Autumnal Emojis & Symbols

⠀⠀⢀⠀⣀⡀⣀⡄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠁⠈⠛⠡⠯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤
⠀⠤⠠⠈⠈⠲⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢈⠁⠀⠀⢀⡤⠒⢉⠖⠰⠄
⠄⣁⠀⠩⠅⣀⡄⠣⠑⡀⠀⢀⢁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣴⡤⠤⣤⠀⣄⠀⣀⠀⣀⡰⢋⠀⣴⠁⠀⠰⠁⡀⠠⠘
⠐⣤⢠⠄⣰⠞⣷⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠃⠹⠿⠟⠿⠶⠒⠀⠀⠃⠓⠉⠐⠠
⠀⠁⠀⠀⠠⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⡐⠢⠀⠀⠀⠀⠀⢠⡀⢀⠀⠰
⠀⡀⠘⠀⡥⠘⠆⠀⠀⠀⠀⠀⠀⠒⠑⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠸⠁⣤⠀⠀⠂⠀⠀⡁⠀⠂
⡎⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠡⠀⠠⠃⠀⡼⠀⠀⠀⢀⠆
⠀⠀⠀⢠⠙⢄⡈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢴⣏⡅⠠⠀⣀
⠚⠉⠁⠘⠂⠈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡾⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠃⠀⠁⠀⢀⠐⠊⠠
⠀⠀⠀⠀⡀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠳⡄⠀⠈⣀⠀⠀⢶
⠀⡠⠂⠀⠈⡰⣾⠫⠀⠀⠀⠬⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠉⠂⠠⣄
⠒⠁⠀⠒⢁⠔⢉⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠈⠙
⠀⠠⠴⠛⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠂
⠆⠁⠀⢰⠋⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⣀⡠⠔
⠐⠀⠀⢸⠖⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈
⠀⠀⠀⠞⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡤⢀⡕⠛⠃⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⠈⠁⠈
⢠⣾⠾⡏⠉⢀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣿⡀
⢠⡿⠈⠋⠉⠀⠀⠀⠃⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢤⡆
⠏⠐⠒⠂⠀⠀⠀⠀⠀⠃⠉⠠⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠶⡶⡴⣥⠓⢠⡄⠀⠙⢲⠄
⠀⢄⠀⠠⢀⣀⡘⣶⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠠⠂⡼⠉⠀⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡄⠀⠀⠀⡄⢀⡀⠀⠀⠀⠈⠉⢀⠀⡀⠀⠀⠈⠠⢤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⢀⠀⠚⠁⣀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⡤⠀⠀⠘⡂⢤⣀⣄⠀⠚⠀⠀⠐⣀⢀⠀⠈
⠚⠳⡶⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠤⡎⠒⠁⠀⠀⠀⠉⠑⢯⣄⣀⡀⣀⡀⡠⠀⠞⣁⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⡐⠁⡀⠈⡬⢿⢦⣄⡀⠘⠋⠀⠣⡀
⠀⠘⠓⢤⣀⠀⠀⠄⠀⠃⠀⠀⠛⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡅⠛⢇⠉⠀⠤⡼⣤⠄⠀⠀⠀⠀⠀⠰⠀⠀⣥⡄⠃⠀⡖⠺⢶⡒⠚⠙⠛⠃⠒⠥
⠀⠀⠀⠁⠐⠀⢘⡞⠀⠀⠀⠀⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠮⠁⠀⢀⠜⠙⢷⠤⢀⡐⢰⠃⠀⠀⠀⡀⠀⠁⠚⠩⠇⠀⠁⠨⠀⣤⠁⡄⠀⠀⠀⠀⠈
⠤⠀⠀⠀⠀⠄⠁⢦⠔⢀⣀⠀⠈⢤⣑⠀⠀⠀⠀⠀⠀⠀⣠⠏⢃⡀⠀⢠⠐⠁⠀⠀⠀⢉⠙⠀⠀⠀⠀⠀⢄⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⡀

⡿⠿⠀⠀⠀⠀⢉⡛⣿⣿⣿⣿⣿⡿⠋⠀⠀⣩⣭⢹⣷⡄⠉⠀⠀⠸⣿⣿⣿⡿⣽⣿⣁⣀⠀⠀⠀⠀⢶⣿⣿⣿⣿
⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⡏⢉⠁⠀⠀⠀⢿⡏⠀⠙⠓⠀⠀⠀⠀⣤⣶⣾⣿⢿⡏⣿⣟⠃⠀⠀⠀⣾⣿⣿⣿⣿
⢀⣤⢀⣴⠀⠈⠙⠉⣹⠿⠋⠁⢀⠀⠀⠀⠀⠈⢀⠀⢀⣤⣶⡇⠀⠀⠻⢿⠟⣱⣿⣿⠻⣿⠇⠀⠀⠀⠛⠛⠻⠟⢠
⣸⣿⣼⣿⣶⡾⠂⠀⠀⠀⠀⠀⢹⣿⣷⣦⠀⠠⣾⣷⣾⣿⣿⣷⣶⣴⣦⡄⠀⠻⠿⠟⠀⠀⣠⣤⡄⠀⠀⠀⢶⡄⣿
⠸⣧⣙⢿⣶⡄⠀⢠⣶⣶⣦⠄⠘⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢠⣄⣀⠀⠀⠀⠿⠿⠁⠀⠰⣤⡘⣿⠸
⣷⣝⠻⢧⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⣤⡀⠀⢾⣿⣿⣷⡄⠀⠀⠀⠀⠙⠷⣝⢷⡘⣷
⠈⠙⠀⠀⣠⣶⠀⠀⠀⣾⣿⣶⢠⣶⣶⡄⠈⠀⠠⠟⢿⣿⣿⠿⡿⠛⠁⠀⠸⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠈⢿⠘
⠀⢀⡀⠈⠛⠁⢠⣶⣦⡹⣿⣿⢹⣿⣟⣁⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⢠⣤⣀⠀⢀⠠⣄⠀⣾⡇⣴⣟⡀⠀⣤⣄⡀
⣿⣿⣷⡄⠀⠀⠘⠿⢿⡿⣮⣿⣾⣽⣿⡿⠃⠀⠀⣀⡄⢀⡄⠀⣀⠀⠈⠙⠋⠀⠘⠿⠟⡀⣨⣤⣌⠉⠁⢀⣿⣿⣿
⣿⣿⣿⡶⠃⠀⠀⢴⣿⡿⢿⡿⠙⠿⠷⠀⠀⠀⣰⠟⣴⡿⣡⣾⣿⣴⡖⢀⣀⠀⠀⢠⠋⠀⠙⠻⠄⢠⣴⣤⣙⣿⣿
⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⡀⠀⠀⢸⢇⣾⢅⣼⠛⣹⠿⣻⣾⣿⣥⠄⠀⠀⠀⠀⠀⠀⢀⣄⠈⠙⢻⣿⣿
⢀⣀⣀⠀⠀⡀⠀⣰⣄⠀⠀⣴⣼⣿⡇⠀⠀⠀⢸⠟⣼⣿⢸⣷⢠⣿⣵⣿⣷⣶⣶⡤⠀⠀⢶⣿⣾⣿⣤⠀⠈⠉⠉
⠿⣿⣿⣧⠀⠁⠀⣿⣿⣿⡄⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠏⢸⣿⠀⢿⡇⠙⢿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡈
⠀⠀⠉⠉⠀⠀⢀⣈⣿⣿⣿⣿⣿⣯⣴⣶⣶⡤⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠿⡿
⣆⢠⣷⠀⢠⡄⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣾⣀⣤⣀⡀⠀⠀⢠⣾⣿⣦⠀⠉⠈⠀⠀⠀⣀⣀⡀
⡿⢸⣿⢠⣿⡇⣠⣶⠀⠀⠆⠙⠻⢿⣦⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⣾⠿⠿⠋⠀⡀⠀⠀⠀⠀⠈⠻⢿
⣷⡾⣁⣺⠟⣼⣿⢃⣤⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⠀⠀⠀⠘⣻
⣿⣿⣿⣥⡴⠛⣱⡿⢃⠀⠀⠀⢻⣿⣷⡀⠀⠀⢰⠿⢻⣿⣿⡻⣿⣿⣿⣷⠀⠀⠀⣿⣷⣼⣿⣿⣿⣠⣴⣶⠀⠀⠉
⠰⠿⠛⣫⣶⠿⣉⡴⠏⠀⠀⠸⢿⢿⡿⠇⠀⣀⣀⠀⠘⢿⣿⠇⠈⠋⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⢀⠈⠉⠁⠞⠋⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠙⠻⠃⠀⠈⠛⠀⠀⣰⣾⣶⣦⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⠀⠀⠀⢠⣤⣄⣄⠀⣰⣿⣆⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⢸⡿⠟⠛⢁⣀⠀⠉⠉⠿⠛⠙⢻⡟⠙⠋⠀⠀⣤
⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⣹⣿⣿⢁⣀⠀⢻⣿⣮⡛⡛⢿⣆⠀⠈⠀⣠⣄⣸⣿⣧⣴⡄⠀⠀⠇⠀⠀⠀⠲⣿⣿⣿
⠀⠁⡁

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠶⠶⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⠂⡄⢰⠴⣠⢦⢰⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠉⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⣀⠱⣴⣡⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⢉⠉⠁⠉⠀⠀⠀⠈⠙⢦⣘⡇⢠⠏⠀⢀⡤⠞⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣞⡉
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠑⠒⠤⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢩⠇⠱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠠⠂⠈⢼⠀⠠⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⢄⡀⠀⣸⡰⠁⠀⠙⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡀⠈⠑⢿⠣⣠⡹⢑⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡂⠂⠁⡿⢀⠤⣌⡡⢻⢦⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠒⡒⣒⠊⡉⠐⠒⢉⠢⡀⠀⠀⠀⠀⠀⡃⠄⢀⡠⠀⢾⢚⢰⠙⡡⣳⠁⠀⠀⠀⣸⠟⠢⢂⠄⢐⣒⠰⢒⠋⠁
⠀⠀⠀⠀⠀⣌⡷⡦⣄⠀⠈⢆⠈⠉⠧⡐⣌⠠⠇⠄⡎⠀⠀⣯⠚⡡⠆⡴⣩⣀⡔⣃⠂⡃⠘⢀⠜⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⠒⠀⠀⣀⠈⠉⢷⠀⢠⢬⣨⡦⡾⡟⠔⣡⠈⠉⠓⢷⢀⡇⣀⡂⠷⠀⠒⠒⠂⠀⠐⠁
⠀⠀⠀⠀⠀⢀⣗⠦⠠⠀⠄⠠⠐⠉⠓⢢⣈⣇⠸⠃⡎⢼⠁⣟⠴⠁⡆⠀⠀⣸⠝⠁⣭⡄⠉⠀⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠈⠀⠐⢤⠀⠀⠔⢀⡀⠀⣻⡬⡽⠳⢄⠱⣘⣆⢳⠂⠀⠀⢠⢚⢧⡂⢀⠐⠂⢀⠖⡾⢢⡤⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣈⠁⡌⠀⠘⢷⢒⠆⠳⢤⣈⠟⠀⣠⡞⠉⠁⠈⢿⡸⠆⠯⠷⠞⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⣱⣞⡠⣤⠄⡿⠷⡖⠷⡲⢿⡶⠶⡍⠂⡤⠆⢀⣄⠻⢆⣀⣤⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⡡⠖⢺⡟⢸⠀⠆⠀⠈⢈⢠⢆⣡⠞⠀⠀⠈⠲⣀⣠⠊⣉⣀⢨⡟⢭⣱⡚⠵⠦⠄
⠀⠀⠀⠀⠀⠀⠰⠗⠚⠀⠢⠬⠤⢌⣑⠚⠂⠀⣝⡠⠛⠁⠀⢀⠀⠀⠀⠈⢂⣩⠵⠎⢄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢎⡟⣄⡀⠀⠀⠀⠀⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠛⣄⢨⢽⣻⠃⠀⠀⠀⢀⡴⠋⢠⠷⣤⣄⣤⡴⣋⣱⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⢳⣄⡀⠀⠀⠀⠀⢠⡟⠀⠨⢹⡼⡽⣇⠀⠀⡠⠫⠒⡫⠨⢍⠢⣢⣴⠾⢙⡼⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡴⠃⢸⡀⢻⡇⠀⠀⠀⠀⣾⢷⠀⠉⠀⣧⡎⠙⡷⡞⡡⠻⢷⣅⢎⣦⠿⣯⡤⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢢⠸⡇⢠⠹⡄⠀⠀⢸⢭⠂⠑⣄⠀⡇⣧⠅⢭⡚⡐⠉⣦⣾⠛⠁⠣⢈⡿⢯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢂⣿⡔⠀⢙⢦⣠⡏⠀⢆⠀⠈⢦⢻⡇⠉⠙⢇⣨⡶⠛⠍⠈⣷⠴⢿⣽⣢⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡜⣀⣯⠀⠀⠀⢙⢣⠀⠀⢂⠀⠈⣶⠃⢀⣤⠟⡉⢊⢶⡊⢴⡟⣱⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠫⠎⠕⣻⡄⠀⡀⡞⠀⠇⠠⢤⡂⠀⢹⡧⠟⡁⠀⠈⡆⣸⠃⠤⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⣿⠚⠘⠀⢈⢧⡙⠁⠀⠀⣎⠀⠀⡸⠞⠛⠑⠿⠶⣥⣔⣲⠇⡠⣀⢛⠷⠒⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⡌⠓⠤⣀⡿⠀⠀⢠⡀⢸⣧⠀⢀⠼⣠⣥⣞⠓⡄⢢⡀⢀⠤⠚⠉⢩⠝⣃⠶⠟⠧⠶⣶⣶⣑⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⣻⡄⠀⢀⠁⡀⠀⢀⡇⠸⣯⣄⠈⠂⠌⠁⠈⠑⢾⡟⠊⢁⣀⣀⣱⡯⠎⠀⠀⠀⠀⠀⣬⡥⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢣⠀⠀⠀⢰⠀⣸⢁⠌⠸⣫⣄⣀⡀⠀⠀⠀⢠⠞⠉⠀⠀⢩⡯⠶⠒⠛⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡽⠀⢀⠆⠀⠀⢰⣤⣯⡿⣀⠾⠿⣻⠞⢛⡓⠶⠶⣁⠀⠄⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠈⠐⠦⢢⣾⡿⣩⠞⠋⠓⢀⣀⠀⠀⠈⡑⢦⡈⢑⠖⢦⣤⣄⣀⠀⠉⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠈⡿⣫⢶⣑⣂⠀⠀⠀⠀⢈⠑⠆⠀⠀⡠⠊⢠⠔⠻⡌⠉⠋⡐⠂⣀⣬⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢆⢂⠔⠓⠒⠒⠉⢭⣐⠀⠀⠀⠀⢠⡶⠶⠿⠒⠛⠛⠒⠚⠓⠶⢅⣜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣰⠃⠀⡅⠀⠐⠂⠁⠨⠉⢓⢦⣄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠋⠉⠙⠓⠦⢄⣄⣀⠸⡷⢄⣛⣁⡌⠻⣦⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠻⠞⠛⠷⠄
⠀⠀⠀⠀⠀⢀⠠⢐⠨⠒⠁
⠀⠀⠀⠀⢀⠕⠂⠁
⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⡄⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⣆⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠄⢄⡈⠐⠁⠆⠀⠀⠉⠋⠐⠐⢦⣀⠄⠀⠀⠀⡘⠶⣀⡔⠉⠀⠀⢩⡀⠄⢠⠔⠲⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠑⢤⠀⢈⡀⠉⠖⠃⠀⠀⠀⠀⠆⠀⢀⠀⡉⠘⠁⠀⠐⡀⠁⢸⠁⠀⠀⠀⠀⡿⣯⠀⢀⡀⠈⡄⣀⠄
⠀⠀⠀⠀⠀⠀⢄⠈⠊⠄⠀⠂⠈⡃⠀⠀⠀⠀⠈⠢⡨⠄⠀⠹⠀⠀⠀⠀⠐⠁⣹⣠⣼⠀⢀⣠⡤⠞⣅⡇⠀⢨⠀⢸⠙⠁⠠
⠀⠀⠄⠄⠲⠤⠀⠙⠊⠁⡄⠀⠀⠳⠂⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⠑⠒⠐⠀⠀⠛⠟⠛⠻⠁⠀⠀⠀⠀⠑⠰⠂⠠⢆⠐⠚⠀⠀⠂⠴
⠀⠀⠀⠀⠐⣀⡀⠀⠀⠑⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠈⠀⠀⠈
⠀⠀⠀⢉⠁⠀⠈⢲⡋⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣆⢁⠠⠀⠄⠤
⠀⠀⠀⠈⢄⡀⠀⠀⢿⣺⡇⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠂⡠⢀⠄⡰⢠⢀⢆⡄⠔⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⣺⠞⠀⠀⠀⡆
⠀⠀⡜⠁⠀⠉⠛⠚⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠌⠀⠀⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣏⣀⣀⡤⠆⠤⡀
⠀⠐⠀⠀⠀⠀⢀⣴⡋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠜⠁⠁⢀⠈⡤⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢩⣃⠒⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠁⠇⠐⠁⠏⠸⠀⠃⠺⠰⠇⠊⠇⠼⠀⠁⠀⠀⠀⠀⠀⠀⣽⢫⠀⠱⡄⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠉⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠊⠉⠇⠃⡈
⠀⠀⢀⣀⣁⠀⡀⢀⡀⢥⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀⠈⢠⡌⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠋⠁⡂⠀⠉⠀⠙⠦⣠⡤⠴⠞⠋⣿⠿⢽⠈⠁⢁⠉⡉⠀⡀⠀⠨⠏⢄⠀⠀⠀⠀⠀⠙⡀⢀⠀⠐⢁⠙⠠
⠀⠀⠀⠀⠀⠀⢀⠔⠱⡃⠀⠃⠀⠷⡼⠁⠀⣀⠀⠀⡇⠀⠹⠒⠁⢀⠐⠀⠀⠁⠀⢐⠂⠈⠃⠀⠀⢀⡀⠘⠆⠀⡦⡀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣐⡠⠄⠪⡟⡄⠀⠀⠀⣸⠷⣼⡐⠀⠀⠈⢁⠳⣤⣌⡀⠀⠀⠀⠀⢀⠘⡈⠒⠢⢐⡔⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⢁⡤⡈⠁⠀⠀⠀⠀⠀⠌⠀⠀⠈⠘⠀⠀⠀⠐⠙⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠛⣁⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⢴⣁⠀⠀⡀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠉⡃⠀⠉⠑⠓⠄⠀⠀⡀⠀⠰⠶
⠈⠛⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣤⠂⢀⠀⠀⠀⠐⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⢈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠀⠀⠈⠊⠂⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⣀⠀⠠⠄⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠈⠁⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⣀⣉⣉⣂⣄⠀⠠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⣁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄
⠀⢀⠤⠀⠀⠀⡰⠖⠋⠀⠀⠀⠈⠛⢉⡀⢀⠀⠀⠀⠀⠀⡀⢌⢀⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠁⠀⠠⠔⠂⠀⠰⡅⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠚⠶⠤⣄⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠙⠐⠒⠤⢈⣢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⣀⡀⠀⢠⠏⢠⡀⡜
⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⠘⠁⠀⠀⠀⠀⡃⠤⣀⡉⠢⣠⢸⠘⠿⠁⡠⠔⢒⡂
⠀⠴⢀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠐⣀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣨⣙⣓⣼⣷⣴⣇⠠⠔⢀⡰⠁
⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠈⣠⡾⢁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⠆⠘⠉⢉⠉⢛⣿⣿⣿⠟⠋⡉⠉⠉⠑
⠁⠀⠀⠀⠹⠒⢤⡄⠀⡠⠀⠀⠀⢀⠈⢁⣷⠟⣁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢠⣧⡴⠺⠋⠈⡴⠫⠟⠻⢍⢠⣄⠀⠈⠁⢀⠈⠂
⠀⠁⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⢀⡶⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠠⠖⠈⠀⠘⠀⡴⠘⣤⠌⢆⠉⠁
⢄⠀⡄⠒⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠁⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠘⡀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⡠⢔⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢠⠂⢰⠀⠀⠇⡗⠀⡦⠊⠉⡁⠀⠀⠀⠀⠀⠠⠌⣡⡟⠀⠀⠀⠀⠠⠀⠄⢐⣾⣧⡀
⢀⠀⠀⠀⠀⡀⢀⠀⠀⠰⠅⠀⠹⠂⣁⠴⠋⠀⠀⠀⠀⣶⡞⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁⠈⠁
⡆⢸⠀⠀⢘⠀⠜⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠇⣸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠤⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠂
⠁⠠⠔⠁⣀⣄⣈⠉⠀⠂⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠃⠀⠈
⠀⠀⠀⠤⠲⢄⣀⣈⠉⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣥⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄
⠐⠲⠂⠒⠀⢀⠈⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⠐⠀⢁⡀⠀⠀⠇⠀⠀⠀⠉⠒⢦⣀⠁⠀⢱⠆⣀⣧⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠩⢷⣤⡀⠠⠈⡉⠦⡃⡀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠷⠆⠈⠙⠻⢧⣶⣀⠁⠡⡄
⣥⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣈⣐⣚⣁⣈⣉⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣐
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠱⣦⣄⡀⠀⢠⣄⣿⣿⣏⣠⠄⠀⢀⣠⣶⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢻⣿⣧⣴⡄⢻⣿⣿⣿⠏⣦⣰⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣽⣿⣿⣏⣀⡀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠟⠻⠛⠉⠈⠙⠟⠻⠿⠿⠦⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢻⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣽⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⢸⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡐⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⢠⡄⡀⠀⠀⠀⠀⡠⠀⠀⠀⣈⠁⡄⠀⠀⠀⠘⠠⠈⠀⠀⠐⠿⢩⣝⡢
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡀⠁⠀⠠⠄⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠮⣶⠀⢹⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠢⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⡆⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠰⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣶⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⢡⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠉⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣠⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠂
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠐⡆⠀⠀⠀⠀⢀⣰⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⠎⠀⠀⠀⠀⠀⣾⡏⢸⠁⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠗⠁⠀⠀⠀⠀⠀⢸⣿⢀⠇⢠⣾⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠀⣠⣤⡄⠀⠀⠀⣾⣿⡞⠀⣾⢇⠎⠀⠀⢀⣀⠀⡠⠚⠉⢀⡤⠖⠂⣩⠟⡿
⢀⣤⣄⡠⡀⠀⠀⠁⢹⣿⠞⣴⣿⠁⣀⡀⠀⢻⣿⠀⢸⣿⠏⠀⠀⡆⠙⣿⡿⠀⠀⡴⠃⠀⣠⠞⠁⢠⡇
⢠⠿⠣⣅⠓⢰⣀⣀⠈⠉⢰⣿⠇⣼⡏⡼⢀⡞⠻⡤⢾⣿⠀⠀⡼⢧⣠⡿⠃⠀⠀⣳⢶⠊⠀⠀⢀⡜
⠈⢹⠓⠈⠳⢌⡁⢠⡇⠀⢸⣿⠀⣿⣏⣠⠊⠀⠀⠀⢸⣿⣠⠞⠁⠀⠀⠀⠀⠠⠊⠁⠀⠑⠒⠛⣉
⠀⠀⢡⡏⠀⣨⣹⠲⢍⡀⠀⠉⠉⠈⠉⠁⢠⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⡏⠁⠀⠳⣤⡀
⠀⠀⠀⠉⠛⠁⠁⠀⠀⢉⣀⣀⣀⣀⣀⣀⣿⡏⠀⠀⣀⣀⡤⠤⠈⠁⢠⣤⠊⢹⣿⠁⣿⡇⠀⠈⠒⠒⠋⠺⠃
⠀⢠⣶⠛⢢⡀⠀⠀⠐⠉⠀⠀⠈⠉⠉⣻⣿⠛⠋⠉⠉⠁⠀⠀⠀⠀⣾⡏⠀⣼⡇⢰⣿⠃⠀⣀⡀
⢠⣿⢁⣴⣿⠁⠀⣰⣦⠀⠀⣴⡆⠀⠀⣿⡏⠀⢀⣾⠂⠀⣠⡀⠀⠀⡿⠃⠀⠈⠀⢸⣿⠀⠀⣿⡟⠉⢉⣷
⠘⠟⠋⣽⡟⠀⣰⣿⠇⢀⣼⣿⠇⠀⡰⢻⣷⣠⢾⣿⠀⢰⣿⡇⠀⡼⠁⠀⠀⠀⠀⢸⣿⠀⢸⣿⠇⠀⣰⣿
⠀⠀⠀⢿⣇⡼⠉⢿⠴⠋⣼⣿⠀⡼⠁⠀⠉⠀⠘⢿⡴⠚⣿⠀⡼⠃⠀⠀⠀⠀⠀⠐⢿⣀⠼⠟⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠴

⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡚⠄⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠂⠀⠀⡀⢉⠉⡡⠆⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠃⣀⠈⠢⡄
⠀⠀⠀⠀⣄⠢⢀⢸⣏⢛⠂⠤⠀⠀⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠉⠀⠀⠀⠠⠀⠀⠀⠄⠀⠤⠆⠀⠀⠀⠘⠀⠀⠀⢀⡄⠀⠀⠀⠂⠀⠈⡀⠀⠁
⠀⠀⠀⠀⣈⠁⠈⠁⠀⠀⠓⡄⠀⠀⡀⠀⢀⠀⠀⠘⠃⠀⠀⢀⠀⠄⠁⠁⠠⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⠀⠀⠀⠑⠢⠀⠀⢀⠀⠀⢁⠀⢰
⠀⠀⠄⠀⠀⠘⠀⠠⢀⠓⠀⠀⠁⡄⡄⠀⢀⡀⠀⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠁⠀⢠⡄⠃
⡲⠍⢇⢲⡀⠈⢢⠄⠊⠀⠈⠁⠉⠙⠃⠀⠀⣀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠁⠀⠐⠉⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠁⠁⠘⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠒⠀⠀⠀⠉⠀⠀⠠⠖⢰⠀⠀⠙⢄⣀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠰⠂⠁⠀⠀⠀⠀⠀⠦⠀⡰⠀⠀⠄⡈⠀⠀⠀⠈⢉⠀⠀⠁
⠈⠁⠀⠀⡄⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠆⠀⠜⠀⠀⠀⠀⠀⠀⠀⠠⠆⠃⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁⠠⠀⠺⠁⣀⠀⠤
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢀⠄⠀⢦⡀⠀⢠⡄⠀⠀⠀⠀⠀⡀⠂⠀⠀⠈⠁⠈⠉⠀⡀⠀⠔⠀⠀⢉
⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡄⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠸⠀⠀⠸⠀⠀⠐⠈⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⡀⠀⠑⠂⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠠⠄⠀⡄
⠠⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠀⠄⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠴⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠂⠐⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⠀⢀⠆
⠀⢠⠀⠀⣀⠀⠀⠈⠀⠀⠺⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠩⠿
⠀⠀⠺⡄⠁⠑⢤⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⡀⠀⠀⠀⠁⠒⠠⢅⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⢀⠀⠠⠀⠄⠀⠠⠀⡠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣐⣤⣀⠀⡠⠄⠀⡀⠀⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠆⠀⢠⢲⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢁⠏⢹⠍⠀⠁⠀⠒⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠈⠑⠂
⠀⠀⠀⣀⣀⡘⢦⢾⡙⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠩⠀⠁⠀⡌⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠉⠈⠁⠀⠀⠀⠀⠓
⠀⠀⠘⠳⠜⣷⢸⣪⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠔⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤⠄
⡀⢀⣀⢀⣀⣉⣀⣉⣀⣀⢀⢀⣀⣀⢀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⡀⣀⣌⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⡄⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠂⠀⠖⡉⠑⠀⡀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠢⣰⠂⠈⠁⠋⢶⠀⠚⢰⡀⣊⣀⡬⠤⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠢⡄⠈⡆⠀⣏⠠⠂⠀⠀⠸⠀⠀⢀⡟⠉⠀⠀⡄⠀⠀⠀⢨⠏⠈⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⡀⡸⠀⣇⠀⠀⠀⠀⠀⣇⡴⢋⡶⢈⠁⢤⠀⠀⠀⣸⠃⢂⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⡴⢠⠀⠱⢇⠀⢹⠀⠀⠀⡦⢠⣏⡤⢋⠆⠸⠀⠀⠀⠀⠀⣅⠤⠚⠉⠩⠀⠑⠂⠀⠀⠊⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡆⠀⡀⠁⠀⢆⠀⠈⢧⠀⡇⣄⠐⣁⣾⡏⠀⠴⠀⠀⢇⠈⡀⣀⡴⠃⠀⠋⠀⠀⠆⠀⠆⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡹⠣⡀⢸⠀⢰⠈⢻⡇⠀⣠⠏⠈⣷⠀⠀⠀⠀⠈⡤⠴⠚⣤⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⠀⠙⢾⠀⠀⡀⠀⣿⡞⠁⠀⠀⢸⡆⠀⠀⣠⠚⠀⠁⠂⠠⠀⣰⡄⠀⢠⡄⠊⠀⠀⠀⠀⢀⠀⠀⠀⡅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠒⠒⢾⡀⠀⠈⢧⠀⢡⠀⠸⣧⠀⠀⠀⠀⢻⣦⠚⠁⠉⠀⠀⠈⣀⠠⠢⣄⠀⢈⠁⠀⠀⠀⢀⠄⠛⠀⢦⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠳⡀⠀⠈⠓⣎⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣰⠁⠠⠀⠀⣀⡜⠒⠒⠖⠒⠣⢄⣴⠡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠃⣠⠙⠲⣤⡀⠸⡄⠀⠙⢷⠀⠀⠘⡛⠀⠁⠀⠀⠀⣸⢁⣠⡾⠛⠋⠉⠀⠀⠀⠀⠀⣤⠄⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣀⠞⠚⠶⣿⣦⡀⡀⢀⠀⢰⣷⠀⠀⣀⣤⣦⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠓⠁⠀⠀⠀⠀⠈⠙⠻⣿⢷⡸⣿⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠞⣹⣿⣿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⣿⣽⣿⣟⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡇
⠀⠀⣠⠀⡀⣄⣠⣀⡀⢀⣀⣀⡀⢀⣠⣠⣾⡿⣿⢿⣿⣿⡿⣿⣿⣾⣾⣿⣿⣷⣶⣄⠉⣁⡀⠀⣀⢀⣀⣀⣀⣠⡀⠀⢠⣀⣀⣀⣀⠀⠃
⠀⠀⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣟⣽⣟⢸⣯⣽⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡎⣿⣿⣿⣞⣿⣷⣽⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠈⠀⠀⠈⠈⠀⠀⠁⠀⠁⠈⠁⠀⠁⠈⠀⠈⠀⠀⠀⠉⠁⠀⠀⠉⠀⠉⠀⠀⠁⠉⠈⠁⠀⠀⠁⠀⠈⠀⠀⠈⠁⠀⠈⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣄⣈⣧⣀⣜⠁⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⡀⢠⡤⠀⣀⠀⠀⢀⣿⡿⢶⣀⣼⣿⣿⣿⣿⡿⠉⡙⢒⣀⣄⣀⣀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⡟⣹⣿⣿⣷⠋⠁⠀⠀⣟⠋⢻⠃⠀⠀⢏⢈⡇⢰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠛⡿⠋⠀⠀⠀⠙⠋⢙⠉⠁⢰⠀⠀⣠⣾⡿⡇
⠀⠀⠑⠉⠀⠉⣈⠷⠄⠀⣀⣼⣶⣯⣀⡀⠀⠀⢴⠇⠁⢣⣿⣿⡋⠙⣿⣿⣿⣿⣿⣿⡀⢀⡀⠀⢷⣅⡀⢈⠀⣀⣼⠀⢀⣾⡻⢹⠁
⣀⡄⠀⠀⠀⢸⠇⠀⠀⣸⢻⣿⣿⣿⡟⣷⠀⠀⠀⡀⢄⢼⣿⣟⠑⠀⠉⠙⣤⣾⣿⣿⣿⣿⢿⡖⣄⠙⠿⠿⠿⠛⣁⠀⡈⢙⡁
⣿⣿⣶⣤⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠉⠈⠈⠙⡛⣿⣗⠀⠀⢿⣿⣽⡟⣿⣏⠀⠀⠘⣧⡀⢒⡔⡿⢁⣾⣿⣿⠋⠈
⡟⠉⠈⡟⣦⣠⣶⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣷⣤⣤⡤⠤⣿⣤⣼⠻⠤⠤⠤⢽⣿⡗⢻⠈⠀⠀⣸⢻⣿⡓⢾⠁⢸⣿⣿⣯⣽⣦
⠛⡶⠾⣿⢽⠟⣿⣷⣿⡟⣠⣿⣿⣿⣯⣿⣿⣿⣿⠁⠀⠀⠀⠀⣛⠁⠀⡀⢀⠀⠀⠁⠀⡉⢳⡀⣶⣾⣟⣓⣈⣶⠘⣿⣿⣿⣿⣿⣷
⠀⡆⣰⡷⠋⠀⢻⣿⣿⣷⢡⡍⢹⠋⠉⣿⣿⣿⠇⠀⢳⢹⡿⡇⡇⣿⡼⣭⣗⠀⠀⠀⠀⠉⢸⡇⠈⠙⠻⠿⡄⠀⠀⣿⣿⡿⠿⣿⣿
⢠⣾⣿⣿⣶⡶⣮⢻⣿⣿⡀⣒⠀⢖⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠱⠼⢦⠤⣴⣿⠀⠀⠀⠀⠉⠟⠐⠶⣭⡿
⣿⠿⢟⣙⡋⣁⣀⡀⢻⠉⡶⢙⠛⠋⡓⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡬⠃⠙⠓⢦⣀⣠⡖⣠⣷⣄⠀⠀⣈
⣿⣿⣿⣴⣿⣿⣿⢣⣾⡆⠇⠛⠿⠿⠛⠂⠀⠀⠀⢠⢤⠀⢠⣦⣠⡄⣶⠴⠆⡤⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⣿⣿⡻⢟⣿⣹⣷⣿⡿
⠈⢻⣿⣿⡟⠫⠅⠀⠮⠙⣾⠶⠐⠶⠖⠂⠀⠀⠀⠘⠚⠒⠘⠃⠛⠓⠛⠀⠀⠚⠀⠀⣴⣶⡈⣿⠀⠀⠀⠹⣿⣿⡿⠈⣿⣿⣿⣿⣿
⣠⣾⣿⣿⣿⣿⣧⡄⢠⠰⢷⠲⠿⠂⠶⢖⣦⣠⡤⠀⣄⢀⡀⣀⠐⢒⣆⣴⣛⣆⠀⠀⢹⣿⣷⣿⣦⡄⠀⠸⣿⣿⡃⢐⣦⣿⣿⣿⣶
⣿⣿⣿⠻⣿⡟⠻⠦⣭⣿⣽⣿⣥⣬⣉⣠⡿⠟⢀⠀⠀⡀⣸⡏⠙⣥⡶⠶⠾⣋⠉⠉⠻⣿⠻⠿⣿⡁⠀⠀⠈⢻⡃⢠⠤⠴⢿⣿⣿
⣿⣿⣿⣦⢤⡜⠾⣦⠌⢭⢿⡿⣷⣦⣄⠀⠀⠀⠛⢳⡞⠿⣿⠇⠀⢿⣴⡶⠟⠛⣿⢠⣾⣿⣿⣯⣾⣿⡆⠀⢀⣿⡃⠶⠐⠚⣛⣿⣿
⣿⣿⣿⡳⣄⠀⠀⢹⡄⠙⠲⣤⣿⢿⣿⡇⠀⠀⠘⠶⠷⠿⠇⠀⠀⠀⢠⡶⠞⠛⠉⠀⢻⣿⣿⣿⣿⡟⠀⠀⣸⣿⠀⣉⣉⣭⣯⡶⢿
⢋⠴⣠⣄⢘⣦⣀⣘⣇⣑⣿⣾⣹⣷⣛⠁⠀⠀⠀⣤⣶⣤⠀⠀⠀⠀⢿⡀⣤⣶⣦⡀⠀⠛⠛⠛⠛⣡⣶⣶⣿⣿⣶⡬⣥⣴⣿⣿⣟
⢻⣤⣾⣿⢂⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⡉⡱⢁⠃⢀⣀⠀⠀⠽⣏⠀⢘⡷⢄⡀⣀⢀⡠⢛⠅⣁⣸⡿⣿⣇⣧⣿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠓⠒⠄⢀⠞⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⡀⠀⠀⢌⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠐⠸⢇⠀⠀⠀⣀⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠦⠄⠌⢉⣙⠚⣧⠔⠉⣀⠤⠀⠐⠀⠤⢀⠉⠢⢄
⠀⠀⠀⠀⠀⣠⠴⣂⣀⣐⡂⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⡝⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⡈⠐⢄⠑⡄
⠀⠀⢀⡴⢋⠔⢉⡠⠤⠔⠚⡿⠁⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⣀⠶⠒⠋⠉⠉⢡⠋⠀⠀⠀⡠⠀⠀⠀⣀⠀⠀⠀⠈⠑⣄⢡⢸
⠀⡰⠋⠀⠀⠔⠁⠀⠀⠀⢐⡇⠀⠉⠉⠉⠉⠉⠩⠁⠒⠋⠉⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣊⣠⠀⠀⠀⠀⠈⠐⠄⠀⠀⠈⣠⠞
⡼⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⠂⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣪⡴⠁⠀⣠⣤⣾⣭⣀⣀⠀⠀⠀⠀⠀⡀⠀⢀⡰⠃
⢧⡀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⠓⠦⠤⢤⣤⣤⣤⣤⠤⠖⠚⠟⠛⠉⣻⡃⣠⠞⠉⠉⠉⠉⠙⢿⣷⠀⠀⠀⢂⣇⠔⠉
⠀⠙⢦⣀⠀⠀⠀⠀⠐⠊⠕⠒⣠⠤⣀⣤⣤⣤⣤⠤⠤⢤⣤⣦⣶⣿⡿⠏⢀⣤⣗⡒⠒⠄⠀⠀⠙⢀⡮⠔⠊⠁
⠀⠀⠀⠈⠙⠲⢤⣅⣐⡂⠀⠐⢂⠬⠍⠉⠀⠰⢆⡛⣋⣩⣥⠶⠟⠉⣀⣼⣿⣿⣿⣿⣆⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣟⣶⣶⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋⠁⢀⣴⡀⣶⡄⠀⠙⠻⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣳⡆⠀⠀⠀⠀⢰⠀⠀⠈⠛⠀⠙⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣷⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⠄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣿⠁⣸⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⣤⣆⡀⣀⠀⢰⡇⢠⣆⣀⣆⣤⣾⠾⠻⡃⢀⣴⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⢄⠀⠀⠘⠩⠉⠟⠛⢻⠛⠙⠋⡹⠃⠀⣠⣦⣮⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⠷⢦⣤⣤⣥⣤⣀⣼⡄⠠⢾⣤⡤⠾⠿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠋⠀⡘⡆⠀⠀⠿⠇⠀⠀⢀⠆⢀⡠⠀⠀⠠⣶⠧⠀⠀⠀⠀⣤⠘⠏⠃⠀⠀⠀⠀⠀⠀⠀⢀⠖⡉⢀⠈⣆⠀⠀⠀⠠⢶⠯
⠀⠀⠀⢀⣠⠏⠈⣡⠁⠙⢖⡆⠀⠀⠀⢲⢦⣧⣾⡥⠀⠀⠀⠀⠀⠀⠠⡼⠯⠙⠁⠀⠀⠀⠆⠀⠀⠀⠀⠀⡌⠀⢁⠈⠀⣿
⠀⠀⠀⠈⢳⠀⠀⠈⠀⠀⣾⠀⠀⢀⠰⢞⡻⢿⠲⠄⠀⠀⢀⠀⢠⢤⠺⠃⠀⠀⠀⠀⠀⠸⠴⠶⠜⠀⣀⠀⡇⠀⠈⠀⠀⢹⠀⠀⠀⠀⡀⢠⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠁⠀⠀⠉⠙⠀⠀⠀⠀⠦⣙⡮⠋⠀⠀⡒⠠⠀⠀⠐⠶⠶⠶⠶⠚⠁⠀⢳⠀⠀⠀⠀⠈⠳⢄⡀⠬⠖⡹
⠀⠀⠀⠀⢿⣀⣀⡀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣲⡎⠁⠀⠀⠈⠓⠁⠀⢠⡀⠀⢀⣆⡀⠀⡀⠀⢠⠳⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠠⣴⡄⠀⠰⣬⡓⠊⠀⠀⠀⠀⢀⣤⠀⠀⠀⣹⣫⡵⡿⣥⢟⢣⠀⠙⠃⠈⠑⠦⠤⠤⠐⠊⠁⢠⣀
⠀⠀⠀⠀⡄⠀⡀⠀⠀⢀⣀⡤⢤⡠⡀⠀⠀⠀⠀⠀⠀⠁⡀⢠⣶⣄⠀⠈⠋⠀⠠⠤⣧⢶⡵⣿⣹⠾⢦⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⡧⢨⠇⠀⠀⠪⢾⠖⠻⢯⠁⠀⠀⠠⢀⠜⠁⠀⠙⠿⠟⠛⠷⢄⣀⠄⠀⠀⢹⢾⣅⣯⢝⡲⣎⠀⠀⠠⣾⠀⠀⢀⡤⠖⠂⠄⡀
⠀⠀⠀⠀⢡⣞⣀⠤⠀⠀⠁⠀⠀⠀⠀⠀⣄⣀⡮⠀⠀⠀⠀⠀⢀⡠⠤⣄⡀⠀⠀⡀⠁⠀⠈⠹⠁⠀⠀⠀⠀⡀⠀⠀⢰⠋⣀⠀⣀⠀⠘⡆
⠀⠀⠀⢀⡿⠟⠀⠂⠀⠀⣀⣰⡃⠀⠀⠀⠣⠭⠟⠀⡠⠀⢠⠞⣁⠀⣠⡀⢻⡄⢰⣨⣗⣦⣤⣀⠀⠀⠀⠀⠉⠟⠂⠀⣿⠀⠿⠃⠻⠇⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠑⠒⠒⠒⠚⠉⠀⠀⡏⠀⠿⠀⢿⠇⠸⡇⠀⠀⠈⠙⠓⠿⣿⣲⢦⣤⣀⣀⡀⠀⢻⠀⢶⣶⣶⠟⢀⡇
⠀⠀⠀⠀⠀⠀⠛⠃⠀⡠⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠹⣃⠇⠀⢸⠀⠀⠉⠁⠀⢸⡇
⠀⠀⠀⠠⡤⠀⠀⠀⠚⠀⠟⠟⠑⠄⠀⠀⠀⡘⠆⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⠄⠀⢨⠃⠀⣦⠄⠀⠀⠈⠀⠀⡸⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠿⠗⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⠶⠒⠲⠴⠲⠞⠁⠀⣀⠀⢠⡇⠀⠈⠙⣀⠠⠤⢤⠀⠀⠑⠒⠉⠂⠞⠉⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣤⣆⡄⡀⠀⠀⠀⠀⠀⠀⠘⠥⠤⠀⠋⡰⠀⠀⠣⡴⠖⠎⠀⠀⠦⡤
⠀⠀⠀⠀⠠⠄⠠⠀⢀⠀⠀⠀⠀⠀⡠⠆⣀⠎⠀⠀⠀⠈⠙⠿⢶⣄⡄⡀⠀⠀⠀⠀⠐⠂⠉⢀⣶⡀⠀⢷⣒⣰⠀⠈⠒⠃⡠⠊⠁⠈⠑⡄
⠀⠀⠀⠀⣀⣶⠀⠀⠈⠁⠀⠀⠐⠈⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢀⡔⠡⡀⠀⠀⠀⠉⠀⠀⠤⠬⠥⠱⠀⠀⡸⠁⠘⠃⠛⠀⠸⡀
⠀⠀⠀⠀⠙⠁⢀⠀⢀⡶⠀⠀⠀⣤⡞⠇⠀⢠⠎⠀⠀⠀⠀⢢⠀⢀⠀⣴⣾⢿⠇⠀⠃⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠀⢠⠋⠀⠀⢠⣲⠋⠁⠀⢠⠋⠀⠠⢠⡆⣤⠀⢇⠉⢀⠛⠉⠁⠀⢰⢶⠒⠛⣩⠆⢑⠀⣠⡖⠀⠀⠀⢸⠀⣄⢀⣄⣀⢀⡀⡇
⠀⠀⠀⠀⠀⣸⠲⠾⠀⠀⠘⠌⠃⠀⠀⡰⠁⠀⠀⠃⠀⠰⠀⠀⢸⡀⠀⠁⠀⠀⠐⠈⡠⡿⡍⢹⠅⣠⢾⠃⡆⠀⠀⠀⡈⠀⠟⠐⠊⠞⠘⠀⡇
⠀⠀⠀⠀⣀⡈⠀⠘⣉⡰⠀⠀⠀⣀⣼⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠠⡾⢾⢶⢴⢥⣼⣿⣿⣭⣸⣠⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣠⣿⠋⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠈⠸⡄⢢⠶⠋⣺⠙⢦⡁⠠⠉⠀⠀⠀⠈⠀⢒⠰⠀⠤⠆⠚⠁
⠀⠀⠀⠀⣠⡀⠺⠆⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⡇⠀⢀⡀⠀⠀⠝⠩⢐⢄⣯⠠⠀⠙⠇⠀⠀⣀⣀⠀⠀⣈⢨⠀⡀⣇
⠀⠀⠀⠀⣉⠁⠗⠈⠀⠀⣾⣿⣾⡏⠀⠀⠀⠀⠤⡼⠀⠀⠀⢸⠄⠇⠀⢤⡨⠁⠀⠀⠀⠀⠙⡿⠊⠀⠀⠀⠀⠐⢿⠿⠀⠀⡏⢹⠀⡏⢻
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣅⣀⠀⠀⠙⡗⠀⠀⠀⠀⣠⢀⣴⠋⠙⢯⠀⠀⢹⠶⠒⠄
⠀⠀⠀⠀⢤⣤⣤⣀⣧⣤⣄⡀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⡄⡀⣀⡈⢶⣹⣷⢤⡊⠁⡀⠄⢢⠞⡟⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⢠⣇
⠀⠀⠀⠀⠈⢠⠋⠉⢹⠉⢫⠻⣷⡄⠀⠤⠁⠀⠀⠀⠀⠀⠀⠸⣏⡵⡞⠉⠁⠀⢡⠀⠁⢀⠀⢀⠷⠤⠄⠀⢀⣤⣦⣤⣆⠀⠐⠉⠉
⠀⠀⠄⠀⠀⠁⠀⠀⢸⠀⠈⡇⢹⢨⡌⠀⠀⠀⠀⠀⠀⠀⠤⢊⣠⣄⠡⠀⠀⢠⠾⠀⠀⠘⡷⠀⡀⠀⠀⣀⢼⣿⣤⣷⠃⠀⠀⠀⠴
⢀⢀⠀⠀⠀⠀⠀⠀⣌⡖⢀⣇⣸⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⠋⠁⠀⠀⠘⠁⠀⠀⠀⠀⣀⡀
⠀⠹⢦⡀⡄⠀⠀⠐⢳⠟⠻⡉⠲⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠂⠀⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠉⢩⠶⠀⠀⢸⠀⠀⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠠⠙⠀⠀⢀⠘⠁⠀⠀⢀⡀
⠀⠀⠀⠀⡊⠀⠀⢀⠈⡄⠀⣸⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡈⠉⠉⠁⠂⡀⠀⠀⢰⣀⣠⠀⢠⢀⡄⠀⣆⢀⡀⠠⢀⡀⣠⣀⣠⡄⠀⠀⠀⠀⠀⡀⠀⠄⠄⠈
⠀⠀⠀⠁⠀⠀⠀⣀⣄⣀⠃⠂⠀⠀⠀⠀⠈⠀⠉⠀⠈⠈⠁⠀⠉⠈⠁⠈⠈⠁⠁⠀⠈⠀⠀⠀⠀⠀⠀⠡⠀⠀⠘⠀⠀⠃⠀⢀
⠀⢠⠀⣶⠛⠛⢿⠀⠀⠈⣷⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠐⢁⠀⢀⣠⡀⠀⠃
⠀⡔⠋⠛⠄⠀⠀⠀⠀⠀⠋⠀⠀⢀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⢦⣠⣶⣿⣛⠛⠳⢭⡑⢄
⠘⣆⣀⠀⠀⠀⢀⣠⣀⣀⡄⢀⠠⠚⠛⠄⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠄⢠⣆⠝⠻⢄⠀⠉⠢⣄⠉⢶⣡
⠘⠁⠀⠈⠀⠰⣾⡟⢿⣹⠋⠀⠀⠀⢀⠀⠀⠀⠤⠀⠄⠀⠀⠒⠀⠠⠀⠀⠀⡄⢀⣀⣰⣏⠁⡠⠛⠋⢹⠀⠀⠀⠑⡄⠀⠈⢢⠀⣿
⠐⢤⡤⠤⠒⠉⠻⠟⠛⠃⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⣾⠠⠁⠀⡀⠀⠀⠀⠀⠈⣸⠛⠛⠏⠻⣌⢀⠀⠆⠀⠀⠀⠈⢆⠀⠀⣅⢸
⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠆⠀⡠⠀⠀⠀⠀⠛⢀⠈⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠓⠀⢸⠌⠀⠈⠀⠀⠀⠀⠈⣆⠀⣼⠟
⠠⠀⢠⠀⣤⠁⠀⠀⠀⣃⠀⠀⠀⠀⢠⡞⠃⠀⠀⠀⠀⠢⡀⠀⠀⠀⠈⢢⡠⢄⢀⡄⠀⢀⡎⢀⣾⠚⢀⠀⠈⠂⡀⠀⢀⡿⠞⠁
⣦⣤⣥⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣥⣤⣭⣿⣾⣯⣭⣥⣤⣤⣤⣷⣤⣤⣼⣿⣭⣤⣤⣤⣤
⣿⣿⣩⣙⣫⣍⣹⣝⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⡀⠀⠀⣴⠀⠀⠆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⣿⡇⣀⡀⢻⣟⠀⠀⠀⣤⣀⠠⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣄⠌⠀⠀⠀⠐⠀⠈⢻⣷⣿⣷⣿⠏⠀⠀⠀⢨⣷⡀⠀⠈⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠘⠛⠛⠁⠀⠀⠂⠀⠘⠻⢋⠀⠀⠀⠂⢀⡁⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡟⠠⡴⢶⡔⠂⠀⠀⠀⢳⠏⠀⠰⡀⠀⠀⠀⠀⠀⠂⠘⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣐⢀⣀⠀⠈⡀⠀⠈⠙⠛⠁⠀⠀⠀⠁⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⡀⠀⢰⢠⠀⠀⡀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠐⠉⣶⡍⠂⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠠⠶⣦⢀⡶⠶⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⠂⠀⠀⣠⣤⠀⠉⠀⠀⠘⢷⣄⣏⣤⡞⠀⠀⠰⠾⣶⡀⢠⡀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠴⡟⠁⠀⣀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠛⢾⠓⠲⣏⢈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠶⣄⠀⡰⠈⣷⡐⢹⡇⠀⠒⠀⠀⠈⠁⠀⣶⠀⠤⠘⣤⠤⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠀⠁⠀⠐⠀⢸⡃⠾⣧⠀⠀⡀⠀⢀⡀⠀⣿⠀⢤⣀⠀⠑⠀⣠⡔⠀⠰⠆
⠀⠀⠀⠀⠰⡆⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⣠⣶⡀⠠⠄⢸⡇⣀⣿⠃⡟⡳⢰⡟⡗⠂⠿⠀⠰⣿⣷⠀⢸⣿⡗⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠇⣰⠃⠐⣶⣆⠀⠃⠀⠀⠴⠿⠿⠷⢆⠀⠸⠋⡴⠃⠀⠉⠀⠀⠉⠀⠀⣀⠀⠀⣿⡏⡀⣀⣿⡗⠀⠂⠁⠥⡀⠁⠉
⠀⠀⠀⠀⠀⠘⡿⠀⠀⠛⠁⠀⡀⠀⠁⠀⠹⠛⢧⠐⠁⠁⠉⠀⠀⠀⢆⠀⠐⠀⣀⠀⠀⠀⠀⠻⣿⣿⣷⣿⠋⠀⠀⠐⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⣼⣷⡀⠀⠆⠀⠐⠊⠀⠀⢀⠀⠈⠶⢀⡀⢀⠠⡊⠈⠀⠀⢠⣤⠀⠈⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⡟⠃⠀⡴⢶⡀⠀⠀⠀⠈⠀⢀⠀⠔⢀⡛⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⡄⢸⡇⠈⠀⠀⠀⠀⠠⠀⠀⠠⠀⠠⠀⠀⠀⠘⠀⠀⠠⠀⠀⠐⣶⣦⠀⣤⣶⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣸⡇⡀⠀⠁⢠⠂⠀⠀⠀⠀⠘⠀⠀⠘⠀⢀⠀⠰⢀⡄⠀⠀⣽⠃⠿⠘⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠏⠀⠁⠨⡙⣈⢁⠂⠁⠀⠀⠀⠀⣄⠀⠠⣹⠀⡴⠋⠀⠀⠀⠘⢒⢀⡒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠍⡆⠀⣀⡄⠀⠀⠘⠿⠀⢀⣿⡼⠁⠀⠀⠀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢶⡶⠀⠑⡳⠃⠀⠀⠀⠀⣠⣴⣿⡯⠔⠋⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠄⠀⠀⠰⠾⠿⠋⠁⠰

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣧⠀⠀⢠⣀⠠⣿⣿⠀⠀⢨⣶⣦⣀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⢶⡿⠀⠀⢘⢿⣷⣿⣯⣶⣶⠀⠛⢿⣯⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠘⣾⡷⠂⠀⠛⣻⡿⣿⣿⣯⡀⠰⢶⣿⠿⣇⣴⣤⡦⠹⣿⠇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣤⠚
⠀⠀⠀⡀⠀⠀⣠⣾⠀⠈⠀⠘⠃⢩⣤⣤⣴⡄⠀⠉⣁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠃⠀⢢⠇⠀⢀⠄⠀⢀
⠀⠀⠀⣿⣧⣰⣿⠃⠀⠀⠀⣤⣾⣿⣿⣿⠟⢀⣴⣾⣯⡀⢰⣿⣧⠀⠀⠀⠠⡀⢰⠁⠈⠣⣀⡼⠒⠋⠁⡠⠏⠁
⠀⠠⣤⣼⣿⣿⣷⣶⡷⠂⠀⠛⠛⠟⠛⠉⢠⣿⣿⣿⣿⣿⠀⠻⠿⠀⠀⠀⠀⠀⠘⠢⣀⡀⢸⡇⣀⠤⠯⣤⠤⠤⠄
⠀⠀⠀⠀⠉⠻⣯⡀⠀⠀⢼⣿⣦⣶⣿⠀⠀⠉⠙⠻⠿⠛⣀⣧⣀⠄⠀⠀⠀⠀⠉⠙⠉⠙⣾⡿⠁
⠀⠀⠀⠀⣠⣤⣄⡁⠀⢀⣼⣿⣿⣿⣿⣿⠆⠀⠀⢀⣴⠀⣺⣷⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣆⠈⠛⣿⣿⠟⠉⠀⠀⠀⠀⢿⡿⠀⢺⣿⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣠⡉⠉⠉⠉⠀⠀⠙⠁⢰⣤⣄⠀⠀⣤⣬⣶⣆⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠾⠟⠣⣦⡿⢿⣠⣤⡤⠀⣾⣿⣿⡇⢸⣿⠇⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠈⠛⠋⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣴⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠻⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠻⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⠄
⠐⠒⠲⠶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣴⣾⣿⠟⠉⠀⠀⠀⠀⣈⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⢲⣿⣶⣶⣟⣯⣵⣾⢁⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠈⠛⠿⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠛⠛⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⠀⠀⢠⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠉⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠁⠈⠁⠙⠻⠿⠿⠿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠙⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠈⢿⡇⠀⠈⠉⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠻⠄⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠻⢿⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠋

⠀⠀⣄⠀⠀⠦⠀⠀⠀⠠⠠⡄⠀⠀⠰⠖⠄⠀⢀⠀⢀⣐⡠⠀⠀⠄⠀⠀⢠⢄⠠⢀⠀⠀⣀⣀⢠⠀⠀⣄
⠀⠀⢀⣳⠀⣁⠠⠀⠀⢂⠅⢂⡀⠤⠄⢄⠀⠀⢀⠁⠈⠉⠉⠀⠑⠠⠒⠀⡀⠂⠐⠀⠐⢀⠹⠋⠀⠀⠀⠛⠁
⠀⠀⡀⢡⢤⠄⠃⢠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠘⠘⠀⠤⠐⠀⠆⠀⠒⠡⠐⠠⡀⠂⠐⢀
⠀⠀⠈⠺⠃⠀⡀⠀⠀⠛⣛⠒⠒⢲⠆⠒⠂⠐⠃⢀⡐⠀⠐⠂⠳⠛⠀⢃⠄⢠⡆⠁⠀⢀⠐⠀⠆⢀⡀⢆
⠀⢘⣦⡤⠀⠀⣠⡄⠀⠀⠉⢂⠀⢸⠀⠀⠐⠀⠀⠁⠀⠴⠂⠀⠠⠌⡁⠸⠍⢻⡇⠀⠀⠀⠀⠖⡀⠀⠀⢈⢃
⠀⠈⠉⠀⠀⠀⠀⣀⣴⢀⠀⠀⠀⢸⠀⢁⠊⠉⠀⡛⠀⠀⣇⠀⠱⠂⠀⠀⣇⢚⣻⠇⠀⠀⠀⠀⠐⠀⡔⠄
⠀⣀⡠⡡⠀⠀⠀⠖⡗⠂⠀⠀⠐⠢⠀⢀⠀⠈⠀⠀⠀⠀⢿⠀⠘⠀⢑⠄⢀⠀⠐⠀⠀⠀⠀⡀⠀⢰
⠀⠁⠐⠐⠁⠀⠀⠠⠁⠂⢀⡘⠀⠰⡈⠀⠀⡰⠀⠀⠀⡂⠀⠀⠠⠀⠌⠀⠈⠀⢀⣠⠀⠰⠈⠁⠀⠌⠜
⠀⠀⠀⠁⠀⡀⠀⡆⠀⠀⠂⠄⠀⠀⠒⠀⠢⠖⠀⠀⡞⠃⠐⢀⠄⠀⡠⠀⠈⠀⢈⠉⠀⠀⠀⠀⢡⡀⠀⠈⡁
⠀⠸⠀⠀⠀⢈⠉⠀⠀⠀⠀⠂⢀⠄⠀⠈⠘⠇⠀⠤⢐⠿⠒⢂⣤⢞⡄⢠⠀⠀⠀⠙⠀⢀⣴⠄⡃⢩⣭⣦
⠀⠘⠀⠀⣦⡈⠀⠰⠛⠻⠋⠀⠋⠀⠔⠂⠈⠁⠀⠀⠀⠀⠁⠀⠙⢄⣁⡀⠀⠠⠄⢠⠀⣠⡿⢿⣭⣯⡿⣿⣇
⠀⢠⡘⠷⠄⠀⠀⠀⠀⠀⠀⡀⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣧⡆⢀⡀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠘
⠈⣄⡙⠂⠀⣀⠀⠠⠄⠤⠠⠂⠀⠰⠛⠂⠀⠀⠀⠀⠀⡀⠘⠖⠶⠀⠡⠀⠀⠀⡠⠀⢰⣲⡆⠀⠀⠀⣄⣀⣀
⠀⠀⠀⣀⠛⠊⢠⡒⡔⡄⠀⠄⠀⡀⠠⠀⠀⠀⠙⠒⠉⠠⡀⠀⠀⠀⠁⠁⠀⠩⠒⠁⢀⠀⣤⡀⡄⠀⠈⠉⠁
⠀⠘⠻⠈⠁⡀⠀⠉⠚⠁⣤⡈⢙⡤⠀⠐⣶⣶⣦⠰⠀⠄⠀⡄⠀⠠⢀⠀⠀⠀⠀⠠⠐⠂⠀⠃⣠⡄⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⢧⠀⠀⢹⡉⢹⠀⠀⣉⠀⣀⡘⠀⠁⠀⠃⠀⠀⠀⣀⣂⠀⣀⠙⠃⠰⢵
⠀⡀⠀⠀⡈⡀⠀⡁⠈⡀⠀⠀⣀⢀⠘⠯⣉⡤⡴⠀⠀⠁⠀⡡⡿⠀⠀⠀⠀⠈⠀⢀⠀⠁⠀⢀⠀⠐⠄⢁
⠀⠀⡀⣄⠀⡄⢀⡆⠠⡤⠀⠀⠦⠁⠱⡀⠀⢀⠀⠀⠠⣂⠀⡪⡧⢄⠀⠀⠂⠘⠃⠀⠈⢁⠈⢠⡀⢀⠀⠃
⠀⢦⡀⠄⠀⠀⠈⠀⠀⠃⠀⠀⡂⠲⠁⠀⠆⠀⠀⠄⢦⠈⢀⠀⠀⠀⡴⠀⠀⣀⣀⠀⠠⠈⠀⠁⠠⠀⠀⠀⠑
⠀⠖⣰⠀⡄⠀⠀⠀⠀⠠⢠⠀⢌⠒⠈⠀⠐⠀⠀⠀⠀⡴⡧⠀⠀⠸⡇⠠⠂⣌⢣⠀⠀⠀⠀⡀⠀⠀⢒⡇
⠀⠉⠁⠀⠀⠀⠀⠉⠙⠒⠊⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠁⠀⠈⠉⠙⠂⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠙⠛⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠈⠁⠀⠀⠀⢠⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⠀⠀⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠘⠃⠀⠈⠀⠙⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⢀⡀⠆⠀⠀⣶⠀⠀⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢀⡠⠎⠀⠀⠀⠀⠀⢀⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⡀⠀⠀⢘⣿⠁⠀⠐⠛⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⣄⠉⠁⠀⠀⠀⠀⣀⣴⠟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠈⠂⠀⣉⠀⢇⠀⠀⠀⢂⡀⠀⣶⡀⠀⠀⠀⠀⠀⣠⠛⠐⠒⠲⠶⠒⠈⠛⠁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠲⠶⠾⠛⠒⠒⠛⠷⠸⠇⠠⡐⣛⡥⠚⠉⠃⠀⠀⠀⠀⢰⡃⠀⠛⡟⢶⣄⡀⠈⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠒⢶⠖⢀⣀⠀⠀⣀⠀⢲⡿⠟⣱⠋⣠⠁⠀⠀⠀⠀⢸⡄⠀⠈⢣⡀⠈⠙⠲⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠈⠁⠐⠤⠀⠛⠋⠀⠘⠻⠤⢶⣦⠜⢃⡰⠁⠀⠀⠀⠀⢀⡉⠠⣤⢀⣉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⣄⠀⠀⠀⢠⣼⡇⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡈⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣆⡀⣀⢀⣄⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠉⠛⠻⠿⠻⠟⠉⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠦⠘⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠐⢄⡀⢠⣤⠞⠛⡀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⢸⡅⠆⢀⣉⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣤⡤⣤⡤⠀⠛⠋⠰⠆⠀⣀⣤⡔⠛⠁⠀⠀⠈⢷⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⢈⣠⣤⡴⠂⣠⣴⠿⠶⠊⠉⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠛⠛⠻⠿⠟⠋⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣤⡀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠉⠁⠀⠉⠳⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⡰⠂⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠃
⠀⠀⠀⠀⠀⠸⣇⡀⠱⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⣸
⠀⠀⠀⠀⠀⠀⠈⠳⣆⠈⠉⠉⠳⠦⣀⡀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣠⠄⠻⡄⠀⠀⠀⡄⠈⢻⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⡠⠎⣱⡄⠀⠀⠀⠀⢰⣧⠀⢸⠛⠢⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢠⡴⠛⢀⣴⠟⢻⣦⠀⠀⣠⠟⢈⣧⠘⠦⢀⣽⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠰⣄⠴⣿⠁⢀⡿⠁⡇⢸⡃⠀⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⣴⡀⣠⣾⠃⢸⡷⠈⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠙⠁⠰⠶⠎⠑⢶⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢀⠀⠀⣃⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡆⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⢷⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣶⢤⣀⣀
⢀⣤⡶⠶⠶⠶⠲⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠉⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣌⣿⣦⣀⣠⡀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⠟⠛⠛⠃⠀⠠⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⡇
⠙⠷⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐⠶⠶⠖⠛⠉⠉⠉⠉⠉⠛⠷⣦
⠀⠀⠀⠈⠻⢦⠉⣉⣉⣉⣉⣉⣛⣛⡛⠛⠛⠛⠛⠛⠛⠋⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾
⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⡿⠟⢻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⡀⢠⠛⠀⠃⠀⣀⠀⠀⣴⡟⢃⢂⣴⠶⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡄⠠⡀⠁⠂⡀⠀⠟⠀⣀⠀⠁⠚⠀⠀⢀⡇
⠀⠀⣼⠿⠛⠒⠒⠀⠠⢿⡇⢠⡇⢄⠁⡿⢃⠌⠀⠀⣼⠉⢻⠂⢠⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠐⠄⠀⠉⠀⠇⠀⠓⣠⡿⠁
⠀⠀⠀⠀⠀⢀⢀⠠⢤⣴⠀⠘⣜⢦⡁⠉⠀⣷⠀⠀⠈⠉⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠀⠀⠀⠀⠈⠐⠠⢤⣞⠝⠁
⠀⠐⠂⠃⠉⠀⢀⢔⣿⣿⠀⠀⢀⣠⣤⣤⡔⠈⢷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠀⣀⢀⡀⠀⠀⠀⠀⠀⢀⠔⠊⠉
⠀⠀⠀⠀⢠⠼⣁⠌⡞⠨⠀⢉⡿⢿⣿⠎⠉⠀⢸⡇⠀⠁⠈⠀⠀⠐⠀⠀⠐⠂⡀⠀⠁⢨⢀⠲⡀⠀⠀⠀⠃⠀⣀⠴⠾⠃⠀⠀⡤
⠀⠀⣀⠘⠀⣐⠊⢨⠃⠨⠀⠀⠀⠰⣄⣠⣤⡄⠘⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠁⠤⠚⠂⠀⠀⠀⠺⠶⠀⠀⢠⣄⡀
⠀⠐⠁⠀⡰⠁⠀⠃⠀⣈⡀⠀⠀⠐⠙⠿⡿⠿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠍⠀⠋⣼⢁⢻⣦⡄
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠰⡶⢀⣤⠀⢠⠄⡀⠀⠀⠈⠀⠀⠀⢈⠀⠀⠀⠀⠀⡄⢣⠀⠀⠁⠀⠀⠄⠀⢀⠀⠈⢅⠀⠀⣌⠌⣐⡝⡃
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣴⢂⠉⠀⡈⠀⠀⣠⡄⠀⠀⠀⠀⣈⠄⡈⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠐⠁
⠀⠀⣠⠞⠁⠀⠀⠀⠀⣆⠀⠀⢆⠀⠐⠃⠀⠀⠉⠁⠀⠀⢀⠜⠁⢀⠤⠠⠀⠀⠀⠒⣉⠀⠀⣅⠀⠀⠀⢀⢴⡖⠲⡶⠂⣄⠀⡆⢠⡀
⠀⢞⡿⢃⢖⠀⡀⠀⠀⠀⠀⠀⠈⣱⠄⢀⠀⠀⠀⠀⠀⣴⣿⣶⣦⣤⠀⠀⠈⠀⠀⠀⠙⠁⠀⢉⡀⠀⠀⠌⢀⠀⠀⠁⠀⠈⠂⢿⣘⡅
⠀⠀⠰⢣⠎⡼⢀⡎⡀⠀⠀⠀⠔⢁⠀⢸⢷⡖⠀⡀⠊⠁⠈⠉⠉⠈⠀⠀⠸⡀⠀⠀⠘⠳⠿⠛⡁⠀⡠⢬⢬⣀⣈⠁⢀⡀⠀⠸⣦⡇
⠀⠀⠀⠀⠈⠀⠌⠰⠁⠀⠀⠀⠀⢁⡴⠎⠁⠀⢈⣁⡀⠀⢠⢰⠀⠀⠀⠈⠀⠙⠂⠀⠚⠒⠀⠀⠀⠀⠀⠐⠲⠹⠋⠰⣆⡀⠀⠀⢯⣳
⠀⣮⡀⠀⢱⠆⡀⢀⡠⠔⠒⠀⠐⠋⢀⡀⠀⠐⢻⣿⣷⠀⠸⣄⣀⣴⠀⠀⠀⣀⣾⡉⢫⢷⠀⠀⣖⣶⡬⠄⢃⠠⢠⠀⠀⠀⠀⠀⠈⠄
⠀⠻⠥⠤⠞⠋⠉⠩⠖⠛⢉⠀⠀⣠⣧⡄⠀⠀⢠⣿⣿⠀⠀⠈⠉⣡⠴⣚⠋⠁⡠⠞⠐⣀⣀⢀⠈⠉⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠄⠐⠞⠛⠂⠀⠀⢰⠄⠘⠁⠠⠅⠈⠀⠠⠀⠈⣿⡏⠀⠀⠀⠸⣅⣈⣡⠞⠋⠀⠀⠘⠄⠛⠀⠁⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠸⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢂⠀⣷⠀⠂⠀⡄⠀⢠⠀⢀⠀⣄⠀⡰⢡⡡⢋⡔⠁⠀⠀⠀⠀⠄⢀⠔⠠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣁⠀⠐⠀⠇⠀⢈⢀⠀⣠⠃⡠⢡⠁⣠⠊⠀⠀⠀⠀⠀⢀⠴⡁⠊⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⡇⢱⠀⠀⠄⢐⠀⠈⠌⡐⢡⡞⡠⠁⠊⠀⠀⠀⠈⠀⢀⡴⠛⣁⢀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⢘⠀⠀⡄⠈⣁⠸⣾⣶⡀⠉⠈⠀⣀⡰⠀⠀⠀⢀⡴⠋⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠸⣯⣦⢰⣿⣿⣿⣿⣿⠇⠀⠀⡰⠊⠀⠀⢀⡄⠋⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠻⡀⠀⢈⣤⣶⣿⣿⣿⣿⣿⡏⠀⠀⠄⠠⠆⠁⡴⢋⠤⠎⠡⠀⠄⠀⠀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⢣⡀⠱⡰⢿⣿⣿⣿⣿⣿⡿⣿⢃⡼⡿⠛⢁⠔⠋⠉⠀⠀⠀⠀⠀⠈⠀⠀⢢⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠱⡘⢷⣏⣻⣿⣿⣿⣿⣿⢻⣿⣇⠠⠚⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⣵⣵⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠚⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢀⠀⡸⢛⣴⣟⣿⣟⣿⣿⣿⣿⡏⠀⠁⠿⡦⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠛⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣀⣌⣓⣲⣆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣏⣸⣯⠉⣧⣛⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⢻⣿⣿⣿⣿⣿⣿⠸⣿⢯⡿⡬⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠘⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡄⠀⠀⠸⣿⣿⣿⣿⣿⣿⡔⢟⣛⣛⣁⡻⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢰⣴⢿⣿⣿⣿⣿⣿⣧⢘⢯⣏⢉⡵⠋⠄⠈⠉⣰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣾⣿⣿⣿⣿⣿⣿⣦⠀⢻⠸⠀⢀⣐⣄⠀⢳⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⢻⣿⣿⣯⠖⠓⠢⠀⠨⡟⠛⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡝⣿⣿⣧⡀⢲⠐⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⢹⣿⣇⢻⣿⣿⣧⡘⢈⠁⠉⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⣶⠀⠀⠀⢸⣿⣿⢨⣿⣿⣿⣿⠀⠡⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢠⣴⡖⠛⣿⣿⠈⣿⣿⣻⣿⡇⠠⡀⠄⠀⠀⠀⠐⣿⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣏⠀⠈⣿⣿⢰⣿⣿⣿⣿⣿⢠⠀⠀⠳⣀⡀⠀⠸⣿⡄⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢧⠄⠹⣿⣿⡄⢠⣿⣿⣸⣿⣿⣿⣿⣿⣼⠁⠀⡥⢮⡇⠀⢢⢹⡣⠀⣸⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢔⣳⣶⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⠇⠀⡁⢶⣤⣾⣿⣾⣡⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⢩⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣧⡏⠌⢠⠃⠀⣿⣿⡿⠋⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣴⣿⢿⣾⡿⢟⣿⣿⣿⣧⢻⡟⣿⡟⣿⣿⠏⢾⡀⡎⢠⡴⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠠⡌⠀⢻⠈⠛⠻⠙⠣⡛⠙⠓⠹⡟⠎⣦⢱⠇⠀⠃⠈⠉⠈⠁⢶⣦⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠙⠀⠀⠀⠀⠀⢣⠀⠻⡀⠀⠚⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠈⠂⢁⠁⡜⠿⠢⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⢈⣙⣆⡀⠂⣶⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⣷⣬⠉⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⠀⠀⠀⠀⠀⠀⢰⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣠⠊⠀⠀⠀⠀⠀⣾⡟⢰⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠔⠁⠀⠀⠀⠀⠀⣸⣿⠁⡎⠀⣼⢏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢀⣀⠀⠀⠀⠀⣿⣿⡼⠀⣼⡏⡼⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⣀⡤⠤⣶⡟⡿
⠀⣀⡀⠀⠀⠀⠀⠖⢹⣿⣃⠞⣻⡿⠀⠀⠀⠀⣿⡿⠀⢰⣿⡷⠁⠀⣠⠰⣻⣶⠊⠁⠀⡴⠋⠀⢀⡴⠋⢠⡇
⠀⣟⢟⠋⢳⠤⡀⠀⠈⠿⠋⣼⣿⠃⣼⠟⡆⠀⡽⣷⢀⣼⣿⠀⠀⢠⣇⠀⣼⡿⠀⠀⠸⣁⣠⠖⠁⠀⠀⡼
⠸⢬⡤⠙⢦⡐⠷⠛⣦⠀⠀⣿⡟⢸⣿⠔⢁⡜⠁⠉⠉⢹⣿⠀⣠⠏⠈⠒⠋⠀⠀⣠⠔⠋⠻⣄⣠⡤⠞⠁
⠀⠘⠄⠤⠄⡙⠶⣄⡳⠀⠀⠻⠧⠜⠿⠶⠋⠀⠀⠀⠀⠘⠛⠚⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣤⡴⠖⠠⣄
⠀⠀⠀⠧⣄⠜⠳⠃⠙⠦⠀⠀⠀⠀⠀⠀⢀⣾⡗⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⠤⣤⡤⢶⣦⠀⠘⢧⣀⣀⣼⣻⠆
⠀⠀⢀⣀⣀⠀⠀⠀⠀⡠⠴⠶⠶⠶⠶⢶⣾⣿⣧⣤⣤⠴⠖⠚⠉⠀⠀⢰⣿⠃⢀⣿⠃⣸⣿⠀⠀⠀⠀⠀⠀⠉
⠀⣴⡟⠁⣸⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣠⡀⠀⠀⠀⠀⠀⢸⣿⠀⠸⠿⠀⣿⡏⠀⢀⣶⣄⡤⢤⣀
⢰⣿⣠⢾⣿⠃⠀⣰⣿⠀⠀⣰⣿⠀⠀⢠⣿⡇⠀⢰⣿⠀⠀⣴⡆⠀⠀⡞⠃⠀⠀⠀⠀⣿⡇⠀⢸⣿⠃⠀⢨⣿
⠈⠋⠁⢸⣿⠀⡰⣿⡏⢀⡼⣿⡿⠀⢠⠏⠹⣧⠖⢻⣿⠀⣸⣿⡇⠀⡼⠀⠀⠀⠀⠀⠀⢿⡇⠀⣾⣿⠀⠀⣾⡟
⠀⠀⠀⠸⢿⠞⠁⠙⠗⠋⢰⣿⡇⣰⠇⠀⠀⠀⠀⠈⠿⠞⠉⣿⣇⡼⠁⠀⠀⠀⠀⠀⠀⠘⠧⠴⠛⠃⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡑⢢⣷⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⢠⡏⠒⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡆⠀⠀⠀⠀⠀⣰⡣⢌⣇⠀⠀⠀⠀⠀⣼⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠡⢸⡇⠀⠀⠀⠀⠀⣿⠁⠀⢿⡀⠀⠀⠀⠀⣿⢠⠉⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣡⡀⣼⠃⠀⠀⠀⠀⢸⡇⠰⢂⢸⡇⠀⠀⠀⠀⢹⣄⣄⢡⡏
⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⣟⣁⣀⣀⡀⠀⠀⠈⣇⢁⠀⣸⠃⠀⠀⣀⣀⣀⣙⣿⣋⣀⣀⣀⡀
⠀⠀⠀⠸⠁⠘⠿⠿⠭⠭⠿⠭⠽⠿⠟⠂⠙⠀⠙⠻⡷⠋⠀⠋⠐⠻⠿⠿⠯⠿⠯⠿⠿⠿⠃⠘⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠸⣿⣿⣟⣻⣿⣛⣿⣿⡷⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠛⠉⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣹⡄⠀⠀⠀⣇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡭⠖⠚⣻⠷⠖⠒⠶⢿⣟⠓⠶⣭⡙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⠉⠀⣠⠎⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠙⢦⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣠⠏⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠻⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠏⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢹⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡟⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢷⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⡄⠀⢷
⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢠⡇⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣘⣇⣀⢸⣇⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠤⣄⡀⢸⠁⢀⣸⣁⡀
⠀⠀⠀⢀⡞⠁⢀⡶⢏⡭⢶⣽⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡞⢄⢠⢻⡿⢻⣶⢿⠉⠀⢸⡀
⠀⠀⢰⡚⠉⣹⡿⢧⡞⠀⠀⢻⣁⣤⡖⠳⢄⣀⣀⣀⣀⠀⡀⢰⡖⠗⠉⠁⠘⡿⣀⣀⡀⠀⣈⣱⡤⣶⠓⠢⣄
⠀⢀⣴⣷⣮⠤⠴⠶⢷⡀⡞⠾⠈⠀⢸⣢⠎⠀⢀⡇⠈⠉⢧⢯⢀⡤⣀⡟⢦⣹⡏⠀⠈⠑⣿⠀⠀⢸⡀⢀⡼
⠲⠾⣧⣌⣇⠀⠀⠀⠸⡝⠃⠀⠀⠰⡞⠛⢶⠤⠾⣶⠀⠀⠀⢿⠟⠋⠀⠀⠀⢿⠛⠦⣄⣀⣸⢀⡴⠛⠛⠓⢦
⠀⠀⠶⢾⣏⣓⡦⢤⣤⡞⠢⣄⣺⡉⠁⣠⠋⠀⠀⢈⡷⢀⣠⣧⣀⠀⣤⢠⢶⣼⣦⡤⣬⢷⢤⣙⣄⣀⣀⣠⠔

⠀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠘⢮⠁⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠘⠷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⡀⣦⡄⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠑⠶⠘⠺⠃⠀⠀⡀⠠⠆⣤⠖⣄⢦⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠠⠀⢡⣾⠮⠀⠀⡹⠀⠀⠀⠀⠀⠀⢀⡘⣿⣿⣿⣿⣿⣴⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣶⠁⠘⠉⢠⣇⠀⡁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠟⣩⠀⠀⢀⡈⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣪⠃⡄⢰⡈⠃⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢸⡆⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣧⠀⢻⠀⡇⢠⡆⠐⣇⠘⠁⣤⠀⠀⠀⠀⠀⢰⡏⠀⠈⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡀⠿⠀⠀⣀⠴⠆⠠⡏⠀⢸⠀⣷⠀⠃⠀⡇⠀⠀⠀⢰⠃⡀⢀⠀⢸⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⠀⠀⠉⠰⠂⠀⢹⣀⢸⡄⢸⡤⣄⠜⣷⠘⣇⢠⡇⢠⣄⡈⠐⢈⡇⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠰⠋⣧⠀⠰⣴⠚⢶⠀⣏⠐⡇⠀⠀⠃⠀⠉⠀⢸⡞⢷⡀⢈⡁⠈⢿⠀⣿⡀⠀⠄
⠀⠀⠀⣦⣀⣶⠀⠀⠀⠀⠀⠘⡄⣠⠀⠘⣆⠀⠘⠀⠈⠀⠷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⠆⠛⢶⣿⠼⢹⡆
⠀⠀⢰⣿⣿⣿⣷⣄⡀⠀⠀⠀⢳⣁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡄
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠫⠟⠻⠛⢟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢶⣤⡀⠀⢠⣤⣶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠶⣋⣽⣆
⠀⠀⠀⠀⠀⠾⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣬⣭⣡⣠⣄⣉⣅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⡄⣹⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⡿⠻⠽⠯⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⡀⠀⠀⠐⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⣶⠾⠿⠟⡟⢿⠿⣦⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠠⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡐⠠⠰⡀⠀⠀⠀⠙⠛⠃⠎⢬⣽⠠⠧⡾⠄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣰⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠟⠻⠲⠄⠀⠀⠀⠀⠀⠀⠀⠴⠿⠴⠦⠤⠤⠤⣤⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠉⢮⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⠤⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣰⠁⠀⠹⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠇⠀⠀⠀⠱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⡜⠙⡆⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⠀⠀⠸⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⢀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣇⢸⡇⠀⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣀⣀⠺⣍⣡⣴⣒⣒⣚⣀⣀⣿⣇⣀⣐⣒⣒⣲⣤⣨⣽⢂⣀⡨⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⠖⠲⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣄⣠⣿⣴⣶⣼⣤⣴⣦⣷⣤⣴⣾⣤⣥⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣶⣶⣾⣿⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠒⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠰⠁⠀⠥⠖⠒⠒⡢⠀⠀⠀⢀⡀⠤⠦⠤⢀⣀⠈⠁⠀⠀⠂⠠⠄⠁⡆⠠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠀⣀⣰⠊⡀⠀⡔⣲⠯⠣⣀⠔⠒⣄⡳⠾⡈⡷⠒⠦⣀⠵⠀⢀⡦⠀⠀⡠⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠔⢄⡏⠀⢸⡞⠀⢸⠉⡍⠀⡗⢧⠀⠀⣧⡀⠀⣿⠀⠀⠛⠀⠈⠎⠀⢱⠋⠉⠱⠤⢎⣁⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠘⣤⠾⠄⢸⠛⡄⢨⢹⠀⣼⠘⡇⢸⡉⠣⠇⢰⠇⡅⠀⡏⡇⢀⠶⠀⠀⣦⠀⣸⢳⠀⣠⡄⠸⢢
⠀⠀⠀⠀⠀⠐⠉⢈⢰⣩⡀⠸⣿⠇⠸⣾⠀⡏⢼⠀⢸⡀⢰⠀⢸⠀⡇⠀⡇⡇⢸⣼⠀⢸⣿⠀⢸⡼⠀⣿⠁⠘⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠢⣀⡹⡆⠀⠋⠀⠙⢾⡀⠀⠣⢼⡀⠈⠲⠃⠀⢧⠇⠈⣿⠀⠀⣷⡀⣸⣇⣀⠟⠖⠚⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢁⠜⠲⠖⠪⢇⠀⠀⡨⠣⣀⡠⢄⣠⠼⢄⡠⠛⠶⠖⡋⠉⠁⠀⠁⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⢠⠐⠀⠀⠤⠀⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠐⠒
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠒⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢋⡀⠀⠂⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡑⡄⠀⢀⡆⠄⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⡠⠐⠀⠈⠁⠠⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠈⠀⠸⠁⠀⠀⠁
⠀⠀⠀⠀⣠⡡⠂⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠅
⠀⠀⠀⢰⠏⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡀⠀⢀⠄⠂⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠃⠀⠐⢀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠃⢀
⠀⠀⠀⢰⠀⠘⠀⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠱⢄⠀⠀⡉⠀⢠⡀⠀⠀⢈⠀⠀⠀⠄⠀⡘
⠀⠀⠀⠀⢂⠀⢇⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⢆⠀⡄⠤⠤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠑⠬⣆⡁⠂⢤⡀⠀⠀⢀⠀⠀⣠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠓⢼⣄⠀⠈⢦⠀⠀⠀⢠⠆⠀⣠⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠓⠂⠒⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠓⠂⠒⠃⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠀⢰⠇⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠀⢸⠃⠀⠀⠂
⠀⠀⠀⠀⢠⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠠⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠸⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠤⠄⠀⠀⠀⠀⠤
⠀⠀⠀⢠⠀⢈⠀⠀⠀⠈⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⢀⠈⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠈⡄⠈⡆⠆⠈⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⢠⠎⠀⠀⠀⠘⡄⠀⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠃
⠀⠀⠀⠀⠈⠢⣱⡈⠀⠁⣀⠈⠀⠀⢀⠀⠀⢀⡀⠔⠋⠀⠀⠀⠀⠀⠘⠦⣱⡈⠀⠁⣀⠀⠀⠀⢀⠈⠀⢀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠬⠦⠄⠤⠮⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠼⠦⠄⠤⠮⠄⠂⠉

⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⢰⣀⣀⣀⣴⣇
⠀⡆⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰
⠀⢦⡄⢠⠀⣍⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃
⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⠄
⠀⠀⠀⠀⠂⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⢿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠠⡠⣿⣤
⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⡄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣥⠀⠀⠟⢷⢲⡄⠀⠀⠀⠀⠀⠰⣀⣨⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘
⣬⠹⣿⣓⣒⣒⣾⣯⣧⠀⠀⠀⠀⠀⠃⢼⠀⡧⠄⠧⠃⠀⠀⠀⠀⠀⠀⠸⢻⡄
⠀⠉⠓⠒⢃⡖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠨⠀⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⡄⠀⠀⠀⠀⠀⠀⠇⠀⠐⠄
⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⢄
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⡠⣄⠘⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⡤⢴⣴⠦⠼⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠒⠈⠩⡿⣭⠿⠞⠃⠀⠀⠀⠀⠸⠤⠄⢀⣧⣾⣿⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⢠⡤⣴⡧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⡿⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠉⠉⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⢠⡀⠀⠐⠀⠀⠂⠒⠁⠀⠀⠂⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⡤⠤⠜⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠻⢶⣄⡀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛
⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣧⠀⠀⠀⢼
⠀⠀⠀⢴⡟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠆
⠐⢀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠁
⠄⠀⠁⠙⠓⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠇⠀⠤⠖⠛⠉⠁⠀⠈⠉⠁⠀⠀⡀⠀⠂⠈⡅⠀⠂⠀⠀⠀⠀⠀⠉⠉
⠐⠀⠀⢀⠐⠀⠀⠀⠀⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⢠⠆⠀⠀⠀⠁⠤⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠀⠂
⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠈⢷⠀⠀⠀⠀⠘⠈⠈⠀⠀⠀⠀⠀⠁⠄⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢿⠗⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠄⣀⠀⠀⡀⠀⠀⠀⠀⠈⠓
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⡐⠀⠀⠀⠀⠀⠀⢦⣠⠃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⠈⠀⠀⠀⠀⠠⢀⠙⠁⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠁⣤⠀⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⡰⠀⠀⠀⠀⠀⠀⠈⢟⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⣿⠉⠻⣆⠀⠀⠀⠀⠀⠘⠃⢀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡀⠀⠀⢻⡇⠀⠉⠀⠀⠀⠈⠁⢠⠔⠉⠉⠉⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⡀⠀⡄⠀⠀⠀⡠
⠺⠀⠀⠀⠁⠀⠀⠈⠛⠀⠀⠀⢀⠀⠀⠀⠈⠠⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠁
⠂⠀⣀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⡝⠁⡈⠄⠀⠀⠀⠀⠈⠀⢤⣠⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡒⠆⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⢀⠀⠈⣀⠀⠈⡀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡀⠀⠄⠆⠀⠀⠀⠀⠠⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⢀⠀⡀⠀⠠⠀⠀⠀⣦⠇⢀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠄⠀⠀⡀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠆⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠊⠉⠃
⠀⠀⠱⠾⡤⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠃⠀⠀⠀⠀⠐⠁⠀⠉⠁
⠀⠀⠀⠠⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠨⠀⠰⠞⠀⠀⠈⠀⠀⢠⢀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢁⠀⠀⠀⠋
⠀⠀⠀⠘⠀⢀⠆⠀⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣈⣁⣀⣠⣄⣀⣠⣄⣀⣀⣀⣀⣀⣀⣤⣀⣈⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⢀⡐
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⢠⢌⣘⣏⣿⡧⡚⠣⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣴⣿⣿⣾⣿⣾⣿⣶⣿⣿⣿⣴⣯⣦⡿⣦⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠅⠀⠀⠀⠀⠀⠂⢐⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣁⢀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣭⡧
⠀⠀⠀⠀⢤⣶⣾⣿⣿⡇⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠉⣿⣿⣿⠿⠀⠀⠀⣠⠢⢾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣦⡄⠀⠀⠀⠀⠸⠛⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⠻⢇⠀⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⣹⣿⣿⡟⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠉⠁⠀⠉⠽⠛⠉⠉⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⣄⣀⡂⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⡀⣀⣠⣴⣦⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣸⡿⢿
⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠘⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠶⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⠄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡤⠞⠪⢊⠛⠒⣂⠄⡆
⠀⠀⠀⠀⠀⠀⠈⠲⣴⡧⠤⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠙⠌⣀⢸⣷⡬⠼⠃⠀⠀⠀⠂⢾⣙⢠⡏⢸⢸⠇⠘
⠀⠀⠀⠀⠄⠀⢀⡀⢻⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⠥⣢⡈⠛⡩⢁⠀⢀⠀⠀⠀⠀⠢⠬⠿⢹⠼⠬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⣀⢠⣤⡀⠉⢱⠛⠋⠅⠭⠅⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣔⡀⡙⠛⢙⠢⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⡙⢷⡀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠺⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠋⠛⠂⠀⠀⠀⠀⠠⠀⠀⠄⠑⠠⢌⡞⢁⡄⠁⠀⡀
⠀⠀⠀⠀⠀⠠⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⡀⢀⡀⠀⠀⠀⠀⠀⠒⢤⣀⢀⢰⠉⡠⢁⣤⠘⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣠⣰⠲⠆⠬⢶⡾⣿⠀⠀⠀⠀⠀⠀⢀⡐⠉⠑⣯⣦⡷⠃⠄⠁⠁
⠀⠀⠀⠨⢄⠶⢐⠀⠉⠁⠆⠀⠀⠀⠀⠀⠀⣠⠤⠲⢌⣳⣶⢞⣻⣿⣝⠄⠀⠀⠀⠠⠐⢄⠀⣶⡼⣿⢿⠓
⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣈⡺⢿⠋⠤⡟⡀⠿⠀⠀⠀⠀⠀⠀⠐⠡⠈⡡⠼⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠄⠋⡬⠹⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣭⣴⣭⣯⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣆
⠀⠀⠀⣠⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠁⡀
⠀⠀⠀⠀⠀⣴⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠘
⠀⠀⠀⠀⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠙⠉⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠁⢀⣀⣤⡤⠰⢂⡄
⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⢀⠀⠁⠀⢀⣶⣿⡆⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⢠⣈⡁⠱⠒⠂⢰⣿⣿⣦
⠀⠀⣀⣀⣄⠀⢠⠀⢀⠐⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠒⡀⠐⠀⠀⠀⠀⠑⠀⠈⠀⠐⠀⠄⠀⠀⠁⠃⠀⠀⠀⣾⣿⣿⡄⠀⠀⠸⡿⠿⠛
⠀⠀⠿⣽⠛⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠈⠁⠉⠁⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠨⢍
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⢀⠰⠀⠄⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡆⣥⡄⠀⠀⠀⠀⠘⠂⠁⠀⠀⠚
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⡈⠐⠀⠤⠒⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⢀⠒⣀⠀⢀⡄⠀⠠⢄⠆⠀⡀
⠀⠀⠀⠀⠀⠈⠃⠀⠈⠀⣁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⣤⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡼⠀⠀⠛⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡣⡝⡒⡂⠄⠀⠀⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⣧⣷⡀⠑⠶⠀⠀⠀⢀
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠊⠉⠁⠀⠀⠈⠀⡀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠆⠀⠈⠂⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠰⠄⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠒⠀⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⢈⡖⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣽⣿
⣤⣀⠀⠀⠀⠀⠀⢀⣀⡤⠋⠉⠉⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⢀⣠⣤⣶⣶
⠉⠛⠿⣦⣄⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉
⠀⠀⠀⠈⠹⣷⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⡏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡀⠀⠠⣾
⠀⠀⠀⢀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢹⡷⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠻⠃⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠐
⠀⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠁⠀⠘⢃⣁⡄⠀⠄
⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠴⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠦⡀⣀⠀⠀⠀⠀⠀⠈⠁⠀⢀⢂⣀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡄⠁⠠
⡀⠀⠉⠀⠛⠓⠀⠀⠀⠆⢀⠀⠠⡄⠀⠀⠀⠈⠀⠀⠀⠇⠀⠀⣠⡶⠞⠛⠉⠁⠀⠀⠏⠉⠃⠀⠀⠀⠀⡠⠆⠒⢹⠡⠄⠂⠀⠀⠀⠈⠀⠀⠘⠋⠉
⠠⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⠁⢀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⡈⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⢁⢠⡀⠆⠚⠀⠀⠀⠀⠄⠀⠐⡀⠀⠀⠘⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠨⣄⠀⠀⠄⠀⠀⠀⠀⠀⠈⠢⡄⣀⠀⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⢤⡰⠞⠀⠀⠀⠀⢠⠀⠃⠠⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈
⠠⠀⠀⢀⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠠
⠀⠀⠀⢸⣿⡷⠀⠀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⡀⠀⡄⠐⠀⠀⢀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠥⠂
⠄⠰⠂⠀⠈⠀⡀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠠⠀⠀⠀⠠⢀⠘⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁⠈⠀⠂⠉⣀
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⢀⠀⡘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⣀⠁⠐⠀⠁⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢬⠐⠄⠀⠀⠀⠀⠀⠀⠀⣄⠀⣠⠂⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠈⠓⠀⠆⠀⠀⠈⠀⠀⠀⠉⢷⡧⠀⠋
⢀⡐⣄⠠⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⣶⠄⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠁⡀⠀⠀⠀⠀⠀⠉⠢⣀⡀⢀⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠈⢴⡆⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠂⠀⢠⣿⠉⠻⣷⡀⠀⠈⠀⠀⠀⠀⠰⠿⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠄⠀⠀⠈⣿⡆⠀⠘⠃⠀⠀⠀⠀⠾⠂⠀⣀⡖⠳⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠄⠀⠀⠘⢦⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠒⠀⠘⠀⠀⠀⠀⡴⠋
⠈⠂⠀⠀⠀⠘⠀⠀⠀⠀⠈⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⣣⡼⢀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠘⠀⢀
⠂⠀⢀⡀⠐⠀⠠⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠐⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡆⠀⠀⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⡀⠙

⠀⢈⠀⠀⠀⠀⣀⢀⠀⠀⠈⠀⠠⡗⠀⠤⠐⠀⠇⡎⠐⠒⠀⠀⠀⠀⠀⠀⠀⢦⣤⣤⠄⠀⠘
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⢰⠃⠠⠆⠬⣀⠄⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠊
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⠍⠉⣦⡀
⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⢸⣑⣟⠀⣒⢶⡇⠀⠠
⣀⡀⠀⠀⠀⠅⠰⠂⠀⠀⠀⠀⠀⢄⠀⠀⠂⠔⠀⠉⢅⠉⡙⠛⢁⡐⠀⣀⠀⠀⠐⣿⣍⡁⠀⠀⠘⣻⡆⠀⠠
⠀⠁⠀⠀⠀⣀⠀⡁⠀⠀⠀⠀⢀⠈⠀⣴⣷⣾⣶⡄⠈⠀⠁⠈⠉⠀⡄⠀⠀⠒⠂⠘⢿⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠋⢀⠀⠀⠀⠀⠀⠁⠀⠛⠟⠋⠉⠀⠐⠖⢀⠀⠒⠀⠀⠈⠉⠀⠠⣀⡀⠉⠉⠉⠁⠀⠀⠀⠅
⠀⠀⣠⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⠉⠀⠐⠀⠐⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠉⠋⡉⠙⠛⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠄⠀⠒⠂⠂⠀⠀⠈⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡜⠇⢰⠉⡤
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡄⠀⢀⣠⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠰⡀⠀⡁⣠⠎⠀⡀⠀⠀⢀
⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠋⠂⠀⠀⠀⠸⣤⡀⠀⠀⠀⠀⣀⣤⣤⣴⣄⠐⠔⠁⠀⠠⠀⠀⠘⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠐⠲⠂⠀⠀⢤⠀⠇⠀⠀⠀⠀⠻⠿⢿⣿⣾⢆⣤⣤⣄⣀
⠠⠤⢀⢀⣾⡃⠀⣴⠛⡍⠉⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠉⠁⠙⠛⠛⠻⠿⠃
⠀⠄⡠⠎⠀⠁⢸⠃⣝⠀⠠⠼⢼⡆⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠂⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣤
⣠⡞⢁⠀⠘⢠⣿⠛⠛⠀⠈⠁⠾⣧⡌⠛⠛⠛⠛⢀⠀⠀⠀⠈⠀⠀⡀⠀⠀⢤⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⢈
⠇⢠⠀⠙⠀⠈⢿⣿⣷⣤⣄⣤⣶⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠤⠀⠄⢰⡆
⠀⠤⠄⠀⠤⠀⣈⠻⣿⣿⣿⣿⠿⠋⠀⣀⠄⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠂⠀⠀⠂⠀⢴⡜⢃
⡀⢠⠀⠂⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠀⢀⠀⠀⠠⣌⠳⠟
⣀⣀⣀⣀⣀⣀⣀⣘⣖⣀⣀⣈⣀⣜⣈⣄⣀⣲⣂⣀⣠⣀⣀⣂⣀⣄⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣙⣳⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⢸⣀⡆⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣼⡯⡀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣃⠞⠠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣦⠉⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠋
⠀⠀⢰⠇⠀⠀⠀⠀⠠⠞⡫⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠶⠃⠀⠈⠓⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠤⠀⠀⠀⠀⢀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠀⠀⠀⠤
⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⢀⡀⠀⠀⠀⠠⡀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⢀⠂⣄⠀⠀⠰⠀⠀⠀⡄⢀⠀⢠⡀⠀⠀⠀⠄⢠⠄⠀⢀
⠀⡮⠷⠀⣠⠈⠀⠀⢀⡀⠀⠙⢆⠀⠈⠁⠀⡛⢌⡀⠀⠤⠀⠀⢻⡁⢲⠀⠈⠱⠀⢁⡁⠀⠺⠛⠁⢀⠖⠀⠘⠀⠀⠫⢠⣫⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠈⠺⠀⠠⠀⠀⣴⠼⠧⢹⠀⣁⠁⡀⠐⠆⠀⠂⠀⠀⠉⠐⠀⠀⠀⡀⡂
⠀⡐⢖⠩⢀⠀⠀⢀⠴⠒⠈⠉⠉⠓⠂⠀⠆⠀⣄⣀⣠⡄⠀⣈⠉⠉⠁⠀⣤⠀⠃⡀⠀⠀⠀⠀⠀⠀⠊⠀⠠⣠⣀⠈⢉⡆
⠀⣚⣅⠤⠑⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢾⣿⠄⠀⠀⠄⠀⠀⠘⠀⠀⠇⠸⠀⡀⠉⠀⠄⠀⠠⡀⢉⠁⠀⠁
⠀⠠⡈⠁⡐⠀⡉⠀⠉⠉⠁⢻⠂⠉⠉⢁⣍⡁⠘⠒⠊⠀⢀⠁⠀⠤⠄⠀⡐⠂⣂⠀⠂⠁⠀⠀⠈⡀⡋⠁⠈⠏⣈⣁⠄⢶⢀
⠀⠠⣈⡁⠀⠀⢹⠃⠉⠀⠀⢸⠀⢤⠀⠨⢱⠀⠀⢰⢈⣄⠊⠀⠀⠀⠀⠀⠂⠀⠉⣉⠰⢢⡄⠀⢀⠁⠁⠀⠈⠱⠛⠓⠀⢠
⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⠀⠀⢪⡇⠀⠀⠀⠀⢈⠀⠀⢀⠀⢀⠄⣴⡀⠀⡀⡀⠀⡀⠘⠛⠃⠀⠀⡀⠠⣀⠂⠄
⠀⠠⠁⠀⡄⠂⠁⠀⢀⡀⢴⡸⠀⣀⠀⠠⠈⡇⠀⠁⠀⠀⠘⠀⠤⠚⠃⢀⣸⠁⡱⠀⢠⣴⠀⠹⢄⠀⠀⢀⠀⠀⠠⠐⠐⡀
⠀⢐⡂⠀⠈⠈⠀⠀⡉⠀⠀⡀⠘⠀⠄⠀⠠⠐⠄⠄⡀⠀⠀⠀⠒⠀⠀⠀⠉⠀⠀⢀⣤⣌⡄⠀⠒⠋⠀⢀⣄⠀⠀⠀⠀⠇
⠀⠈⠃⠀⠁⠐⠀⠺⠗⢀⢀⠁⠀⢀⠀⠠⠂⠀⢈⠂⠡⠀⠀⠀⠀⢠⠄⠀⢶⣦⣤⡄⠀⠀⠁⠀⢀⣶⡤⠐⢀⣉⢓⠄⠀⢀⠄
⠀⠤⠀⠀⠐⠀⠂⠀⠀⠀⠀⢀⠀⠈⠂⠀⠁⠐⠀⠤⠐⠂⠀⠠⠀⠢⠄⠀⡈⠀⠀⠉⠀⢰⡇⠀⣄⢻⣺⣟⣃⣞⣿⣯⡄⢀⡀
⠀⠀⠀⠀⢂⡁⡀⠀⢦⠀⠀⠢⠘⠀⠀⡅⠀⠀⠂⠀⢈⠁⠀⢀⠢⠀⢐⡀⠂⠀⠀⠀⠀⠈⠁⠘⠉⠃⠈⡏⡍⠋⠈⠁⠑⠀⠁
⠀⢌⠤⠀⠈⣄⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢜⠀⠈⠀⠀⠀⠑⠀⡀⠂⠀⠀⡀⠀⣤⣄⡄⠀⠀⠃⠀⠀⠠⠀⠀⠦
⠀⠠⠎⡄⠀⠘⠀⠀⠒⠋⢀⠀⠃⠉⠘⠀⠃⠉⠐⠁⡀⠈⠁⠀⠀⠀⠀⡀⠈⢴⡥⠀⠀⠃⠀⠁⢛⠃⠀⠀⠀⠀⠂⡀⢠
⠀⢁⢚⡠⢡⠀⠀⠀⢀⠀⠉⢀⡁⠀⠁⠉⠁⢈⡁⠈⠁⣠⠘⠠⣀⣀⠶⠃⡀⣈⠈⠁⠀⠀⠀⡀⠘⠶⡄⠓⠃⠠⠀⠉⠠⠠⠆
⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⢀⠃⢀⠀⠀⠀⠀⠀⠀⢀⠈⢠⣀⠀⠀⠀⢠⠅⡊⠁⠀⠀⠀⠀⢉⡁⢁⠁⠀⠂⠀⠄⠠⣌⡀⠂
⠀⡎⠀⠀⠀⠆⠀⠰⣶⡴⣧⡄⠩⠤⠀⠀⠐⠋⢱⠀⠀⠈⢐⠃⠀⣀⠀⠐⠒⠁⠀⠒⠂⢠⠀⠀⢂⡊⠒⠀⠀⠀⡐⠀⠉⣀⡀
⠀⠀⠘⠈⠣⠀⠀⠀⠋⡏⠉⠇⠀⠀⠁⠄⠀⠀⢊⢄⠀⠁⠁⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⡐⠀⠀⠇⠐⡁⠀⢠⠀⠀⠀⠩⠐
⠀⠀⠦⠀⠄⠀⠲⣒⠚⢁⣐⡇⠀⠀⠤⠀⠀⠄⠀⠽⠇⠀⠠⠄⠁⢀⠀⢀⡂⠈⡆⠙⠂⠁⢰⠘⠀⢩⢨⠅⠀⠒⠀⠀⠀⠀⠅
⠀⠀⣀⢠⠀⠀⢠⡌⠉⠉⠉⠁⠀⠄⣷⠲⠀⣠⢶⣖⠤⣄⠀⠲⠆⠀⠀⠶⢄⠀⠀⠀⠀⢤⠖⣆⠀⠒⠰⠂⠀⠀⠀⠐⠔⠁
⠀⠀⢘⠬⠆⠀⢈⠉⠢⠀⢀⠈⠀⠀⠀⠀⢨⣶⠋⠉⠙⢶⠆⠀⠄⢀⠘⠈⠁⠀⠀⠀⠀⢊⡗⢤⠀⠀⠂⠀⠤⣥⢀⢤⠀⠀⢄
⠀⠀⠈⠓⡯⠂⠈⠠⢀⠀⠀⠉⠀⠗⠀⠀⠈⢭⣷⣠⣶⡿⠂⠀⠂⢁⠀⢀⠀⠘⠉⠀⠀⠼⠧⣐⠀⠂⠀⢤⠀⠁⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣈⣁⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⣴⠚⣿⠛⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⢳
⠀⠀⠀⠀⠀⠀⠸⠛⣿⡿⢿⠄⠀⠀⢈⣧⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣴⣖⢠⣴⣾⣶⣿⢷⠁⠀⠀⠀⠀⠠⢿⣶⣦⣄⣶⣄⠀⠀⢰⠀⠀⠀⠀⠀⢣⡄⠀⢿⡀⠀⠀⢸⠉⠉⠁⢁⡠⠂⠀⠀⠀⢀⡇
⢰⣿⡟⣿⡙⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠱⠯⠟⠂⠀⠀⠄⢻⣦⡀⠠⣾⡟⠀⠀⢹⡤⠔⠁⠀⠀⠀⠫⠀⠀⠀⠀⡢⠛⠞⡀
⠈⠉⠋⠙⠃⠀⠀⠀⠀⠀⢀⠔⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⠉⠁⠀⣰⠀⠀⠀⠀⠀⢀⡤⠀⡴⠖⠚⠀⠀⠀⠀⠀⡦⣶⠃
⠀⠀⠀⠀⢀⠄⠀⡐⠧⣶⠯⠙⠷⠰⠅⠀⠒⣄⠀⠀⡰⠂⠀⠂⠉⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⣿⠓⠶⠃⢀⣀⠀⠀⠀⠀⠐⠆⢹
⠀⠀⠀⢰⠃⢀⠆⣀⠀⠀⠀⠀⠀⠀⢀⠐⡀⠈⣆⠀⠷⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠂⢀⠈⠁⠀⠀⠀⠀⢐⣰⠂
⠀⠀⠀⡇⠀⡾⠈⠻⣦⡄⠀⠀⢀⣴⡿⠀⢻⠀⢸⠀⠀⠐⠾⠷⣄⣸⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠆⠸⡀
⠀⠀⠀⢧⠀⡁⠀⢀⠋⠀⠾⠆⠈⠛⡁⠀⢘⠀⣸⠀⠀⠀⠀⠀⠈⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠞⠛⠖⠚⠀⢀⣄⡀⠀⠈⠙⠰⠒⠊
⠀⠀⠀⠈⠻⢷⣄⣈⠿⢧⡴⢦⡾⠾⠁⢀⣼⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠤⣀⢀⣀⠄⠀⠀⠀⠀⠀⠀⣸⣿⣦
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠠⠄⠀⠀⠒⠒⠊⠀⠀⠀⠀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⢀⣀⠀⢼⣧⣾⣿⣿⣿⣿⣇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⠉⠁⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣾⡟⠀⠀⠈⣽⣿⡿⢿⣿⡟⠛⠃
⠀⢰⠀⠀⠀⠀⣦⡀⢰⣦⠀⢀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠻⠿⣿⡯⠿⣿⣧⢀⠀⢠⣿⠏⠀⢹⣿⢀
⠀⡟⠀⠀⠠⢠⣿⡇⡘⣿⡄⠻⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠰⢸⡇⠀⠀⠀⠀⢀⣠⣹⣿⣭⣿⣿⣶⣶⣾⣿⣶⣶⣾⣷⣿⡖
⠀⠹⣀⠰⢃⡀⡉⠐⠛⢀⠀⠀⠂⠀⠀⢰⣥⠃⠀⠀⠀⠀⠀⠀⢸⣳⣄⠀⠀⠈⢻⣿⡿⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣸⣿⣇⣐⣦
⠀⠀⠈⠉⠙⠁⠾⢴⠶⡇⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⣽⡟⠀⠀⣠⣸⣿⣿⢘⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡿⡿⠿⢇⠰
⠀⠀⠀⠀⠘⠈⠀⠀⠈⠁⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢲⣿⠀⠀⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡟⠀⣳⠄⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠤⢀⠀⠀⠈⢓⠐⠉⠳⠤⠄⢤⡼⠾⠗⠀⠀⠀⠀⠀⠀⠈⢿⣧⢽⣿⡏⠄⠽⢿⣟⣹⣿⣷⡄⣧⣤⠼⢡⠎
⠀⠀⠀⢠⠖⠲⣄⡜⠀⠀⠀⠀⠀⠑⢀⡀⠀⠀⠁⠀⡀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡏⡃⠃⠉⠈⣿⣿⣿⡏⢻⣿⣀⡴⠛⠒
⠀⣀⣀⡼⠲⣄⣰⠖⢲⣤⡀⠀⠀⠀⠀⠝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣿⣿⣇⣀⣀⣀⣀⣿⣿⣿⣷⣆⠀⠉⠂⠀⠈
⠐⠋⠛⠁⠀⠉⠁⣠⣿⡟⠛⠛⡅⢚⡘⠂⣤⡰⠦⠀⣐⢒⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡆⢉⣻⣿⣿
⠀⢤⣀⣴⣶⠖⠚⠛⠛⠛⠒⠚⠛⠃⡉⠀⣀⠀⣩⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⡛⠋⠁⠀⠛⠿⠿⣿⣷⣶⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠚⡦⣄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠙⠅⠆⠁⠈⠸⡄⢠⡔⢲⠖⡚⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⡑⠚⠃⣰⠂⢀⣇⡇⠀⠀⣎⠀⠊⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡊⣑⣒⠤⣀⠀⠀⠀⣤⣴⣶⠀⠀⠀⠀⠳⣤⠬⠒⠄⢉⠠⠢⠩⠁⢃⣠⠃⣤⢒⣡⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⣧⡤⣀⠀⠙⠢⢝⠢⡀⠘⣿⣼⡄⠀⠀⠀⠀⠈⠑⣄⣰⣃⣀⣘⣁⡠⠚⠁⡠⠊⠉⡸⠐⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠇⠇⠀⠈⠻⡳⡀⠀⠀⠙⠮⡳⣼⡷⣧⢀⣠⡴⠖⠛⠉⣹⠁⢷⠠⡉⢂⠈⠏⠛⠐⠶⠶⡴⢀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠨⡜⡀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠈⠪⣧⡹⣏⠀⠀⠀⡰⠋⠀⡠⠋⡀⠈⡦⢆⠀⠘⠆⠰⡗⢴⣄⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠳⡳⢄⣀⠴⡣⠃⠀⠀⠀⠀⠀⠀⣽⡽⡺⣆⠀⠀⣇⡄⠊⢀⠊⠋⠐⢧⢸⡠⠊⣃⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⣏⡳⡛⢿⣆⠀⠈⢣⡀⣆⢠⢛⢢⡀⡇⢣⡴⣍⣍⣫⠁
⢠⠖⠓⠦⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠫⣝⠫⠩⣣⢝⢦⡀⠀⠉⠉⠣⣴⡏⠉⠁⠀⠀⠀⠈⠁
⡏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⠀⣠⣴⣿⣦⣅⣈⣸⣷⣶⣦⣾⣷⣄⠀⣀⣀⣈⡀
⢻⡄⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣠⡴⠿⣉⠣⡀⠡⠉⡟⢹⠡⣿⣝⡏⢹⠋⡠⢊⣀⣐⠈⡙⣟⠛⠟⢉⡟⠳⢦⣄
⠀⠉⠓⠶⠚⠋⠁⠀⠀⠀⠀⣠⢾⡭⣤⣄⠈⣆⢰⣠⣏⠳⣌⠲⠔⠊⡀⣮⣼⢰⠋⡖⣮⡧⠠⣿⠈⢮⣹⠀⣴⡭⣝⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⢸⡸⢽⠟⢁⡏⣸⣟⡓⢔⣁⠮⠥⠥⠤⡬⣿⢘⢦⣉⣩⣀⠶⢅⢁⠘⣿⣄⠘⠛⣃⡜⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠐⢄⠑⠒⠛⠋⣰⡟⢢⠒⡡⠔⠂⣒⣀⣐⠂⣿⠐⠑⠈⡅⠀⢩⢋⣉⡉⢻⡎⠙⡉⠃⢸⢀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠑⢠⠬⢉⡉⣿⣿⠑⡄⢋⢀⡴⠋⠡⠀⠌⡉⣿⡠⢀⢁⠐⠿⠻⡘⠿⡻⠈⣷⡠⢓⢩⡉⡺⡔⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠕⡈⣐⣠⣐⡀⣿⡿⠇⠇⡀⢸⠠⢵⣫⢭⡑⡄⣿⡢⡕⠣⠐⠀⣐⢍⠋⢍⠐⣿⠡⢰⢻⢻⡇⣿⡄⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⢠⠎⢁⣤⢤⡙⣿⣴⣈⣼⣤⣈⢧⣀⠛⠚⣠⠇⣿⢐⠴⠛⠓⠲⢬⠂⠯⠠⠑⣿⠀⢊⢦⣥⡞⢁⡽⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠀⠸⣜⣚⡡⣿⢀⣀⡀⠑⣌⠢⡉⢍⣩⡣⢵⣿⡏⢀⡔⡿⣦⠘⡎⠡⡱⢈⣿⡤⡢⢲⣾⠲⢳⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢈⠳⣌⡀⢂⠌⣿⠡⣞⡿⠀⡼⠀⡇⠈⠟⠗⣈⣿⠐⡈⢧⣓⣃⣼⠖⠚⠙⢻⡿⢈⢔⠒⡐⢤⡽⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠤⡂⠩⠉⠩⢹⡗⢦⠴⣎⣠⢴⣁⡰⠸⡀⢴⡟⢈⢌⢄⣼⡆⣏⢰⣿⡟⣾⡧⠟⠓⢤⡈⡆⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⣡⠜⡓⢌⢷⣠⠟⠡⢀⣂⡀⠹⣖⠱⣸⠇⡤⣆⣈⠄⡰⢸⠳⠬⢶⢿⠡⣾⣷⡄⢹⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣼⣨⡏⣤⢰⢱⡒⡿⠠⡇⠡⠈⢠⢎⣥⣌⠻⣆⣡⠂⠀⡋⠈⠓⠮⣾⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠷⣼⣦⣍⣤⣞⣀⣤⡴⠿⢮⣿⣿⣀⣯⣬⡴⠷⠷⠾⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⡀⠁
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢁⢠⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⢈⠁⡔⠀⠀⠀⠘⠠⠀⠀⠀⠐⠿⢉⣝⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠠⠄⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠏⣶⠀⢙⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠲⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⠂⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠠⠂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣦⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡀
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣀⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠆
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣀⠀⠀⠀⡚⠃⠀⠀⠀⠀⠀⠀⢀⡰⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⠀⠀⢠⣶⣶⡆⠀⠀⠸⣷⠀⠰⣁⣺⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠶⢿⠟⠋⠀⠀⣼⣿⣿⣿⡀⢠⠞⠋⢁⡀⠉⡛⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⣶⣄⠀⠀⠰⣄⣴⣿⣿⣿⣿⣷⣄⡆⠀⠸⣄⣾⡿⠀⠀⠀⠀⠀⠰⡇⡠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠈⣹⣿⣿⣦⣀⡀⠀⣿⣿⣿⣿⣿⣿⠀⢠⣤⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡀⠀⡄⠀⠀⠆⠠⠴⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠢⠸⡇
⠀⠀⠀⢠⠁⠘⣇⡴⠋⠀⠐⠞⢻⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⡟⠆⠀⠀⠀⠀⠐⢧⣷⠠
⠀⠀⠀⢸⡀⢸⡟⠀⢰⣶⣶⣶⣾⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣤⣤⡄⠀⠀⠀⠈⣿⡄⡀
⠀⠀⠀⠀⠑⢼⣇⠌⣼⣿⣿⣿⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠓⣿⠏
⠀⠀⠀⠀⠀⢸⣯⠘⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣀⢰⡷⠀⣿
⠀⠀⠢⠘⢌⠙⣿⠀⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⢀⣿⠀⠋
⠀⠀⠀⠀⣾⠀⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⠀⠀⢸⡟
⠀⠀⣧⠄⢹⠀⢿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢺⠃⠀⣾⡇⠀⢰⠇
⠀⠀⢈⣧⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣀
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⡶⢶⣶⣶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠒⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠋⠉⢉⡟⠡⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⠀⠀⠸⣆⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⣿⡖⠒⠒⠂⠒⠛⠛⠉⠉⠁⢀⡾⠉⢧⡖⣒⣿⣿⣿⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⠋⠀⣷⣤⣀⣀⣀⣀⣀⣀⣤⣴⣾⡁⠀⠀⠻⡅⠙⠿⡟⢷⡀
⠀⠀⠀⠤⣄⣀⢀⡤⠚⠁⠀⠀⣠⠞⠉⠀⢀⠜⠉⢳⣄⣀⣀⣀⡀⣀⣰⠏⠈⠳⣄⠀⠀⠙⢦⡀⠋⠈⠉⠢⡀
⠀⠀⠀⠀⠀⢨⠛⠒⢦⣤⣖⠋⠁⢀⣤⠞⠋⠀⣰⠟⢷⡀⠈⠉⢉⡿⠋⠣⣀⠀⠈⠳⣄⡀⠀⢙⣲⣄⣠⡤⠬⢶⠖⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠈⠙⢿⠿⠤⣤⣴⠊⠁⠀⠈⢧⡀⢀⡾⠁⠀⠀⠈⣳⣤⡤⢾⡿⠋⠉⣹⠃⠀⠀⢀⠏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⢸⠇⠀⣿⠉⠙⠓⠦⣤⣨⡷⠛⣧⡤⠖⠛⠉⡽⠁⢀⡞⠁⠀⣼⠃⠀⠀⢀⠎
⠀⠀⠀⠀⢀⡏⠀⠀⢠⡇⠀⠀⣼⢀⣠⣿⣤⡤⠴⠖⠚⣿⣤⣴⠿⣤⡀⠀⣼⠃⢠⡞⠀⠀⣸⠃⠀⠀⢀⠎
⠀⣀⣀⣀⣼⣁⣠⣤⢾⡤⠖⠚⠛⣯⠉⠙⢧⠀⢀⡴⠚⠁⠀⣿⠀⠀⢙⣶⡇⢀⣿⠀⠀⣰⠃⠀⠀⢀⡞
⠀⠀⠀⠀⠈⠑⢤⡀⠀⠙⢦⡀⠀⠈⢷⡀⣨⡷⠛⠲⠶⢤⣀⣿⡴⠚⠉⠀⣉⣿⣇⠀⠀⡏⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠙⣆⠀⣸⠿⠛⠲⠦⢤⣀⠀⠈⣿⢀⣤⠖⠋⠁⠀⠈⢳⣤⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⣻⡾⠷⠶⠤⠤⣄⣀⠈⠙⠲⣿⠏⠀⢀⣠⠤⠒⠊⠉⠙⠳⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣾⣋⡀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣽⣤⠖⠋⠀⠀⠀⢀⡠⠴⠒⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⠉⠑⠒⠢⠤⣄⡀⠀⠀⢸⡅⠀⠀⣠⠔⠊⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣸⣇⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣀⡀⣀⣠⣔⠝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠈⠉⢻⡀⡏⠀⠀⢸⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠻⡠⠔⠊⠉⠉⠉⠛⠋⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢆
⠀⠀⠀⠀⠀⠀⠀⢰⢡⠃⠀⠀⠀⢀⡼⠀⠀⠀⡠⢾⠀⠀⢀⡴⣄⠀⠀⡏⢆
⠀⠀⠀⠀⠀⠀⠀⠇⣼⠶⣀⣀⠴⠺⡥⠤⢒⠍⠀⠳⡒⠊⠁⠀⠈⠒⠲⡟⣼⡄
⠀⠀⠀⠀⠀⠀⢸⡴⡟⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠘⣷⡇
⠀⠀⠀⠀⠀⠀⢸⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇
⠀⠀⠀⣀⡀⠀⢸⠀⢱⡀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠚⠁⠀⠀⠀⠀⠀⠀⢰⠁⡇
⢠⠾⡕⠃⠘⣤⣸⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣇⡰⠋⡧⢲⣄
⡯⠁⠀⠀⣠⠃⠀⠉⠑⠒⠤⣙⡢⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢖⣉⠤⠔⠊⠉⢣⠀⠀⠁⢞⡆
⠙⠒⠠⢞⡁⠀⠀⠀⠀⠀⠀⠀⠉⢧⠌⣉⣉⣉⣉⣉⣉⠭⠤⠏⠉⠀⠀⠀⠀⠀⠈⠳⣄⣠⣬⣇
⠀⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⢀⡜⢲⡤⠤⠤⣤⠤⠤⠔⠺⠀⠀⠀⠀⠀⣀⡤⠔⠺⣯⠤⠤⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⠎⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⢇⣠⠴⠒⠉⠀⠀⠀⣀⠙⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⢷⠀⠀⠀⢱⠀⠀⠀⢸⡀⠀⠀⢀⠴⢊⡭⠟⣛⠿⠖⠒⠾⢿⡛⠯⢍⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⡀⢀⠎⠸⠤⠤⣴⠒⠃⠀⠀⠀⡇⢀⡴⢁⡔⠁⢀⡞⠁⠀⠀⠀⠀⠀⠙⢆⠀⠙⢆⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡞⢀⠎⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢧⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡞⠀⡞⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⣀⣀⡀⠀⠀⣿⠀⠀⠀⣀⣸⠃⢰⠃⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠉⠉⣻⡋⠉⠉⠀⡿⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⡇⠀⢸⠀⠀⢸⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⣳⡶⠴⡒⢦⠀⣿⢸⠀⠀⠀⢷⠀⢸⡀⠀⠈⡇⠀⠀⢀⣸⠉⢉⣷⢦⣀⣀⢰⠿⠖⠲⣼⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⠥⣤⣼⡍⣱⠊⠙⣾⡄⣿⢘⡀⠀⠀⠸⡄⠀⢇⠀⠀⢻⣠⡖⠬⠏⢳⡜⠘⠛⠁⠛⠹⢄⠀⢀⣿⡀⣸
⠀⠀⠀⠀⠀⠀⠀⢻⡀⡤⠛⠛⠓⣇⠀⣀⣸⠷⠟⠫⡉⢱⠖⠛⣷⠖⠾⢦⢀⡽⠉⠁⢀⣀⠀⣇⡶⠶⠤⣄⣰⠾⠛⠻⡍⠉⠙
⠀⠀⠀⠀⢀⣀⣶⠟⢻⠒⠋⠉⠉⢹⣄⡏⠉⠀⠀⠰⣧⡋⠀⢀⡟⠀⠀⠘⠛⣧⣴⡖⠾⠏⢻⣼⣇⠀⠀⠀⢹⠀⠀⣈⣧⣤⠖
⠀⠀⠀⠀⠈⠙⠛⠲⣾⢦⡀⠀⠀⠘⢆⡀⠀⢀⣘⣯⠉⢹⠟⠛⠻⢇⡀⠀⢈⠟⠈⠀⠀⠀⠀⢻⠈⠑⢶⡤⠼⢠⡞⠉⠁⠈⠙
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠥⣭⣵⣶⣿⠏⠙⠦⣽⣆⣀⣴⣋⠀⠀⣠⣼⣣⡤⢾⠦⢤⣠⢦⡼⠻⠾⠓⠒⠶⠻⠗⠦⠷⠤⡤⠤⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠓⢤⣄⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠄⢠⠀⡀⢸⢠⠊⠙⡉⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⣠⢄⡀⠀⠀⢀⣤⡄⠀⠀⠸⣄⠀⠄⠘⡁⠌⠚⠰⠰⢃⡤⣊⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢮⠿⢤⣄⠉⠚⢕⠤⡈⣿⣧⠀⠀⠀⢀⣑⣄⣯⠠⣜⢠⡀⣁⠌⠉⡸⠊⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⠂⠀⠀⠹⡇⠀⠀⠉⠪⣺⡻⡦⠖⠋⠉⡠⠎⠸⠀⠀⡀⠀⢁⠉⣋⣒⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠘⣴⣀⢀⡰⡇⠀⠀⠀⠀⠈⣿⠽⡄⠀⢸⡀⠀⠀⠓⠰⡍⣇⠸⠀⠙⡌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⣰⣟⣞⡿⡄⠈⠣⣠⡄⠘⣀⣸⠱⡴⣩⣹⠁
⡴⠉⠑⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠑⡏⣀⢓⢙⣆⠀⠀⠈⠲⠃
⢇⠀⠀⠀⢀⣰⠋⠀⠀⠀⢀⣤⡶⢞⠛⡓⡶⠞⣻⣿⠳⠶⢛⠟⠛⠛⢳⡶⠶⠶⡦⣤⡀
⠈⠓⠶⠖⠋⠀⠀⠀⢀⣴⣯⣴⡈⡆⢀⣴⠲⠐⠬⠛⠠⣤⢠⠪⡿⣷⠀⡏⢠⣸⠀⣾⣽⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠸⣜⢛⣡⢇⡾⠋⡈⠔⠒⣒⣂⢹⡆⠳⢬⠥⢟⡠⢄⣿⠦⣉⡡⢎⢻⣆
⠀⠀⠀⠀⠀⠀⢠⣏⠢⢑⡀⠉⣠⡾⠄⢣⠀⡠⠔⠒⠒⢼⡇⠀⠀⣤⣼⢴⣶⠘⡇⣠⠴⠮⡄⣽⡆
⠀⠀⠀⠀⠀⠀⢸⠛⠐⢀⣀⣀⢸⡿⠀⠀⢸⠀⣴⢿⠪⢸⡇⠔⠦⠀⠈⢓⢛⠀⣿⠁⣶⣷⢘⣆⢻
⠀⠀⠀⠀⠀⠀⢸⠇⡜⢡⣶⡆⢻⠦⠴⢥⠬⠧⣌⣋⡴⣹⣧⠞⢉⡑⢢⣈⠃⠀⣿⠀⠓⣷⢊⠸⢻
⠀⠀⠀⠀⠀⠀⠸⡇⢧⡈⠛⠗⣿⣔⣶⡄⢣⠐⠀⠶⡆⢽⡇⠰⡻⡿⢸⣁⠤⢴⣿⠐⠘⠛⠉⡅⡾
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⢓⠒⠺⡧⠭⢵⣃⣔⣀⠀⢀⣽⠃⠀⢩⣮⣏⢰⣶⢾⡧⠶⢄⠑⢘⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡁⣒⣢⢳⡰⠉⣠⣄⠙⣶⠲⡿⢠⡤⣄⠀⡉⠒⢳⠿⡰⡿⡆⣹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⣷⡂⡟⠽⢃⠇⢀⣠⣏⣶⡆⢳⢐⣠⣌⣠⣩⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠛⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠒⠒⠈⠙⠁⠒⠀⠴⠞⠛⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠓⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⢠⡶⠶⠴⠠⠤⠤⠤⠤⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣦⡀⠀⠀⠀⢺⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠛⢿⣆⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⡰⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢿⣿⣦⡂⠀⠀⠤⣤⣾⣿⣿⡿⠀⠀⠀⠀⠀⠈⢿⣆⣤⣴⡚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⣿⣿⣿⡟⠀⠀⠈⠻⠟⠛⠁⠀⠀⠀⠀⠀⡰⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣤⣄⣒⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠤⣄⣀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣿⠋⠉⠀⠘⡏
⠀⢀⣴⠖⠂⠈⠒⠒⠊⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⢷⣦⡾⠃
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠶⣄
⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⢀⣠⡤⠀⠀⠀⣤⠞⠛⠂
⠀⠛⠛⢧⠀⠀⢀⡀⠀⠀⠀⠀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡟⠻⠛⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠈⢧⡀⢘⣿⣀⠀⠀⠀⢹⣿⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠛⠿⠿⠙⣷⣄⡀⣸⡿⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⢿⠅⠀⡀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⢄⣤⣤⣄⡀⠀⠀⠀⠀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠾⠇⠀⠈⠛⠲⠶⠿⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂