⠀⣀⣠⣴⠟⠀⠀⠀⠀⢀⣈⠁
⠀⠀⠀⢀⣾⠏⠛⠷⣶⣾⡿⠃⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠉⠉⠙⠛⠛⠉⠉⠀⡄⠀⢀⣤⠞⠉⠉⠳⢦⣀⣀⣴⠶⠿⠶⣶⣤⣄⣀⣳⣄
⠀⠀⠀⢸⣿⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⡾⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⢀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠛⣻⣿⡿⠃
⠀⠀⠀⠀⢿⣧⡘⣿⣇⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⣷⡀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⡀
⠀⠀⠀⠀⣀⣻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣦⣤⣬⣿⣶⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡟⠿⠶⢦⣤⣀⣤⡴⠖⠋⠉⠙⠒⠶⠤⠤⠞⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠛⠛⠿⠶⠿⠟⠃⠀⠀⠀⠀⠈⠁

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠤⢤⠀⠀⠀⠀⠀⠀⣤⣴⣶⡶⠀⠀⠀⠀⠀⠀⢀⣐⣦⣄⠀⠀⠀⠀⡰⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠊⠁⠀⡴⠋⠀⠀⣀⠤⠒⠋⠉⠟⠉⠀⠀⠀⠀⠀⣠⠞⠉⠀⠟⠁⠀⠀⢀⡼⠁⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⣽⠳⣄⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⣼⠁⠀⠀⢿⣄⣽⠀⠀⠀⠀⣾⠃⣀⢤⠀⠀⠀⠓⢄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⡇⠀⠀⣏⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⢀⡜⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢈⢷⡚⠓⢦⠀⢀⡇⠀⠀⢸⡇⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⡇⠀⠙⠒⠚⠁⠸⠃⠀⠀⢻⡷⠀⠀⠀⠀⢀⠤⠒⠂⢤⡇⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⣿⠠
⠀⠀⠀⢶⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣠⠴⠋⠈⢆⠀⠀⠀⠀⣴⢾⠂⠀⠈⠛⠇
⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡄⠀⠀⢰⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠃⠀⠀⠀⠀⠀⡠⠚⠋⠹⠿⠶⠀⠀⠀⢸⠃⠀⠀⣿⠀⠀⠀⠀⠀⢴⣿
⠀⠀⠀⡄⠀⠀⣠⠞⠁⠀⣀⣤⣤⣤⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠑⠤⠞⠁⠀⠀⠘⠁⠀⠀⠀⡠⠤⡀⠀⠀⠀⢀⣤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⠆⠀⠠⠊⠀⠀⢸⡀⠀⠀⠼⢻⡷⠀⠀⠀⡐⠛⢷⠀⠀⢠⡶⢶⡀⠀⠀⢸⡇
⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⣧⠀⠀⠀⠸⣇⠀⢀⣼⠁⠀⢸⣧⢀⡍⠁⢨⡅⠀⠀⣿⠁
⠀⠀⠀⠀⢀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢠⡞⠀⠀⠀⠀⣹⣄⠀⠀⠀⣰⠖⠶⢤⡀⠀⠀⡀⠀⠀⠀⠀⣠⣤⠄
⠀⠀⠀⢀⡁⠀⠀⠀⠀⠙⠃⠀⠀⠘⠋⠀⠀⠀⢧⠀⠀⠈⠉⠛⠋⠉⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠸⢏⠂⠀⠀⠀⡼⠀⠀⠀⠠⡆⠀⠀⠀⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⡿⡗⠀⢰⠉⠀⠀⠉⠉⡧
⠀⠀⠀⠀⠈⠓⠦⠴⠚⠁⠀⠀⠀⠀⠙⠢⠤⠚⠀⠀⠀⠈⠑⠲⠤⠤⠶⠒⠋⠀⠀⠀⠈⠓⠤⠤⠄⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢰⡧⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⢰⣦⠒⠉⠉⠉⠉⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠝⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡴⠋⡤⠊⠀⠀⠀⠀⢀⠤⡄⢀⠖⠉⣇⡴⠋
⠀⢠⣆⣀⣀⣀⣀⣀⣀⣰⡄⠀⠀⢰⣤⠒⠒⠉⠉⠒⠒⣴⡆⠀⠀⡰⠋⠰⠊⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠛⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⢰⡖⠤⠄⠀⡠⢤
⠀⠀⣤⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡾⡖⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠝⠃⠀⠀⠀⠃⠈⠢⢄⣠⣥⠞
⠀⠀⠋⠙⠢⢄⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⢢⡔⠋⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⣏⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⣀
⠀⠀⣄⡤⠒⠉⠈⠓⠤⣀⠀⠀⠀⠀⣀⡔⠁⠈⠒⠤⣀⡀⠀⠀⠐⠁⠀⠀⠀⠀⢀⣀⣀⡤⠂⠀⠀⢀⠔⠚⠋⠒⣤⠤⠤⢤⡀
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡊⠁⠀⢸⣱⠀⠀⠀⡏⠀⠀⠀⢸⣨⠂⠀⠀⠈⢣
⠀⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠒⠒⠆⠀⠀⠀⠈⠉⠑⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⠷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣶⠤⢄⣀⠀⣀⣀⣀⡀⠀⠀⠀⡀⠀⡤⣄⠀⡤⣀
⠀⠀⠓⠀⠀⠀⡷⠀⠀⠑⠢⠤⡷⠀⠀⠀⠀⠐⠠⢀⡷⠀⠀⠘⠦⠬⡷⠀⠈⠀⠀⠈⠙⠧⠈⠧⠘⠆⠀⠺⠗⠒⠃⠀⠉⠃⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⡤⠠⠤⠠⠤⠠⡄⠀⣠⠔⠂⠒⠲⣄⠀⠀⢸⠉⠉⠉⠉⠉⡇⢰⠀⠀⡰⠋⠀⠀⠀⠈⠳⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠈⡆⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⢰⡇⠀⠀⠀⠀⠀⠀⡇⢠⠀⠘⠒⠒⠒⠒⠂⠺⡗⠒⠒⠚
⠀⠀⡇⠀⡀⠀⠀⠀⡇⠈⢆⠀⠀⢀⠀⡰⠃⠀⢸⠀⢴⡧⠤⠤⠇⢸⠀⠀⢧⠀⣶⣂⣀⡠⠞⢀⠎⠀⠀⣀⠤⠤⠀⠒⠂⠠⠤⢄⡀
⠀⠀⠁⠘⠗⠒⠒⠒⠁⠀⠀⠑⠀⠻⠎⠁⠀⠀⠸⠤⠤⠥⠤⠤⠤⠼⠀⠀⠀⠑⠦⠤⠀⠤⠔⠁⠀⠀⠈⠢⠤⢄⣀⣀⢠⡆⠤⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠰⡶⠄⠀⠀⠀⠀⠀⠀⠸⢫⠁⠀⠀⠀⡰⠉⠀⠙⣴⠋⠀⠙⣦⠋⠀⠉⢆⠀⢀⡠⠋⠃⠀⠀⠀⣀⢿⠆⠀⠀⢀⡠⣵⠄
⠀⠀⣤⣀⣀⠃⣀⣠⣄⠀⣦⡒⠢⡠⠊⠀⣀⡀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠛⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣀⡔⠁⠀⢀⠤⢲⠓⢄⠁
⠀⠀⠙⠀⠀⡆⠀⠘⠁⠀⠀⠀⢠⠆⠈⠒⠊⠃⠀⡏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠓⡄⠀⡿⡀⠀⠀⡎⠀⠈⠦⡤⠃
⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠨⠾⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⣦⠀⢴⡦⠤⠤⠤⠤⠤⠴⠁⠘⠧⠃⠀⠀⠘⠦⡀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⣀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠢⡀⠀⠀⠘⣧⡇⠀⡗⠃⠀⡀⠀⠀⡒⠀⠀⠀⠀⡸⡄⠀⢸⢎⠀⠀⠶⡁⠀⢸⢈⠀⠀⢿⡇⠀⠀⠀⡃⡀⠀⢰⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣤⣤⡄⠀⠀⢀⣠⣤⠴⠤⣤⡀⠀⠀⢸⣍⣻⠀⠀⠀⢀⣤⠶⠚⠛⠳⣄⠀⠀⠀⠀⠿⢿⡃⠀⠀⣠⡼⣿⡆
⠀⠀⠀⠀⠹⠟⠳⠶⠛⠋⠁⠀⠀⢀⣈⣙⠳⠶⠶⠟⠛⠛⠛⠛⠉⠀⠀⠀⢀⠀⠈⠀⠀⣶⣶⢀⣼⠃⢠⡾⠉⠸⠋
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣏⠁⠉⢻⡄⠀⠀⠐⠦⣄⣀⣠⣟⣷⢀⡇⠀⠐⠶⠶⠛⠛⠋⠁⠀⢸⡁⢀⡶⠛⣶
⠀⠸⣿⠷⠄⢀⡔⠀⠀⠀⡟⠀⢿⣬⡇⢀⣀⡇⠀⠀⣀⣠⣤⠉⢹⡏⢁⠸⡇⣀⣤⣀⠀⠀⢠⡏⠀⠀⠈⢷⣼⣇⣠⠟
⠀⢰⠟⠀⠀⢸⠀⠀⠀⠀⢷⡀⠀⠀⠀⠘⣿⣷⠖⠀⣠⠞⣿⠀⠰⣷⡿⠀⣿⠯⠤⠜⠀⠀⢸⡷⠛⠳⣦⠀⠘⣯⠁
⠀⠘⣧⠀⠀⢸⣶⠞⠳⣦⠀⠙⢦⣤⣀⣀⡀⠀⢀⡞⠁⠀⠉⠀⠀⠈⠁⠸⣇⠀⠀⠀⠀⠀⢼⠻⢦⡴⠟⠀⢠⡟
⠀⠀⡾⠀⠀⡿⠉⠓⠶⠋⠀⠀⠀⠀⠈⠁⠀⠀⣾⠀⠀⢀⣀⠀⠐⢄⠀⠀⢻⣆⠀⠀⠀⠀⠘⢷⣄⣀⣀⣴⠟⠁
⠀⠘⠧⠀⠀⡇⠀⣀⣤⡤⠀⢀⣠⣴⣶⣤⠀⠀⢻⡀⠀⣿⠈⡷⠀⢸⠀⠀⠀⠙⠻⢶⣬⣷⣄⠀⠈⠉⠉⢀⡴⠖⠂
⠀⠀⠀⣀⣀⣷⠀⢿⡿⠶⠶⠛⠉⠀⢀⣿⠃⠀⠈⠛⠶⠼⠿⠷⠖⠋⢀⣀⡀⠀⠀⠠⡾⠟⠉⠀⠀⠀⠀⣿⣴⢦⡄
⠀⢠⡾⠉⠉⣿⢷⡄⠀⠀⠀⢠⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡟⠉⣷⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⡟⠷⡶⠟
⠀⠈⠿⣤⡾⠃⠈⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⣤⡄⠀⢸⡏⣹⠀⠀⢻⣴⠏⠀⠀⣾⠉⡇⠀⣠⠇⠀⠘⣇⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢹⡇⢠⡄⢿⣤⡶⢦⡄⠀⢹⡟⠳⠶⠶⠟⠳⠶⠶⠛⠙⠳⠦⠤⠾⠛⠛⠋⠁⠀⠀⠀⣹⠿⣥⣀⣨⡿
⠀⠀⠀⢄⠀⠀⢀⢸⣇⣿⠃⢸⣿⣤⣤⠟⠀⠀⠀⠀⢀⣠⡤⠶⣶⣶⡟⠛⠲⣄⠀⠀⠀⠰⣠⡖⣶⠀⠀⡏⠀⠀⠉⠁
⠀⠀⠀⡤⢷⣄⠀⠻⣿⠇⠀⠀⠻⣆⠀⠀⠀⡴⠋⢹⡟⠳⣄⠀⠻⢶⠟⠀⠀⣘⣇⣀⠀⠀⢻⡉⠁⠀⢀⣿⡖⠲⣦
⠀⠀⠀⠓⠊⢈⣷⡤⢤⣄⣤⠀⠀⠈⢳⡄⠀⠀⠀⠘⠷⠴⠏⢀⣴⠟⣷⠀⠀⠹⠟⠉⠀⠀⢈⣿⠀⠀⡟⠀⠙⠛⠋
⠀⠀⢠⠆⠀⠻⠾⠃⠀⠘⠿⠆⠀⠀⣸⠇⠀⣠⡴⠶⠶⣤⣄⣾⣁⣴⠟⠀⠀⠀⢰⣾⣇⠀⠸⣧⡀⠀⣷⢠⡆
⠀⠀⢸⡀⢀⣤⠶⢦⣄⠀⠀⠀⠓⠛⠁⠀⣰⣏⣀⠀⠀⠀⠈⠹⣯⡀⠀⠀⠀⣀⣼⠋⢿⠀⣠⣼⡇⠐⠾⣿⠃
⠀⠀⠀⣷⣏⠀⠀⠀⣹⠆⠀⠀⠀⠀⢠⠞⠻⣏⠙⣧⠀⠀⠀⠀⠈⠛⠛⠞⠛⠋⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⣿⠈⠙⠒⠚⠉⠀⢀⣀⠀⠀⡟⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀⣤⠶⠚⠲⢶⣤⣤⣤⣤⣼⣶⡄
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠴⣿⣿⠀⠀⣧⠀⢠⡶⣦⠀⠀⠀⠀⡞⠉⠀⣾⠛⡆⠀⢠⡟⢷⠀⠀⠀⣾⠉⣷⠀⠀⠰⠟⠁
⠀⠀⠀⠀⠙⠳⠶⡶⠶⠟⠉⠿⠀⠀⠙⢦⣘⣧⣼⡀⠀⣀⡀⠀⠀⠀⠙⠞⠃⠀⠈⠛⠛⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⡴⢆
⠀⠀⠀⢨⡗⠓⠀⠀⣠⠴⠚⠉⠀⠹⠂⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⢼⣀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⢀⠎⠀⠈⠳⡀⠀⠀⠀⢀
⠀⠀⠀⠘⠁⠀⣠⠞⠁⠀⠴⠆⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⠆⠀⠀⠀⠀⠈⠀⠀⡖⠒⠐⠀⠐⠊⠁⠂
⠀⠀⠀⠀⢀⡞⠁⠀⠰⠆⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⢴⠁
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⣠⠴⣾⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠉⠒⣦⠀⠀⠀⢿⠀⠀⠠⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⣴⠞⠁⠃⠀⡀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠶⢥⠀⠀⠀⣸⠀⠀⠀⢠⠟⠂⠀⠀⡇⠀⠀⠀⡀⠿⠃
⠀⠀⠀⠀⠀⠛⠷⠶⠶⠟⠋⠁⠀⠀⣠⠞⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠙⢿⠁⠀⠙⠶⢤⡄⠀⠂⠀⠐⠉⠉⠱⡀
⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⠄⠀⣠⠞⠁⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⢠⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣠⢺⢿⠀⠀⣠⣮⠔⠋⠀⠀⠀⢶⣄⣾⣿⣿⣿⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⠦⠤⡄⠀⠀⠀⢀⠴⡺⠛⢦
⠀⠀⠘⠁⡎⠘⠂⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠈⢧⡀⠀⠀⠀⠀⢀⡜⠁⠀⢀⡔⢁⡴⠁⠀⡿
⠀⠀⠀⢰⠇⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⢸⣿⣿⣿⣿⠟⠉⢀⣤⣶⠀⠀⢀⠔⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠳⢄⠀⠸⠖⠋⠀⠀⡼⠁
⠀⠀⠀⢸⠀⢀⠔⢠⠇⠀⠀⠀⠀⠱⡄⢸⣿⠿⠋⠁⠀⠀⣨⠞⠉⠁⠐⢧⣤⡀⠀⠀⠀⠀⠀⢈⢻⣦⡀⠀⠀⡼⠀⠀⠀⢀⣴⠞⠉⢳
⠀⠀⠀⣿⠀⡎⠰⠁⠀⠀⠀⡤⢤⣠⠇⠈⠁⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⢸⣿⡏⠛⠋⠀⢿⡷⠀⠀⢠⡿⠋⠀⠀⡸
⠀⠀⠀⣿⠀⢧⡘⢢⡀⠀⠀⠓⣺⠃⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⠒⠶⢦⡀⢠⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⡟⠀⠀⣱⠀⡱⠀⢀⣰⢃⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠁⠀⢰⠡⡊⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠀⠀⠙⢷⣶⣶⣤⣤⣼⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⢀⡏
⠀⠀⠀⠀⠀⠈⢢⠈⣷⠀⠀⠀⠀⠀⡜⠁⠀⠀⢀⣮⠴⠚⠉⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⣿⡞⠁
⠀⠀⠀⠀⠀⣀⠠⠃⠧⣤⠀⠀⠀⣷⠖⠀⠀⠀⠙⠓⠀⠀⢀⣠⠖⠹⠃⣀⣤⠤⠤⣄⠀⠀⠀⠀⣀⡐⣶⡶⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⠈⢆⣠⠞⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⣠⠖⠋⠁⠀⠀⠀⣈⡷⠖⠋⠉⠀⠐⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢁⡠⠔⠊⠉⠉⠉⠓⠦⠤⠖⠊⠁⠀⠀⣠⠞⠁⠀⠀⠀⢀⡴⠋⣱⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠗⠀⠀⢀⠔
⠀⠀⠀⠀⢀⡠⠚⠁⠀⢀⡠⠖⣶⠀⠀⢀⣀⠤⠂⠀⠀⡴⠁⠀⠀⠀⠀⢠⠋⣀⡴⠃⠀⣠⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⢀⡔⢁⣀⣀
⠀⠀⠀⠀⠈⠀⢠⣾⡴⠋⠀⠀⠓⠒⠊⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠀⣿⠂⠀⣠⣾⠟⠋⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠤⢤⣄⣀⢤⡀⠀⠀⠀⠀⠠⠾⠷⠒⣰⠆⠀⠀⠀⣿⣤⣾⠟⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⠿⠄⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⢹⣿⠿⠿⠛⠛⠃⠀⠀⠀⠀⣸⠶⠕

⠀⠀⠀⢀⡴⠆⠀⠀⠀⠀⢀⠤⠒⠚⠉⠉⠓⠒⠤⣤⡄⠀⠀⠀⠀⠀⠀⠠⢶
⠀⠀⠀⡎⠐⡄⠀⠀⢰⣶⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢠⠄⢣⠀⠀⠀⠀⠀⣀⢤⣤⠒⠒⠢⢄⣠
⠀⠀⠀⠳⠤⠃⠀⠀⠈⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠰⡉⠙⠋⢱⠀⠀⠀⠑⠤⠚⠀⠀⣠⠔⢾⢄⠸⡀⢱⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠰⡷⠦⢄⠀⠀⠀⠀⢘⠄⠀⠀⠀⠈⠉⠉⡞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⢄⡣⠈⠉
⠀⠀⢠⠒⢢⠀⠀⠀⠀⠀⠸⠏⠑⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⢇⠀⢰⡦⠀⠀⠀⠀⠀⠑⢄
⠀⠀⢸⠀⠀⡇⠀⠀⠀⡠⢄⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠈⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢤⡀
⠀⠀⠈⠀⠀⠣⣀⡠⠊⠀⠀⠑⠚⠛⠀⠀⠀⠀⡸⠁⠐⠋⠀⠀⠀⠀⠀⠀⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠰⡥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⢠⠋⣹⡖⠒⠒⠤⠤⠶⠆⠀⠀⠉⠉⠀⠀⠀⡎⠉⠙⢢⡀⠀⠀⣀⠘⣆⠀⠀⢠⠊⠉⠑⠂⠀⠀⠈⠆
⠀⠀⣤⠄⠈⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠠⢄⠀⠀⠣⣠⠀⠀⡇⠀⠀⠙⠉⠉⠀⠀⠸⣄⡄⠀⠀⠀⠀⠿⠂
⠀⠀⠁⢱⠀⣀⠤⡀⠀⣀⢤⡀⠀⠀⠸⠄⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⡷⠁⠀⠈⡞⠁⠀⠈⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⠀⠀⠀⣠⣤⠴⠊⢀⠤⠢⣄⠀⠀⢘⣴⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠐⠉⠉⠣⡜⠁⠱⣴⠁
⠀⠀⣠⡟⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠈⠢⠤⠤⠔⠋⠀⠀⠀⠀⣠⠀⠀⠀⠀⠠⣴⡀⠀⠀⠀⠀⠀⠀⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠈⣧⠞⡇⢀⠜⠁⠁⠀⠀⠀⠀⠀⢀⣄⡠⠃⠀⠀⠀⠀⢴⠦⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⠤⠊⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠑⢲⠄⠀⠀⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠒⠒⠊⠉⠉⠒⣴⠊⠁⠊⠀⠀⠀⠀⠀⠀⢀⠀⣰⠄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠠⠮⡁⠀⠀⠀⠘⠦⣀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⡀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⢀⣠⠀⠀⠀⣀⣴⡾⠻⣷⡄⠀⢀⡴⣷⠀⠀⠀⠀⢀⣀⣀
⠀⠀⡆⠀⠰⠉⠙⠲⠶⠞⠁⠀⠈⢷⣤⣤⣴⠾⣻⣿⠇⠀⠀⠘⠿⣿⡿⠿⠟⠛⠁⠀⠀⠈⢿⣶⠋⠁⠈⢇⠀⠀⠀⠀⠀⠉⠳⣆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠁⠀⠐⠟⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠀⠀⠀⢀⣠⣤⣀⣿
⠀⠀⣧⠀⢀⣀⣀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣛⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣶⣾⠋⠉⢻⡆⠀⠀⢿⣉⣨⡽⢿⡄
⠀⠀⠘⢷⣾⣉⣽⠆⠀⠀⠈⢧⠀⠀⠀⣦⠀⠀⠀⠀⠈⠻⠦⠉⠙⠳⢦⣄⠀⠀⠀⢠⡏⠀⠀⣿⡿⠀⠀⢀⣿⠀⠀⠀⠉⠉⠀⢈⣿
⠀⠀⠀⠀⢻⣏⠁⠰⢦⣤⣤⠀⢳⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠈⢷⡀⠀⠀⠀⢀⣄⣼⠇⠀⢠⣾⠿⠿⣷⣾⡃
⠀⠀⠀⠀⠀⠉⠛⠛⢛⡿⠁⠀⠀⣷⠀⠀⠀⠈⠻⣦⣄⡀⣶⣄⠀⠀⠀⠀⠀⠘⢷⡄⠀⠙⠦⠀⠀⠘⠛⠷⡆⠀⠘⠿⠶⠿⠋⠙⣿
⠀⠀⠀⢀⡴⠚⠀⠀⠘⠁⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣷⡄⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣿⠃
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢰⣿⣧⣾⠏
⠀⠀⠀⣿⡟⢛⡆⠀⠀⠀⠀⠻⣦⡀⠀⣠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢶⣄⠀⠀⠀⠐⣿⣿⡀⠀⠀⠀⠀⠀⢾⡿⠿⠷⠒
⠀⠀⠸⣏⠉⠋⠁⠀⠀⠀⠀⢠⣼⣷⣼⠟⠁⠀⠀⠙⢤⣀⡴⢳⡆⠀⢠⡟⠀⠀⠀⠙⠳⠶⠶⠟⠋⠈⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠙⠷⣦⣤⣄⣀⡀⠀⠀⠹⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡉⠁⢠⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⣄⠀⠀⠀⠀⣀⣤⣶⡇⠀⠀⠈⠙⠛⠉⠀⠀⠈⢧⡀⠀⢀⡀⠀⠀⠀⠘⠁⠀⠀⢀⡴⠂⠀⠀⠹⣧⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠁⣼⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡟⣿⡀⠀⠀⠀⠀⠀⢰⣯⣶⣤⡀⠀⢀⣿⣴⡟⠁
⠀⠀⠀⣠⣤⣶⣶⣦⣶⠶⠟⠁⠀⠀⠀⢀⣼⠏⠀⠉⠀⠀⢀⣠⣤⣤⡄⠀⠀⠀⠀⠙⠁⠸⣧⠀⢀⡀⠀⣰⡿⣧⣀⣸⠇⠀⢸⣿⠏
⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⠖⠀⠀⠈⢁⣾⣿⡇⠀⢀⣀⣀⠀⠀⠀⢿⡄⣿⠁⠀⣿⠀⠀⠉⠁
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⢿⣀⣀⠀⠀⣾⠇⠙⠃⠀⣴⠟⡿⠀⠀⠐⢾⣿⡏⠀⠀⠙⢧⣄⣀⣠⣴⠾⠿⢷⣆
⠀⠀⠀⠙⠻⠶⠶⠶⠾⠛⠋⠁⡀⠀⠀⠀⠀⠀⢨⡽⠟⠀⢰⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⠉⠉⠀⣤⠶⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⣿⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣼⢿⡆
⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⡿⠛⠃⠀⠀⠘⣧⣴⠾⣇⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢠⡞⠻⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣿⠀⠀⠈⠻⢷⣤⣀⣀⣻⣦⣴⡟⠀⠀⠀⠀⠀⠀⢀⣤⡶⠆⠀⢀⣠⣴⠟
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣲⣶⣦⠀⠀⠀⠀⠲⢿⣿⠀⠀⠀⢀⠀⠈⠙⠛⠛⠋⠙⠳⠶⠦⠤⠴⠶⠀⠘⣿⡛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠞⠛⠋⠹⠇⠀⢻⣿⣓⠀⠀⠉⠀⠀⠀⠈⠳⢦⣄⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢽⠿⠛⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠋⣸⣿⣿⣿⡇⠙⠿⣿⠟⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⣿⣿⣿⣧⠈⠻⠿⠟⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠸⣿⣿⠟⠁⣿⣿⣿⣿⠈⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁

⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⢀⣠⣤⣼⣦⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢀⣤⣤⣄⡀⠀⠀⣀⣤⣤⣷⣄
⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⠿⠛⠛⠛⠿⣿⣿⣿⠿⠛⠛⠻⠋⠀⠀⠀⢸⣿⣿⡿⠟⠛⠛⠿⣿⣿⡿⠟⠛⠛⢿⣿⣿⠿⠛⠛⠻⢿⣿⣿⠿⠛⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⣠⣤⣤⣤⣶⣾⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣷
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣴⣾⣿⣿⣷⣤⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣶⣄⡀
⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠈⢹⣿⣿⣿⣿⣿⣿⠍⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠈⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠁⠁⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⣿⠷⠄⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠾⣿⣿⣿⠿⠆⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠰⣶⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⣶⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣯⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣭⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⢀⡟⢦⠀⠀⢀⡟⢢⡀⢀⡏⠀⠀⠸⡄⠀⠀⣰⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠇
⠀⠀⠀⠀⣼⠀⠈⢳⡀⣸⠀⠀⠙⠞⠀⠀⠀⠀⢳⠀⡰⠃⠀⢳⠀⣠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢦⣀
⠀⠀⠀⢠⠇⠀⠀⠀⢳⡏⠀⠀⠀⠀⠀⣠⡄⠀⠘⠾⠁⠀⠀⠸⠞⠁⠀⠘⠆⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣩⠽⠛⠁
⠀⢰⡖⣾⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡗⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠻⠋⠁⠀⣀⣠⣞⠉⠉⠉⠀⠀⠀⠀⠀⠀⣈⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠘⢿⣶⣶⣦⣤⣤⣄
⠀⠀⠀⠀⢠⠞⠁⠿⣬⡗⠀⠀⠀⠀⠀⠀⠀⢸⣇⡽⢳⡄⠀⠀⠀⠀⡀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿⢷⣦⣄⡀
⠀⠀⢠⡤⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣸⡇⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠙⠻⢷⣦⣄⡀
⠀⠀⠀⠙⠛⠁⠀⠀⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣿⣿⣿⣥⠖⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠋⠁⢀⡤⠤⣄⠀⠀⠀⠙⠁⣹⣦⣀⡀
⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⣴⡯⣄⠀⠘⠇⠀⠀⠀⢾⣁⠟⢀⣽⢦⣤⣀
⠀⠀⠘⠉⢧⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⢥⡈⠧⡬⠇⠀⢀⡀⠀⠀⠀⠀⠀⢿⣀⣸⣣⠼⡦⢤⡀
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢤⡹⣤⡽⠀⠀⢀⡴⠋⠀⢀⡀⠀⠀⠀⠀⠉⠀⢧⣴⢃⡤⢿⠶⣄
⠻⣿⣆⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⡞⠉⢧⣀⡽⠀⠀⢠⣤⣟⣀⠀⠀⠸⣿⣷⠖⠀⠀⠀⠀⠀⠀⠸⢥⠞⠀⠘
⠀⠀⠈⠙⠲⢤⣀⣀⠀⠀⠈⠉⠛⠂⠀⠀⠀⣾⣶⠚⢹⡉⢳⠀⠉⠀⠀⠀⠈⢿⠿⠋⠀⠀⠀⠉⠈⠙⠶⢤⣄⣀⡀⠀⠀⠀⠀⠴⠞

⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠒⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠐⠀⠤⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⢴⠏
⠀⠀⢠⠀⠀⠀⠀⢄⠀⠀⠀⠔⠒⡀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡴⡁
⠀⠀⢸⡆⠀⠀⠀⠀⠂⢄⡀⠑⣤⠃⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠠⣤⠤⠶⠦⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢠⢅⠀⠀⡀⠈
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⠀⠀⢀⠀⠀⠀⠊⠀⠀⠀⢡⠀⠀⠁⠀⠀⢸
⠀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠠⠄⠤⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠃⠒⠈⠀⠀⠀⠀⡀⠀⠀⠁⠈⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⡠⠊⠀⠀⠀⠀⢀⠄⠒⡶⢅⠀⠀⢀⠈⠢⠀⠀⠘⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠐⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢀
⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡰⠁⠀⠠⠀⠀⢡⠀⠈⠀⠀⡂⠀⢀⠁⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠋⠀⠀⠀⠘
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠢⣀⠜⠀⠀⠀⠂⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠠⠀⠒⠂⠀⠘⠗⠲⠒⠂
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠘⠄⢀⣠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡨⠒⢂⠉⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠊⠁⠀⠀⠉⠙⠲⠄⠀⠀⠀⠀⠀⡌⠁⠢⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠸⠀⠀⣠⠀⠀⠀⠀⠀⠀⣠⣤⠤⠄⠀⠀⠒⠂⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⣰⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⡤⠖⠛⠃⠀⠀⠒⠠⠄⡀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠤⢄⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠀⢀
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢆⢀⠄⠸⡄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⢀⠎
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⡬⠈⠂⠂⠈⠒⠊⢘⠀⠀⠸⠀⠀⠀⠄⠂⢄⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡬
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠟⢦⡀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠣⡀⡈⠀⠀⢸⠀⠀⠀⢸⣆⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠐⠁⠀⠀⠀⣀⠈⠢⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠾⣄⠀⠀⠀⡌⠀⠀⠀⢡⠀⠀⠐⣄⠀⡐⠉⠈⡄
⠀⠀⠀⠀⠠⠊⠀⠀⠀⡠⠂⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠐⠄⣀⠠⠂⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⣠⡶⠈⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠀⠀⠀⠈⠓⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀
⠀⠀⠀⠰⠶⠶⠶⠶⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢦⡀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠠⣄⣼⠇⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⢶⠶⢾⣷⠦⠀⠀⠀⠀⠈⠷⣤⣌⣡⣶⣦⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠘⠷⣤⣠⡀⠀⠀⠀⠀⠾⠟⠂
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⣤⡤
⠀⠀⠀⢀⣤⠾⠛⠉⠋⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠙⢷⡄⠀⢀⣠⡴⠾⠛⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⣀⣴⠞⣿⣃⣤⡶⠛⠛⠁
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⢷⣤⣀⣀⣀⣤⡶⠞⠋⠁⠀⢀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠚⠋⠀⠠⠟⠋⠁⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠻⡿⠶⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠆⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠋⠀⠀⠀⠀⠀⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛
⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⣠⡾⠛⠛⠷⣄⡀⡀⠀⠀⠀⠈⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠈⠁⠀⠈⠻⣦⣤⣴⠾⠋⠀⠀⠀⠀⠈⠿⣿⡄⠀⠀⠀⠐⣶⣏⠀⠀⠀⠀⠀⣠⣴⠶⠞⠿⠶⢶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⣤⠉⠀⠀⠀⠀⠀⠈⠉⠉⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢀⡴⠞⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠚⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠻⠟⠃⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⠀⠀⠀⠀⠀⠘⢷⣄⣀
⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣦⡙⢷⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷
⠀⠀⢸⡏⢀⣤⡴⢦⣄⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⠧⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠘⣷⡟⠁⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠹⣧⡙⠷⠾⢋⣰⠟⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠸⣿⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠸⣧⠀⠀⠀⠀⠠⣼⣧
⠀⠀⠀⠀⠘⠳⣦⣤⣀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠘⠷⣤⣀⣄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠠⣾⡷⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠘⠟⠁⢠⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⠿⡿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⣀⣠⣤⣤⣀⡀⢀⡄⠀⠀⠀⠀⠀⠀⠴⠦⡄⠠⠀⠀⡸⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢠⡄
⠀⠀⠺⠉⠉⠉⠁⠚⢻⡟⠑⡀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠠⠁⠀⠀⠀⠀⠔⠐⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠇
⠀⠀⠠⠆⠀⠀⣀⣤⠖⠀⠀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠂⠀⠀⢀⠄⠀⠀⠀⠀⠒⢶⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣷⣤⣤⣤⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠀⠀⠀⠉⠉⠉⠉⠉⢻⠟⠁⠀⢠⠎⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠰⢶⣾⣧⣤⣤⣤⣤⡄⠀⠀⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⢀⣦⠀⠀⢇⠀⢠⠊⢱⠀⠀⠀⠠⣶
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⠊⠁⠀⢀⠴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠊⠁
⠀⠀⠷⠗⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠄⠀⠀⠀⡠⠐⡀⡒⠂⢄⠀⠀⠐⢐⠜
⠀⠀⠀⠀⠀⠀⠐⢻⠇⠀⠀⠠⠤⣤⠀⠄⠀⡘⠇⠀⠀⠀⠀⠀⠀⠐⠁⡆⢀⠀⡂⠈⡄⠀⠀⠈⡹⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⢠⠇⠀⠀⠀⠀⢀⣀⡀⠐⠄⠀⠤⠊⠀⡰⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⠿⠥⠤⠤⠤⠄⠒⠉⠀⠀⠘⠛

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣻⣛⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣴⠿⠛⠻⠿⠷⣦⡀⠁
⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣴⣾⠆⠀⠀⡀⠀⠀⢰⠃⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣥⣶⠿⠛⠁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠀⢰⣤⣄⣀⠸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠝⠀⢀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠛⠿⠇
⠀⠀⠀⠀⣰⡿⠿⠿⣶⣦⣄⠀⠂⠀⠀⡾⠀⠀⠀⠀⠁⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⣀
⠀⠀⡀⠀⠋⠀⠀⠀⠀⠈⠛⠀⠀⠀⢰⠇⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠻⢶⡄
⠀⠀⢰⡀⠀⠀⠀⠀⠠⠶⠿⢿⣷⣶⣼⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⡄⠠⠋⠀⠀⠀⠀⠀⢀⠀⢃⡄
⠀⠀⠀⠛⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠙⢿⠀⠀⢰⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠁⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡾⠀⠀⠀⠙⠻⠷⠀⣠⡄⠀⠿⠿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠛⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⠀⠀⠀⠀⠀⠀⠟⠉
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠉⢿⣦⡀⠀⠲⣧⡀⠀⠀⢀⣾⡷⠃⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢀⣠⠤⠖⠠⠀⠀⢀⣴⠟⠋⠀⠀⠀⠙⢿⣦⣠⣾⠏⠀⠀⠀⠀⠙⠿⣶⣄⡸⠿⠿⣶⣦⡄
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠰⡿⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡛⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠶⣶⣤⣀⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⢀⣠⣮⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠉

⠀⣠⡤⢄⠀⠀⠀⠠⢤⣀⠀⠀⢠⣄⠀⠀⡤⠤⠤⢤⡀⢠⣤⣄⠀⢠⡤⢤⡀⠀⠀⠀⠠⣀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⣀⣤⠤⣄
⠀⢣⡀⢀⡟⠛⠛⠛⣻⡿⠃⠀⣼⢻⠢⡀⠀⠀⣴⠛⠁⢾⠀⢸⠀⢸⡄⢰⡇⠀⡶⠒⠒⢺⣿⠆⠈⢡⡀⠀⠈⠙⠲⠶⠛⠉⠀⢀⠈⡇⣠
⠀⠀⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠁⣸⠀⠀⢀⡾⠁⠀⠀⠸⠀⠸⢤⠼⠃⠀⠳⠾⠃⠀⠀⠋⠁⠀⢀⡟⣏⠲⡄⠠⠴⠶⠶⡄⠀⠈⢳⡿⠃
⠀⠒⠛⠛⠛⠒⠒⠒⠒⠲⠶⠒⠛⠁⠀⢶⣸⣡⠞⠀⠀⠀⠀⠦⠤⣤⣤⡄⠀⣤⠤⠤⣤⣀⡀⠀⠀⢀⡟⠀⣀⣀⣀⠀⠀⠹⣄⣤⢤⡀
⠀⣤⠶⠒⠒⢦⢀⣠⡴⠖⠛⣢⠀⢀⡀⠈⠛⠁⠀⠀⣀⣤⠴⠞⢋⡽⠋⠀⠀⠀⠀⣤⣀⠀⠉⠛⠛⠋⠀⠀⠉⠀⠈⣉⡦⠀⡀⢀⠀⡇⢀
⠀⠀⠀⠀⠀⠛⠉⣁⣠⣤⠞⠋⠀⡏⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠈⠁⠀⢀⣤⡴⠖⠛⣻⠿⠂⠀⠀⣠⣟⣤⡴⠖⠛⠉⠀⠀⣱⠈⠳⣿⠏
⠀⢠⣆⣠⡴⠞⠛⠉⠁⢠⡀⠀⠀⠈⠛⠛⠉⢀⣴⠞⠓⣄⡴⠟⢛⣦⡾⠋⠁⠀⠀⠈⢁⣤⠶⠆⠀⠛⠛⠓⠂⠀⣀⣠⡴⠾⠋⠀⠀⣀
⠀⣾⣿⡥⠤⠀⠀⠀⠀⠀⡇⠀⢒⣶⢶⡟⠀⠛⠀⠀⠰⠏⠀⠀⠾⠃⢀⣤⣤⣄⠀⢰⠏⠀⢠⣴⣖⠂⠀⣠⠶⠛⠉⠀⢤⣀⠀⠀⣴⣿⣄
⠀⠀⠀⠀⣰⠞⠓⠲⠶⠞⠁⣰⠟⠁⠘⠃⠀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣤⠶⣿⠏⠀⢿⠀⠀⠀⠳⠌⣳⠀⠻⠤⠤⠴⠶⠖⣻⠟⠀⠁⣿⠈
⠀⠀⡀⠀⠈⠲⠦⢤⡀⠀⢰⠇⢠⡾⠛⢦⠀⠀⠀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠋⠀⠀⠈⠳⢤⣤⣤⠾⠃⠀⠠⡀⠀⠀⠀⣘⠁⠀⠀⠀⣿
⠀⡟⠉⠓⠦⣀⠀⠀⣹⠀⠘⠶⠏⠀⠀⢸⡆⠀⣴⠋⠀⠛⠛⣋⣩⣿⠷⠆⠀⠀⠀⠤⣄⡀⠀⠀⢠⣿⠦⡀⠱⣤⡴⠟⠉⠑⢦⣤⣴⠇
⠀⠱⡀⠀⢀⠈⠉⠛⠉⠀⢀⣀⡀⠀⠀⣼⢁⡾⠁⠀⢠⣶⣋⣉⣤⡤⠶⠶⠒⠚⠛⢛⣺⡿⠂⠀⠾⢸⠇⠈⠀⢀⣠⡤⠶⠶⠶⠶⠶⠤⣀
⠀⠀⠙⢦⣸⠀⠀⠀⠐⠛⡽⢿⠀⠀⣼⠃⢸⠁⠀⠀⢀⣀⣀⣀⠀⠀⢄⡀⠀⠀⠀⠛⠁⠀⠀⢀⣰⠟⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⠉⠙⠛⠃⠀⠀⢀⡾⠁⠘⠀⠈⠁⠀⠈⠓⠚⠛⠋⠉⢀⣼⠇⠀⠀⠙⠓⠶⠦⠤⠴⠶⠞⠋⠁⠀⠚⠁⠀⠀⣛⣷⣶⡦⠀⣼⣠⡾⠃
⠀⠀⣀⣄⠀⣴⠖⠲⠛⠁⠀⠀⠒⠒⠛⠓⣆⠀⢀⠀⣠⡴⠋⠁⣀⣤⣶⠀⠀⣀⡀⠀⢀⣤⠀⠀⣠⢶⡄⠀⣤⠞⠉⠼⠋⠀⠐⠿⠛⠚⠓
⠀⣰⠏⠀⠻⠁⠀⠀⠶⢶⣶⣶⠄⠀⠀⠀⣿⠀⣾⡼⢋⣀⠀⠈⢉⡿⣿⠀⡞⠁⣟⣠⠟⢹⣀⡼⠃⢼⣡⠞⠁⠀⠀⢠⡤⠤⠤⠤⠤⠤⣄
⠀⠉⠀⣀⣤⣄⣀⡴⠞⠋⡽⠃⠀⠀⠀⣰⠇⠀⠿⠛⠉⠁⠀⠀⣼⠁⠈⠀⢀⣀⣈⠁⠀⠀⠉⠀⠀⠀⠁⠀⢄⡀⠀⢀⣤⠤⠤⠤⠤⠴⠎
⠀⣰⠟⠉⣠⠞⢻⡀⠀⠀⠁⢀⡞⣠⡾⠃⠀⣠⣆⠀⢠⣆⠀⢰⡇⢠⡶⠛⢉⣩⡽⣷⠛⠛⠛⣲⡴⠶⠚⠛⣻⡿⠂⢾⠁⠀⠀⠀⠲⣤⡀
⠀⠁⠀⠀⢏⣠⡾⠀⠀⠀⢴⣿⣿⣥⡀⠀⢰⠋⠸⣤⠟⠘⣤⡞⠀⠀⠀⠀⢺⣡⡼⠃⠀⠀⣞⡡⠃⠀⠀⠈⠁⠀⠀⠀⠙⠒⠛⠛⣫⠿⠋

⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠒⠒⠠⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⢠⠋⢄⠀⠀⠀⢀⣄⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢄⡀⠀⡀
⠀⠀⠀⢸⡀⢀⠇⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢤⡔⢤⠀⠀⠀⠀⣏⢀⡸⠀⠀⠀⢀⣀⡔⠉⢹⠑⢦⠀⠀⠨⠷⠇
⠀⠀⠀⠀⠉⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠐⠒⢢⡀⠀⠀⠀⠙⠦⠤⠤⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⡜⠁⠈⡏⠳⡘⠦⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠑⣤⣀⡀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠒⠃
⠀⠀⢠⠊⠉⢢⠀⠀⠀⠀⠀⠈⠋⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢿⠃⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠈⡄⠀⠸⠀⠀⠀⢀⡤⠦⣄⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⣀⣄⠀⠀⠑⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⢄
⠀⠀⠀⠀⠀⠀⢧⣀⣠⠎⠀⠀⠈⠑⠈⠃⠀⠀⠀⠀⢰⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠐⢛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⢏⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠰⠒⢲⡤⠤⠤⣀⡀⢀⣤⠀⠀⠀⠓⠒⠁⠀⠀⢀⠖⠒⠒⢤⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡴⠒⠒⠢⠄⠀⠀⠀⠃
⠀⠀⢀⠀⠀⠁⠀⠣⠃⠀⠀⠀⠀⠁⠈⠀⠀⠀⣀⣀⡀⠀⠀⠸⡀⠀⠀⠀⢣⠀⠀⠐⢷⠒⠚⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⣢⣇
⠀⠀⠹⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠉⢢⠀⠀⠈⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠾⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢣⣠⠖⠒⠢⣀⠔⠒⠒⠄⠀⠀⠈⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠸⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠆⠀⠀⠀⣴⠦⠖⠉⠀⡴⠊⠒⢄⠀⠀⠀⠵⠇⠀⠀⠀⠀⣀⣀⡀⠀⢠⢤⠀⠀⡠⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⢦⠃⠀⠱⡴⠁
⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠈⠳⠄⣀⡀⠤⠊⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⡀⡴⡆⠀⢠⠞⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⣔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠉⠀⢰⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠌⠁⠀⠀⠀⠀⠀⣁⠆⠁⠀⠀⡝⠏
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠯⣁⡀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⣀⣸⠿⣄⡀⠀⢀⡤⠬⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⢧⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣿⠂⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⡀⠀⠀⠀⠀⠑⠢⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⢤⡀⠀⠀⠀⠀⡇⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠒⠦⠀⠀⢀⡀⠀⢀⡴⠚⠉⠁⠰⠉⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⡇⠀⠀⠀⢠⣧⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣰⡯⠏⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⣥⠀⠀⠘⠀⠀⠀⠀⠀⠉⠉⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣰⣻⠇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠛⠓⢦⡀⠀⠀⠀⠘⣇⣀⣀⡿⠋⠀⠀⣶⠀⠀⠀⠀⠠⡈⠃⡔⠀⠀⠀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⡈⠉⠁⠹⣄⣀⣼⠃⠀⠀⠀⠀⠀⠈⠺⠀⠀⠀⠀⢀⠀⠀⠸⡀
⠀⠀⠀⠀⣦⠀⠀⢠⠀⠀⠀⢠⠄⠈⠶⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡜⠉⠻⡄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⡄
⠀⠀⠀⠀⡿⠀⠀⠸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠀⠀⠀⠙⢦⡀⢆⠀⠀⠀⠈⢀⠀⠢⠄⠀⠀⠀⢀⣀⣀⣤⡤⠴⠃⠀⢹
⠀⠀⠀⠀⡇⠀⠀⠀⢧⠀⠀⠘⠦⣄⣀⣀⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣀⣀⡭⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡅⠀⡄⠀⠀⠀⠀⢸
⠀⠳⣄⠀⡇⢀⠴⠂⠀⠳⣄⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⢦⡃⠀⠀⠀⠀⣸
⠀⠀⠈⠑⡿⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠐⠐⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⡆⢀⡤⣤⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⣤⡴⠖⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡾⠶⠋⠀⠀⠀⢀⡾⠁⢀
⠀⠀⠀⣤⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠉⠛⠛⠒⠲⠶⠤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠙⢦⡀
⠀⠀⡜⢰⡈⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡽⠟⠃⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⢸⡇
⠀⠀⠃⠀⠻⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⣀⡤⠤⠴⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢳⡀⡾⠀⢀⡀
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠙⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠿⠗⠚⠉
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⠀⠈⠉⠀⠂⠀⠀⠠⠄⠀⠀⠘⡀⣃⠔⠀⠀⣠⠖⢦⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢠⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠓⠶⠶⠶⢖⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⣄⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⢁⠄⠀⠀⠀⠀⠀⠲⣈⢠⠃⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠁⢀⡄⠀⣴⣆⢠⡖⠛⠛⠓⠲⠦⠤⠤⢀⣀⣀⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⡾⢹⡴⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⣠⣴⢶⣖⡒⠒⠲⠤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⡾⠁⢇⠀⠀⠉⢦⠀⠀⠀⠑⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠤⠤⠤
⠀⠀⠀⢷⡀⠀⠁⠁⢀⡼⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢲⠀⣾⠞⠁⢈⠁⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⢸⡏⠳⣄
⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠉⠉⠛⠋⠁⠙⠛⠛⠋⠉⠀⠀⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠆

⠀⠀⠀⢀⠀⠀⣤⢄⡀⠀⠀⠀⠀⠄⢠⠀⠀⠀⢀⠔⠢⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⡀⠈⠀⠉⠓⠀⠀⠀⠄⠐⠀⠀⠀⠸⠀⡀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠐⠁⠙⠀⢸⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠈⠢⠀⠀⠀⢀⠐⠃⠄⣀⣀⠠⠳⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠰⠓⠠⡀⠀⠀⠀⠀⡀⠠⠄⡀⠀⠀⡀
⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⠀⠔⠁⠀⠀⠀⠠⠄⠀⠀⠀⡀⠚⢇⠀⠀⢀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⢄⡀⠀⠀⡀⠀⠀⠀⠁⠀⢀⠌⠁
⠀⠀⠀⠀⠀⠀⠈⠢⢄⠘⣆⠀⠀⠀⠀⠃⢀⠄⢠⠁⠀⠀⠈⠀⠂⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⡠⠐⠈⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠌⠛⠀⠀⠀⠐⠄⠀⠀⠀⡠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠑⠄⢂⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠰⡀⠎⢀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸⠞⠁⡐⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠺⠀⠀⠀⠈⠀⠀⠀⠀⠠⡀⠀⠈⠷⠋⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠁⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⣄⡀⠤⠀⡄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠻⢂⠢⠀⠀⠀⠆⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢂⠑⢄⠀⠀⠀⢦⠀⠔⠀⠀⢀⠀⣄⠀⠀⠐⢄⠀⠀⠀⠀⠄⠀⠐⠢
⠀⠀⠀⠈⠊⠀⠀⢄⡀⣠⠀⠀⠀⠀⠀⢠⡴⠂⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠊⠀⠀⠀⠀⠘⠋⠉⠥⣀⠀⠀⠀⠀⠐⠀⠀⠈⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠸⠗⠂⠁⠀⢀⠀⠀⠈⠢⠀⠀⠉⠐⢄⠀⠀⠂⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠶⠂⠀⠀⠀⠈⠓⠁
⠀⠀⠀⠀⠌⢹⠀⠀⠀⠀⡠⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠀⠈⠀⠀⢀⠔⠀⠀⠀⠀⠀⠠⠊⠁⠐⡀⡀⠈⠀⠀⢀⡄⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡠⠊⢸
⠀⠀⠀⠠⠀⠀⠀⠔⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠘⠧⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠠⠊⠀⠀⠈

⠀⠀⠀⠀⣿⣿⣷⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠟⠛⠛⠛⠛⠿⣿⣿⣿⠆
⠀⠀⠀⠀⢸⣿⠛⠻⢿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⡿⠿⠟⠋⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⢀⠄⠰⠄⡐⠁⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⢀⠄⠂⠠⡐⠁⠀⠈⡤⠂⠖⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠰⠂⠀⠀⡆⠁⠀⠀⠐⠁⠀⠃⠀⠑⠀⠀⠀⠁⠀⠀⡀⠀⠀⠐⠀⠀⡎⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠂⠀⠁⡀⠀⠀⠀⠀⢀⠄⠑⢄⠀⠀⡀⠊⠡⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠂⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠒⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⠋⠁⠈⣽⠿⣟⠛⠲⣄
⠀⠀⠀⠺⣿⠶⠛⠁⠀⢀⣦⡄⠀⠀⠀⣠⠖⣾⠻⡄⠈⠁⠀⠀⠀⢸⡇⠀⠀⠀⢷⣤⡿⠀⢀⡞⡗⠢
⠀⠀⠀⠀⣈⣀⣀⡴⠞⠉⠛⠁⢀⣀⣾⡁⠀⠉⠛⠁⣀⣤⠀⠀⣀⣼⡟⠛⢳⡆⠀⢀⠀⠀⠀⠉⠁
⠀⢠⠀⠀⠈⠉⠁⠀⠀⣀⣠⣞⠉⠀⣯⠙⢦⠀⢀⠀⠙⣿⠛⠛⠉⠈⠳⣤⡼⠃⠀⠸⡄⠀⠀⢀⡴⠂
⠀⠸⣤⠶⢶⡄⢠⣀⡾⠉⠹⣤⡗⠀⠈⠓⠛⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢰⣣⡄⠀⣾
⠀⠠⡏⠙⠋⠀⠀⠻⠋⠀⠀⣀⡀⠀⠀⠀⠀⠠⣏⡏⢹⠿⡟⠳⣄⠀⠀⣼⠛⠋⠀⠸⢿⠃⢠⣿⣏⣳⠄
⠀⠀⠻⣄⣀⢠⣤⠀⠀⡴⠋⢉⡉⠳⣄⣰⡆⠀⠀⠀⠘⠚⠁⠀⢹⠀⢸⡇⠀⣠⣤⡀⠀⠀⡏⠀⠉⠉
⠀⠀⠀⠈⠉⢹⡟⠀⢸⡇⢀⣤⣵⠀⠘⠿⠇⠀⣠⢽⡟⠀⠀⠘⣿⠄⠈⠳⣴⣯⡾⠃⠀⢰⡇
⠀⠀⠀⠀⠀⣀⡀⠀⠀⣧⠘⠒⣿⠀⠀⢀⣀⡞⠁⠈⠁⠀⣠⠀⠀⠀⠀⠀⠀⢳⡀⠀⣠⣤⣇
⠀⠀⠀⠀⢸⡉⠙⣧⢀⡟⢠⣶⡏⢀⡞⠉⢹⠙⢦⠀⡄⠀⢻⣤⣤⠀⢴⡳⣄⣸⠃⢸⡅⢠⡟⢳⡀
⠀⠀⠰⡀⠀⠙⠓⣾⠛⠁⠀⢀⡤⢾⠦⣄⠈⠓⢋⣀⡇⠀⠸⣟⠛⠀⢀⣽⠋⠁⡆⠀⠉⠋⠀⢸⡇
⠀⠀⠀⠙⠲⠶⠚⠁⢀⣠⣴⣃⠀⡈⠳⢞⡀⠐⠯⠽⢳⣄⡄⠈⠉⠉⠉⠀⠀⠀⠻⣄⣶⡦⠀⣼
⠀⠀⠀⡀⠀⠀⠀⠐⠁⠀⢿⣈⡇⠙⢲⡿⠟⠀⣀⠀⠹⠟⠀⣠⠿⡿⠀⠀⠙⠲⣄⠀⢻⣴⠀⣿⠀⡀
⠀⠠⢶⡿⣄⠀⠀⠀⠀⠀⠀⠉⠰⣏⣩⠷⣄⡀⡿⣿⠓⠀⢰⠏⠀⠀⠀⠀⠀⠀⠘⣇⠀⠉⢀⡿⣏⣙⡧
⠀⠀⣸⠀⠉⠀⠀⠀⢠⠔⠒⣳⡶⣤⣀⠘⠛⠀⠀⣸⠂⠀⢸⡄⠀⣶⠲⡄⠀⠀⢀⡟⠀⠀⣾⠀⠈⠉
⠀⠀⣿⠀⣠⠶⢤⠀⠀⠀⠀⢯⣠⡟⠈⠙⠒⠶⠚⠁⠀⠀⠀⠙⢦⣽⡶⣧⣤⡴⠛⠀⠀⢀⣿⣰⠆
⠀⠀⠘⢦⣷⣀⡼⠀⠀⢀⠀⠀⠀⠀⢀⡴⢦⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠈⠻⠋
⠀⠀⠀⠀⠈⠙⢤⣀⣀⡀⠙⠲⠤⢤⡬⢷⣟⣀⣠⠾⠉⠀⠉⠳⣄⣀⣠⡴⠞⢋⣭⠿⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿