Vento solar Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⡛⠀⣛⣛⣛⣛⡃⢘⣛⣛⣛⣛⠀⢛⣛⣛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⡄⢠⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣀⡀⡄⣀⢀⠀⢀⣀⢀⡀⣀⢀⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠓⠋⠛⠛⠛⠀⠸⠚⠛⠃⠋⠋⠛⠘

⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠠⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣸⠇⣤⣀⠀⠀⠀⠈⠉⠉⠉⠋⠘⠓⠲⠶⠶⠤
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠛⠲⢦⣄⡀
⠙⠓⠖⠖⠛⠉⣤⡀⠀⠳⣦⡀⠀⠀⠈⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡆
⠀⢰⡆⠀⢀⠀⠈⢳⡄⠀⠀⠙⠶⠀⠀⠀⠀⠀⠀⠈⠁⠲⢦⡄
⠀⠘⠇⠀⠘⣧⠀⠀⠀⣤⠀⠀⠀⠀⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⣦⠀⠀⠸⣆⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣰⠋⠀⠀⠀⢀⡟⠉⠉⠉⣹⠇
⠀⠀⢿⠀⠀⠀⠉⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⣠⣯⣀⣀⣠⣼⣃⠀⠀⠀⣀⡾⠁⠀⠀⢠⡟
⠀⠀⢸⡄⠀⠀⠀⢳⡀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠈⣽⠛⠉⠉⠛⠛⣯⠿⠲⠶⢶⡾⠁⠀⠀⠀⠀⠀⠀⣀⣦⡀
⠀⠀⢸⡇⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⣦⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⢠⡟⢦⣄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠓⠲⢶⣿⣧⣤⣀⣀⣀⣠⡏⠀⠀⠀⢀⡾⠀⠀⠉⠳⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⠞⠁⠀⠀⠈⠉⢹⡿⠛⠓⠶⠶⣾⠃⠀⠀⠀⠀⠈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⡀⠀⢠⡟⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢰⠟⠶⣀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢦⣤⣀⡀⠀⠀⡾⠁⠀⠀⠀⠀⠙⠀⠀⠙⢧⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠺⠧⣤⣀⡀⠀⣴⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠛⢻⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⠀⠁⣤⣤⣤⣤⣤⣭⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡄⠀⢀⣤⣤⣤⣤⡀⣠⠀⣠⡄


⠀⠀⢠⣤⣤⣤⣤⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⡄⡆⢰⢸⢀⠁⡆⡚⠀⠀⡇⠂⢰⠘⠀⡆⠂⢘⢰⡂⣲⢰⡰
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣬⣥⣤⣤⣥⣤⣤⣤⣤⣭⣥⣤⣤⣤⣬⣤⣤⣤⣤⣯⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠂⢀⡀⢰⠃⣀⡀⡀⠀⠀⠔⢻⠑⡆⣀⡀⠀⢀⠀⢀⢰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢈⠗⢎⡸⢻⢸⡡⡇⢹⡀⠀⠀⡿⠈⢸⡡⣇⡟⢹⢸⡈⢼⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⣠⣤⣄⣤⣄⠀⣤⣤⡄⣀⣤⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠁⠀⠉⠉⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢤⠤⡤⢤⣤⠤⢤⠤⠤⣤⠤⠤⠤⠤⠤⠤⣤⡤⠤⡤⡤⠤⣤⠤⠤⢤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠥⡤⡤⠤⠤⣼⠧⠤⠤⠤⢤⣿⠤⠤⠤⠤⠤⠤⢼⡦⠤⠤⠤⠤⢿⡦⠤⠤⠤⠤⢵⡄
⠀⠀⠀⠀⠀⢀⣼⣥⣤⣤⣤⣤⣤⣯⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣿⡄
⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢀⡼⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⣿⠋⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⣿⡉⠉⠉⠉⠉⠉⢻⡄
⠀⠀⠀⣾⣥⣤⣤⣠⣤⣤⣤⣿⣤⣤⣤⣤⣤⣄⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⣠⣤⣤⣤⣤⣤⣼⣧⣤⣤⣄⣤⣤⣤⣽⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡕
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣿⡏⢹⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⡰⠴⣿⠿⡿⠶⢿⠿⢿⠿⢆⠀⣶⣶⣶⣶⡄⠀⠀⠀⣿⡇⠈⠀⠀⢀⣶⣶⣶⣶⡄⢠⠦⣼⠿⣿⠿⢻⡿⢿⡿⢧
⠀⠀⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⡇⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠯⠥⠶⠖⠚⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠙⠿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢀⣴⣿⣿⣷⣦⡠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣤⠹⣿⣿⣿⣿⡿⢃⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣎⢉⣉⠉⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠟⠛⠻⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⣿⡿⠃⠠⠆⠀⠄⠀⠴⠀⠠⢤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡄⠀⣀⣾⡟⠂⠠⠂⠠⠄⠀⡤⠀⢀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠄⠀⠄⠀⠄⠀⣀⣾⠟⠀⠤⠀⢠⠄⢀⣀⠀⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠒⠀⠄⠀⠄⠀⣀⣼⠃⠀⡄⡀⣀⠀⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋⠀⠂⠠⠄⢀⡄⠀⠀⣘⠅⢀⡀⠀⠀⠁⠀⠘⠁⠒⠶⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⣂⠠⠄⠀⡀⠀⠀⣱⣿⣿⣶⣦⣤⢃⡀⠤⢀⡀⡀⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣦⣤⣠⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⢿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠍⠉⠉⠉⠉⣿⣛⠿⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣿⣿⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣶⣶⣬⣝⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡹⣷⣸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣖⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣸⡿⠋
⠀⠐⠾⠿⠿⠿⠿⠿⠟⣹⡟⢾⣶⣄⠀⠀⠀⠀⠀⠀⠒⠿⠿⠿⠿⠿⠿⢋⣿⠳⣷⣤⡀⠀⠀⠀⠀⠀⠀⠲⠾⠿⠿⠿⠿⠟⣹⡟⢾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠈⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣀⠀⢰⣠⣤⣤⣤⣤⣤⣦⠀⢶⣶⣾⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣠⣠⣤⡄⠀⢰⣴⣶⣶⣶⣶⣾⡄⠀⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢸⣗⣻⣇⡟⢿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣗⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠷⠀⠿⠿⡿⢛⣛⣛⣛⣃⣤⣭⡙⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⠿⠿⠿⠿⣂⣀⣛⡻⠛⣛⣩⣭⣭⣤⣤⣭⠙⢰⣶⣶⣶⣾⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣾⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣯⡀⢨⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣙⣉⣉⣹⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠸⡿⠿⡿⠿⠿⠿⠗⠀⠙⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⣻⠿⠿⠿⠻⠿⠋⠅⠀⠙⠉⠛⠓⠛⠉⠀⠀⠈⠉



⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏⠛⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⣇⢿⠣⡠⠂⢹⣿⣿⡿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠛⠛⠱⢿⣵⣽⢿⣫⢂⠀⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⠀⠀⠀⠀⠀⠉⠻⣦⣮⣴⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠈⠉⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢣⣿⣤⢄⡄⠀⠀⠀⠀⠀⠀⠈⢻⣽⢦⢦⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⢁⡧⢿⡿⣿⣡⠀⡀⠀⠀⠀⠀⠀⠀⠻⠉⠋⠛⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⢰⠁⠈⠀⠈⠙⣿⠟⠀⠀⠀⠀⠀⠀⠀⠂⡐⠀⢁⣚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡯⢼⠘⠀⠀⠀⠀⠀⢘⡋⠀⠀⠀⠀⠀⠀⠀⣁⣖⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣼⠠⠀⢰⣷⣿⣏⣼⡇⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣿⡇⠐⠀⣾⣿⣿⣿⠻⠿⠀⠀⠀⠀⠀⠀⢠⣛⠄⡀⠄⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠠⣤⡖⢻⣿⣷⡆⢸⡿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⣷⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⣀⣴⣌⣿⡿⡼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠁⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠈⢻⣿⣿⣿⣾⣿⡇⣿⣿⣿⣇⠃⠀⠀⠀⠀⠀⠀⠀⣀⠐⠁⠀⠘⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢊⠒⣣⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⠀⠀⠀⠀⠀⡀⢠⠺⣿⣆⣀⢀⢀⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⠧⢲⠰⢺⣮⡂⠀⠀⢹⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡇⡆⠆⠁⣿⣾⣤⣀⢜⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡀⢀⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠃
⠀⠈⢡⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰
⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢀⠀⢏⠀⠀⣀⣀⠀⢠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠠⠄⢀⣀⣀⠀⠀⠀⣠⣤⣤⣄⠀⠀⣀⠀⡄⠀⠀⠀⠀⠤⠄⠀⠠⠀⠶⠯⠘⣤⡘⡆⠂⣿⣿⢓⣤⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠒⢾⣻⣻⣿⠿⠂⡀⡛⠃⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠟⠛⣋⢠⣿⣿⣏⠁⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠤⠎⠀⠀⠤⠀⠉⠩⠿⠿⠿⠿⠿⣤⡤⠾⠿⠛⠛⠛⠋⠉⠀⠀⠀⠐⠂⠠⠤⢥⣾⣿⢛⣿⣄⣤⣾
⠀⠀⠀⣀⠀⣄⠀⠰⠀⠘⢀⣈⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠄⢔⣀⣐⠀⡐⠀⣠⠄⠀⠤⠀⢠⠀⠀⡉⣙⠻⢿⣿⣿
⠀⠀⠀⠈⢠⣄⢶⣶⠻⣿⡸⣿⡜⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠰⠒⢠⠦⠤⣆⣀⡌⡀⣸⠏⠉⡰⠘⠃⡖⠂⢠⠴⠁⢀⡜⠀⠀⠉
⠀⠀⠀⠀⠀⠻⠄⠈⡆⠈⣧⠀⢳⡀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡐⠀⢠⠂⠀⠜⠀⢠⡟⠈⠉⠉⠙⢓⠖⠚⢤⠄⠆⢄⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⡀⣿⡆⢻⡇⠈⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠤⢥⣀⣌⠀⢠⡟⠀⠀⡔⠀⠀⡌⠀⠀⡜⠀⠀⢸⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⠶⠆⠀⠀⡀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠏⠑⠒⠘⠤⢄⣐⡀⠀⢠⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠿⠁⠂⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⠶⣾⡶⣾⣶⠀⠀⠀⠀⠀⠀⣔⡟⣵⢆⡦⣄⣀
⠀⠀⠀⠀⣴⣤⣤⣤⣼⣿⣿⣿⣿⡤⣤⣤⣴⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣻⣿⢛⣿⣗⣻⣿⡃⠀⠀⠀⠀⣴⣏⣽⣓⠾⣼⡍⠈⠆
⠀⠀⠀⣼⣿⣿⣿⠏⣻⣻⣟⣗⣿⡘⣿⣿⣿⣷⠀⠀⠀⠀⠹⣦⣀⢀⣠⡾⠁⠀⠀⠀⠀⠀⣐⣿⣿⣸⣿⣿⣹⣿⣇⡀⠀⠀⠀⢸⠶⢯⣟⡿⠇⣴
⠀⠀⠀⠀⠀⠶⠀⠘⠛⢛⣫⡛⠛⠃⠀⠶⠂⠀⠀⠀⠀⢠⡄⠀⠉⠉⠁⠀⣤⠀⠀⠀⠀⠀⢀⡠⠤⠤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⢦⣼⣿⣿⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⡆⠀⠀⠋⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⣴⣶⣶⢰⡄⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈
⠀⠀⠀⠀⢀⢀⣀⠀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⡷⣿⣿⢾⣿⣿⠀⠀⠀⠀⠀⠀⡤⠤⡤⢤⡤⢤⡤⢤⠀⡀⠀⠀⠀⠀⠀⣀⣤⠾⠶⢦⣤⠀⠀⠀⠀⠀⠀⣾⣶⣴⣶⣦⣶⣶⣶
⠀⠀⠀⠀⢰⣾⣿⣦⣿⣷⣴⣿⣶⠀⠀⠀⠀⠀⠀⠗⠰⠆⠰⠆⠰⡇⠰⡀⡅⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠘⣧⠄⠀⠀⠀⢰⣿⣧⣾⣿⣼⣿⣯⡟
⠀⠀⠀⠀⢘⣽⣿⣅⣿⣯⣨⢟⣉⣄⡀⠀⠀⠀⢀⠶⢶⠶⠲⠶⠶⡷⠰⡇⢦⠐⠀⠀⠀⠘⢿⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⣿⣼⣿⣏⡝⣭⢥⣥
⠀⠀⠀⠀⠸⠻⠿⠏⠿⠿⢩⡟⢿⠋⢹⡄⠀⠀⠸⠤⠼⠦⠴⠧⠤⠧⠤⠇⠚⠈⠀⠀⠀⠀⠈⠟⠶⢶⠶⠋⠁⠀⠀⠀⠀⠛⠛⠿⠿⣭⢸⣿⣈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⣤⠤⢤⢤⡤⢤⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠈⠉⠉⠉⠉⢉⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢢⣾⣿⣿⣷⡔⠀⠀⠀⠀⠀⠀⡸⣽⣿⣿⣇⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡇⠃⠀⠀⠀⠀⠀⡇⣭⣭⣭⢀⣭⣭⣍⢸⠀⠀⠀⠀⠀⢸⣿⣥⣤⡄
⠀⠀⠀⠠⣤⡤⢤⡤⠤⢤⠾⢠⣤⣤⣤⠌⢀⠠⠄⠀⠀⠀⠀⠁⠝⢻⠟⠯⠈⠀⠀⠀⠀⠀⢰⣧⣿⣿⣿⢸⣿⣿⣿⢼⠀⠀⠀⠀⠀⠉⠉⣿⠟
⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⢤⠀⠀⠀⠀⠘⠒⠓⠒⢒⣒⠛⠚⠒⠛⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⠴⠒⠶⡄
⠀⠀⠀⠀⢾⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠛⠒⠊⠁⣀⣀⠀⣀⣀⢀⣀⡀⡀⠀⠀⠀⢥⣶⣶⣦⢰⣶⣶⡮⡇⠀⠀⠀⠀⢦⣔⣦⣯⣜⣠⠆⠀⠀⠀⠀⠀⢶⣶⠶⣶⡶⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⠛⣸⣿⢋⣾⡟⡿⠁⠀⠀⠀⠺⣿⣿⡿⠹⣿⣿⠗⡇⠀⠀⠀⣀⢲⣿⡿⠻⢿⣷⣚⣀⠀⠀⠀⠐⣿⣿⠿⣿⣿⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣘⣛⢋⣘⣛⢋⣚⡛⡽⠁⠀⠀⠀⠀⢴⣿⣿⣷⣺⣿⣿⡦⡇⠀⠀⠀⠩⠼⣿⣿⣶⣿⡿⠫⠁⠀⠀⠀⢸⣿⣿⢸⣿⣿⢸⣿⣿⠆
⠀⠀⠀⠀⠀⠠⠼⠿⠯⠼⠿⠥⠿⠿⠽⠁⠀⠀⠀⠀⠀⡙⠿⠿⠟⠸⠿⠿⢃⡇⠀⠀⠀⠀⠞⠩⠝⣟⠫⠘⠃⠀⠀⠀⠈⠉⢉⣿⣉⣹⣋⣉⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣶⣤⠄⠀⠀⠀⢀⣠⡤⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠛⠿⠿⠿⠦⠥⠜⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⣀⠀⠀⠀⠀⠀⢠⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡹⢿⣿⡥⡄⠉⠤
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠈⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣏⣮⡿⠿⣿⣦⣿⣷⣜⣂⡀
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⢿⣿⣿⣿⣿⣷⡶⠖⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡳⣌⠀⠀⠙⠉⠻⠿⣿⣷⣆
⠀⠀⠀⠀⠈⠙⠻⣿⣿⡿⠛⠉⠉⠀⠁⠐⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢛⡛⢯⣗⠦⡀⠀⠀⠀⠀⠈⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠤⣀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠿⠇⢘⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠈⠁⡠⢠⢸⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⠰⠚⣡⣾⣿⣿⣿⣿⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠁⣠⣾⣿⣿⣿⣿⣿⢿⣭⣉⡛⠛⠛⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⠣⣌⠙⠛⠍⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣀⣀⣠⣤⣤⣶⣿⣿⠿⠋⠁⠀⠙⢿⣿⣿⣿⠹⣿⣎⠳⣁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡿⡟⠁⠀⠀⠀⠀⠀⠸⣿⡿⡘⣧⠻⣿⣷⣌⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠱⠘⢆⠸⣿⣿⣷⣌⠙⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⢻⣿⣿⣷⣆⡈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣄⠘⢷⡄
⠀⠀⠀⢤⣄⣀⣠⣄⠤⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣻⣿⡇⡽⡿⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠉⠙⠒⠉⠉⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠀⣠⣶⠟⠁⣰⣿⠀⢀⣠⣶⠟⠁⣠⣶⣿⣿⣿⠿⠋⠁⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠁⣰⢾⠟⠁⣠⣾⡿⢃⣴⣿⣿⣇⣠⣾⣿⣿⡿⠋⠁⠀⡀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡾⡁⠿⡴⣞⡵⢋⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣼⠇⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣺⠏⠀⣰⠏⠀⣡⡴⠛⠉⣠⢿⣽⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣴⣿⠏⠀⠈⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡞⠁⢀⡼⠃⠀⣴⠋⠀⣠⠞⠡⠝⣻⢟⠼⠿⣿⣿⣿⣷⣶⣾⣿⠟⠁⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢾⣀⣠⠞⠁⠀⠀⠙⠲⠛⠁⠐⠀⠁⠠⠈⣤⠀⣩⢾⣿⣿⠿⢋⣡⣶⠟⠁⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠀⠀⣰⠋⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣾⡷⠛⠉⢀⣴⣿⣿⣥⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣠⢞⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⡫⢕⣚⣭⠷⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠉⠛⠛⠓⠶⠶⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠉
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⣶⣿⠆⣀⡀⠀⠀⠙⠛⠒⠒⠶⢶⣶⣄⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉
⠀⠀⢀⣴⠟⠁⢈⣉⡀⠸⠿⠟⠁⠀⠉⠀⠀⠀⢀⣠⡀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⢰⡏
⠀⠀⣿⠁⠀⣴⣿⣿⡿⠀⠀⢀⣤⣶⣶⡀⠀⢰⣿⡿⠁⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⡇
⠀⠀⢹⡀⢸⣿⣿⠟⠁⠀⣴⣿⣿⣿⣿⠀⠀⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⢀⣴⠟
⠀⠀⡼⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣤⠞⠋
⢠⡞⠁⠀⢀⣴⣾⣿⠀⠈⠛⠛⠋⢀⣠⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠉
⠘⣧⠀⠀⣿⣿⣿⠏⢠⠄⠀⠀⠀⠛⠛⠁⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁
⠀⠘⢷⡀⠛⠛⠁⠀⠀⢀⣀⣤⣴⣶⣶⣤⣴⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠈⢻⣦⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠁⠀⠤⠤⢄⣀⣉⠉⠑⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡩⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⡠⢚⣥⣶⣿⣿⣿⣷⡄⠀⠀⠀⠈⠉⠀⠀⠀⠀⣴⣶⣦⣌⠓⢤⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡼⢡⡾⢋⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡝⢆⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⡇⣿⠃⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠻⣿⣿⡌⣇⠀⠀⠀⢸⣿⣆
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠃⣿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀⠀⣽⣷
⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣿⡆
⠀⠀⠀⠀⣿⡇⢠⣶⡀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡀⠀⠀⠀⢀⡄⢿⡀⣿⡇
⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠋⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⢿⡇⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡼⠀⠀⠀⠀⡾⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠁⠀⠀⠀⠀⠁⠀⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣆⣿⣿⣆⠀⠀⠀⠀⠀⠀⢆⠱⣝⠿⣿⣿⠟⠀⠀⠀⠀⣀⡀⣀⣼⣧⡾⠃⠀⠀⠀⠀⠀⡀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣞⣿⣇⠀⠀⠀⠀⠀⠀⠑⠮⢉⡂⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⠓⠒⠒⠀⠀⠀⠜⣱⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠏⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣷⣦⣀⠀⠀⣄⡀⠀⠀⠀⠀⣶⣶⣶⣄⠀⢀⡄⠀⠀⠀⣸⣿⠟⣡⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣍⡻⢿⣿⣿⣟⡻⣦⣄⡀⠀⠈⠉⠉⠉⠀⠈⠀⠀⢀⣠⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣶⣶⣶⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣟⣛⣛⣛⣛⣻⡯⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣿⡄⣸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠞⠁⠟⠹⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠞⠀⠀⠂⠀⠀⠀⠀⠃⠉⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣶⢦⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠶⡡⢿⡞⡏⠀⠀⠀⠀⢰⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⢀⠟⡉⠀⠁⣘⢳⢿⡄⢸⠀⠀⢨⠻⠻⣤⣇⢀⣖⠦
⠀⠀⠀⠀⠀⠀⣴⣥⠄⡀⠀⣹⡗⣡⣾⣿⠃⣰⡇⡸⠀⣿⠿⣄⣠⣿⢣⡀⠈⠹⣾⠁⠀⠈
⠀⠀⠀⠀⠀⠠⠋⠉⠛⠳⢾⣯⣾⣻⢳⠃⢠⣿⠇⡇⠀⢿⣾⡘⡈⢻⣇⢻⣤⠬⢶⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠉⠭⠙⠒⠋⠛⢻⣿⡄⠚⠛⠓⠓⠘⠻⡏⢁⡤⠔⠈⣷⣀⠄
⠀⠀⠀⠀⠀⠢⡀⠀⠀⡀⠘⠇⠀⠀⠀⠀⠀⠀⢸⢸⡇⠖⠂⠀⠀⠀⠀⣹⣀⠀⠀⠀⡸⠋
⠀⠀⠀⠀⠀⠀⠈⠑⠤⠷⠞⢀⣀⠀⠀⠀⠀⠀⡄⢸⠃⠀⠀⠀⠀⢀⠌⠀⢠⠋⠱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠉⠀⠉⠉⢉⡉⠉⢩⡀⠴⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠀⠀⠀⢀⠀⢐⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠐⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⣝⡀⠀⢀⠁⡊⠀⠀⠈⢻⢦⠀⠴⢂⡿⡄⠀⠀⠹⡦⡐⠐
⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠈⠓⢍⠓⢤⣁⠀⠀⠀⠀⡟⢀⠀⢀⠞⠀⡟⠀⠀⢠⠀⠹⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⢧⠀⠈⠳⡀⠐⣦⡙⢮⠢⢸⠁⢠⠃⠀⡠⠋⠀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢖⠈⣀⣀⡀⠀⠀⢸⡤⠀⠀⢧⢠⣇⠹⡌⢳⠘⣆⡿⢀⡞⠁⠀⠀⢀⠆⢀⠎⢣⠀⡀
⠀⠀⠀⠀⠀⠈⠀⣈⠉⢳⡎⢢⡀⢸⠀⠶⡀⠈⠻⠂⠀⢱⠀⠀⡿⢽⣼⠀⢠⠀⢀⡌⢀⠠⡀⡏⠐⠁
⠀⠀⠀⠀⠀⠀⠈⢹⠙⠸⡇⢀⠱⣾⡄⢁⠈⠢⡀⢠⡄⡞⠀⢀⠇⡄⠋⡠⢁⢣⠏⠀⢸⢣⢰⠇⢀⢦
⠀⠀⠀⠀⠀⢀⣆⢺⡊⠀⠹⣇⠰⠠⢄⠀⠂⠀⠰⠂⢠⠃⢀⡞⡐⢸⠐⠀⢠⠃⠀⡰⠃⣸⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⡏⢦⣀⠀⠀⠈⠳⣝⢤⡈⠲⠀⠀⡄⢸⢠⠟⠐⠀⢾⠀⠂⡇⣠⠏⠀⣀⡎⠀⣠⢀⡸
⠀⠀⠀⠀⠀⠀⠱⣄⠈⠑⠢⢤⡀⠘⡄⠱⠀⠀⠀⠆⠈⠿⠀⠀⠀⠀⠀⡆⢹⠇⡄⢠⠎⢀⡰⣻
⠀⠀⠀⠀⠈⢻⠆⠈⠲⢄⠀⣄⡙⠶⣗⠀⠁⠀⠀⠘⢄⠈⠂⠰⠀⠀⠀⠐⡤⠊⢄⣮⠖⢋⡜⠁⣦⡀
⠀⠀⠀⠀⠀⠘⠒⠠⠱⠀⠱⡀⠂⠑⠄⠀⡄⠀⠀⠀⠀⠉⠂⣤⠀⠀⠀⠀⠄⠐⠎⠥⢈⠏⡀⠀⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠢⡀⡇⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢐⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠓⢤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠀⣀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠀⡀⠁⠀⠔⠀⡀⠀⡀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠐⠀⠀⠈⠈⠀⠀⠁⠀⠈⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢸⡇⢸⡇⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣦⠀⠸⣇⠹⡆⠸⡇⢸⠇⢸⠇⣸⠇⠀⣤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⢷⣄⠹⣆⢿⣀⣷⣾⣀⡿⣰⠏⣠⡾⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡈⠙⢶⣽⣶⠟⠋⠉⠀⠀⠉⠙⠻⣶⣯⡴⠋⣁⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣌⣙⠳⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⢞⣋⣡⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣈⣉⣙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣋⣉⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⣤⣬⣭⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢭⣥⣤⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⡴⠟⣉⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣉⠛⠶⣤⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⠾⢋⡾⠋⣿⢲⣤⣤⣤⣤⡖⣿⡙⢧⡙⠷⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢁⡴⠿⠷⡾⢧⠿⠶⡿⢿⠶⠿⡼⢷⠾⠿⢦⡈⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⣁⣀⣠⢛⣇⣀⣀⡄⢠⣀⣀⣸⡚⣄⣀⣈⣎⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣜⣀⣀⣀⡌⣎⣀⣀⣀⡅⢨⣀⣀⣀⣱⢡⣀⣀⣈⣣⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢣⠊⠉⠉⠉⡹⢰⠉⠉⠉⠉⡧⢾⠉⠉⠉⠉⡆⢏⠉⠉⠉⠑⡜⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡡⠋⠉⠉⠉⢉⠃⡎⠉⠉⠉⠉⡃⢘⠉⠉⠉⠉⢱⠘⡋⠉⠉⠉⠙⢌⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠛⠓⠛⠛⠛⠛⠒⠓⠚⠛⠛⠛⠓⠚⠛⠛⠛⠓⠚⠓⠛⠛⠛⠛⠛⠛⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠉⠉⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠲⠤⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣠⡾⠟⠛⠛⠛⠳⢶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢘⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠙⣿⣦
⠀⠀⠀⠀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⣴⣶⡄⣶⣶⣶⣶⠶⠖
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣼⠋⠉⠉⢹⠋⠉⠉⢹⡏⠉⠉⠙⡏⠉⠉⠉⣧⠀⡇⠀⠀⢀⣶⣮⣭⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠰⠿⣧⡀⠀⠀⠀⢰⠿⠒⠒⠲⣿⠖⠒⠒⢾⡷⠒⠒⠲⣿⠖⠒⠒⠿⣆⠘⠀⢀⣾⡟⢹⣿⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⢈⣷⣦⣀⢠⡟⠀⠀⠀⣰⣇⠀⠀⠀⣸⣇⠀⠀⠀⣸⣇⠀⠀⠀⢹⡄⠀⡾⠋⠀⢸⣿⠀⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⡾⠛⠛⠛⠛⣿⠟⠛⠛⠛⢻⡟⠛⠛⠛⠻⣿⠛⠛⠛⠛⢷⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠈⣧⠀⠀⠀⢸⣿⠒⠒⠒⠒⠒⣿⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠿⠿⠶⠶⠶⠶⠿⠆⠀⠀⢸⣿⠀⠀⠀⢐⣿⣿⣿⡿⣿⠉⢹⡻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⢸⣿⠀⠀⠀⢰⣿⣿⡟⣴⣏⡀⠛⣿⡎⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠸⣿⣿⣧⠻⣿⡇⠘⣿⢇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠰⣿⣿⣿⣷⣬⣽⣼⣵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⡤⠠⡄
⠀⠦⠤⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⡠⠀⠀⠀⣴⢀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠆⠆⠀⠛⠀⠃⡴⠆⢠⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠀⠁⠀⠀⠀⠉⠚⠢⣶⡍⢿⠶⣆⣀⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠑⠨⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠔⠒⠀⠁⠀⠘⠓⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡆⠀⠀⠺⠂⠰⢀⠐⠟⠚⣀⡄⠀⠠⢂⡠⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡞⠁⢠⠀⠀⢈⠀⠈⠃⢀⡀⡼⣗⠀⠀⠈
⠀⠀⠑⠀⡄⠀⢾⠿⢀⡀⢛⣤⣽⡿⠃⠀⠀⠀⠀⠀⡴⠲⠷⢆⡄
⠀⠀⠀⢦⠉⣠⡄⠐⠀⣴⣼⣿⣿⡟⠀⠀⠀⠀⠀⠘⡀⠀⢈⠠⣮⠀⠀⠀⠀⠀⠀⢀⡄⠴⣧⣴⣄
⠀⠀⠀⠀⠑⠙⠧⣾⣷⡿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠋⠀⠀⠀⠀⠀⠀⠻⣤⣽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣇⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⡄⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⠀⣛⣛⣛⣛⡋⢘⣛⣛⣛⣛⣛⠀⣛⣛⣿⣿⡿⢛⣩⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⡋⢘⣛⣛⣛⣛⣻⡇⣸⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⠀⣿⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⠀⠿⠿⠿⠿⠿⠃⠿⠿⠿⠿⠿⠿⠀⠿⠿⠷⠸⣿⣿⣌⣋⣴⣿⣬⣉⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⠀⠀⠙⢿⣿⣿⢹⣿⢹⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣦⠀⠀⠀⠈⣿⣿⢸⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⠄

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣼⣁⣀⣼⣀⣀⣽⣀⣀⣽⣀⣀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⣰⡃⠀⢀⣏⠀⠀⣹⡀⠀⢸⣇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⣿⡆⢲⣶⣭⣭⣙⣛⡒⡲⠦⠤⣤
⠀⠀⠀⢠⡏⠉⠉⢹⠋⠉⠉⣻⠉⠉⠉⣿⠉⠉⠙⣆⠀⠀⠀⠀⠀⠀⢹⣿⡀⣿⣷⣽⣯⣹⣿⣻⣟⣿⡌⢧
⠀⠀⠀⠾⠤⠤⠤⠾⠤⠤⠤⠿⠦⠤⠤⠿⠦⠤⠤⠿⠄⠀⠀⠀⠀⠀⢰⣿⣧⠰⣿⣧⣿⣯⣽⣯⣿⣟⣿⡈⣧
⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⣶⡖⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⣿⡿⣿⣆⢸⣿⣮⣿⣯⣿⣯⣿⣽⣿⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⣿⣿⣤⣭⣭⣬⣭⣬⣭⣭⣭⣭⣥⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⣶⡶⢶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣐⣶⠿⠿⢿⣤⠄
⠀⠀⠀⠀⠹⣷⠘⢿⣷⢿⣯⣿⣿⣿⣿⣷⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⢹⣿⡻⣶⢶⣦⣬⣭⣅⣀⠀⠀⢻⡷
⠀⠀⠀⠀⠀⢻⣇⠹⣿⡾⢿⡾⣿⣾⣿⣽⣏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢭⣥⢹⣇⢛⡘⣗⠻⠝⣧⢠⡿⠓
⠀⠀⠀⠀⠀⠈⣿⡄⠻⣿⠿⣿⡾⣷⡾⣷⢿⣞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⣿⣆⣭⣌⣭⡙⣇⢛⡹⣆⠉
⠀⠀⠀⠀⠀⠀⠸⣷⠘⢿⣿⠿⣿⠿⣷⠿⡷⢿⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢰⣶⡔⣷⡬⣧⣩⣌⢭⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣼⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠿⠟⠛⡛⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠁⠀⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠛⠛⠉⠉⠁⠁⠁⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠞⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⣿⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠟⠀⠀⠀⠀⠀⠀⠉⠻⡇⠀⠀⠀⠘⢦⣤⣴⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠷⣄⠀⠀⢀⣤⠖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⣿⣧⠀⠀⠀⠀⠀⠀⣼⠃⢠⣶⣶⡈⣷⠀⡾⠁⢠⣶⢲⡄⢻⡀⠀⠀⠀⠀⠀⡂⠢⡸⣧⣤⣤⣤⣀
⠀⠀⠀⠀⢀⣠⡴⠶⠾⠛⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⠟⢁⡿⠀⢿⡀⠘⠿⠿⠃⣾⠁⠀⠀⠀⠀⠀⠁⢀⠅⠙⣧⠀⠈⠹⣧
⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⠶⠛⠁⠀⠈⠛⢶⣦⣶⣿⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢻⣆
⠀⢠⡞⠁⠀⢀⡴⠋⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⢀⡟⠀⠀⢀⠎⠀⠀⢰⢇⣀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠈⣿
⣼⠇⠀⠀⢸⠀⢀⣰⣏⠀⠀⠀⠀⠀⠀⠀⠀⢡⡏⠉⠙⠀⠀⠘⢧⣄⣀⣀⣀⣀⣀⣤⣼⡿⠀⢠⡴⠿⣟⠛⠃⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⠀⠀⠀⢸
⣿⠀⠀⠀⠈⢻⡉⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⡉⠉⠉⣟⠉⠁⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣠⠞⠉⠻⣤⣀⡤⠊⠀⠀⠀⣾
⣿⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⠀⠀⠀⠀⠀⠀⢇⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠂⠀⢰⡏⠀⠀⠀⢹⠀⠀⠀⠀⠀⣴⡿
⢻⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⠤⠴⠶⠶⠞⠛⠁⠀⠀⢸⡄⠀⠀⣠⠟⠀⠀⠀⣠⣾⠟
⠈⢿⣆⠀⠀⠀⢀⡞⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⢀⣴⣾⠟⠁
⠀⠈⠻⣷⣀⠀⠘⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠈⢻⣧⡀⢳⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢄⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⢹⣷⡀⠙⢦⣤⡴⠃⠀⡀⠀⠀⠀⠀⠀⣰⣀⣀⣎⣀⣠⡂⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣣⣾⡟⠁
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠸⡀⠈⠲⡀⠀⠐⢯⣉⡉⠈⠉⠉⢙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠟⠉
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⣇⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠰⠋⡇⣦⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠰⡆⣨⢛⢥⡶⠀⠀⠀⠀⠀⠀⢸⢸⣄⣧⣠⠀⠀⠀⠀⠀⢀⠀⣲⠛⡏⠀⠀⠀⠀⠀⠀⡾⡿⠜⡄
⠀⠀⠀⣷⣼⢀⡾⣤⠦⡼⠀⠀⠀⠀⢸⣾⠈⡟⠙⢻⠀⠀⠀⠀⠀⠘⢟⢫⣿⣀⡀⠀⠀⠀⢀⠠⢇⠠⣤⢷⡄
⠀⠀⠀⠘⠦⠾⠇⠘⠃⠁⠀⠀⠀⠀⠀⠁⠰⠛⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⠐⢯⠃⠀⠀⠀⠘⣷⠛⠘⢆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡀
⠀⠀⠀⠀⠘⡿⡏⡅⠀⠀⠀⠀⠀⢀⢀⠀⣿⢣⣀⡀⠀⠀⠀⠀⠀⠀⠎⣼⣿⢰⡀⠀⠀⠀⠀⠀⡄⣾⡼⣃⡋
⠀⠀⠀⠀⠸⣧⠛⣇⠀⠀⠀⠀⠀⠈⠉⢷⠾⡌⠛⢛⡁⠀⠀⠀⠀⢰⣜⣇⢹⡾⣧⡀⠀⠀⠀⠀⡁⢏⢁⢹⠠⠇
⠀⠀⠀⠸⣆⣿⢶⣼⠀⠀⠀⠀⠀⠀⣻⡛⠀⡿⣆⠛⠇⠀⠀⠀⠀⠸⣿⠹⢰⡀⠻⠀⠀⠀⠀⠠⣼⡾⢿⡘⢾
⠀⠀⠀⠀⠀⠰⠏⠋⠀⠀⠀⠀⠀⠀⠈⠃⠻⠅⠙⠋⠀⠀⠀⠀⠀⠀⠙⠘⠋⠃⠀⠀⠀⠀⠀⠀⠈⠃⡎⠻⠞

⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢨⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡃⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣠⠿⠿⢿⣄⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⣾⠁⠀⠀⠀⠘⣇⠀⠀⣿⠀⢸⡇⠀⠀⠀⢿⣤⣼⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢷⡀⠀⠀⠀⢀⡏⠀⠀⣿⠀⢸⡇⠀⢀⡾⠋⠁⠈⠙⢦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣼⠿⠿⢯⡀⠀⠀⠙⣶⣶⣶⠋⠀⠀⠀⣿⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢸⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠈⠳⣄⣀⣀⡴⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣧⠀⠀⠀⠀⣸⠇⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡅⠀⠀⠀⣾⠛⢻⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢳⣶⣶⣞⠁⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⣤⣼⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠸⡇⠀⣿⠀⠀⢠⠞⠉⠉⠉⠳⣄⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢀⡇⠀⣿⠀⠀⢾⠀⠀⠀⠀⠀⣻⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢸⡇⠀⣿⠀⠀⠘⢧⣄⣀⣀⡴⠋⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⠛⢻⡀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣴⣾⣿⣿⣶⣦⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⡦⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⢴⣶⣶⣶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⡄⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⢠⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣷⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡆⢰⣶⣶⣶⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⡄⢀⣿⣿⣿⣿⣿⣿⡇⢠⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠘⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⢺⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣿⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠻⣿⡄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣄⡀⣰⣿⡿⠃⠀⢠⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡼⣿⠁⠀⠀⠸⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠘⣿⣿⣷⠈⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣦⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠀⢀⣿⣷⡀⠀⠀⣸⣿⣿⡟⠀⢤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢋⣼⣿⣿⣿⣿⡇⠀⠀⠀⢱
⠀⠀⠀⢤⡀⠀⣴⡿⠀⡀⠙⣿⣿⣿⣿⡆⠀⠀⢸⣷⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⠁⠀⠈⣿⣷⡄⠀⠀⠙⠻⣿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣷⣤⣀⣤⣿
⠀⠀⠀⠈⣿⣶⠟⠀⠀⣿⣦⣾⣿⣿⣿⠇⢀⣴⣿⠟⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⡀⠀⠀⠀⠀⠉⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣇⠀⢀⣿⣿⠀⡀⠀⠘⢿⣿⣿⣿⢟⣴⣿⣿⠋⠀⢠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣀⠀⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⢿⣿⣿⣿⣿⣇⣀⣽⣷⡀⠈⠙⠿⢋⢸⣿⣿⣿⣷⣤⣾⡇⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣷⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡀⣿⣌⣿⣿⣿⣿⣿⡿⢡⣾⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⢠⠀⠙⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⡟⠀⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣷⣶⣿⣿⣿⣿⡟⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣘⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⡟⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠛⢦⡀⠀⠀⠀⠀⠀⢀⣿⡟⣿⣿⢻⣿⡀⠀⠀⠀⠀⢠⣼⣳⠟⡶⣤⣤⡀
⠀⠀⠀⢰⣷⣶⣶⣾⣿⣿⣿⣿⠶⣶⣶⣶⡀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢨⣿⡇⣿⣿⢸⣿⣇⠀⠀⠀⠀⢿⢳⣯⣝⣳⠟⠀⠃
⠀⠀⠀⠿⠿⡿⠟⣼⣯⡯⣿⣽⡄⠿⠿⠿⠷⠀⠀⠀⠀⠻⢦⣤⡴⠟⠀⠀⠀⠀⠀⠀⠾⠿⠧⢿⡿⠼⠿⠷⠄⠀⠀⠀⣿⠙⣿⣾⡋⢰⡇
⠀⠀⠀⠀⠈⠉⠀⠉⠉⠼⠆⠉⠁⠀⠉⠀⠀⠀⠀⠀⡾⠀⠀⣀⠀⠀⣾⠀⠀⠀⠀⠀⡔⠒⠒⠊⢀⣀⣀⢀⠀⠀⠀⠀⠙⠛⠿⢿⡇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠂⠺⠿⠿⠸⠃

⠀⠀⠀⠀⢠⣶⣶⣴⣶⣦⣶⣦⡀⠀⠀⠀⠀⠀⡀⢀⠀⣀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⣤⣄⣤⣤⣠⣤⣄
⠀⠀⠀⠀⢈⣿⣯⣹⣿⣭⣿⣏⠄⠀⠀⠀⠀⢨⡅⣬⠀⣭⠀⣧⢨⡄⡂⠀⠀⠀⠀⢠⡞⠉⠀⠈⠙⣦⡀⠀⠀⠀⢨⣿⣯⣿⣏⣿⣿⣻
⠀⠀⠀⠀⢘⣿⣟⣹⣿⣛⡿⢛⣁⠀⠀⠀⠀⢠⠤⣤⠤⣧⠤⣧⠤⡇⠥⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⣼⣿⣹⣿⢛⢛⣻⣍
⠀⠀⠀⠀⠘⢿⠿⠻⡿⠟⡼⢿⠛⢳⡀⠀⠀⢰⣄⣶⣄⣧⣠⣧⣤⡇⠰⠀⠀⠀⠀⠀⠹⠶⣤⡴⠞⠛⠀⠀⠀⠀⠛⠫⠿⢟⡉⣿⡇⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣄⢠⠀⠀⠀⠀⠀⠀⠀⡤⣤⣤⡤⢠⣤⣄⠤⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡟⠀⠀⠀⡀⠀⠀⠀⠀⠀⢒⣾⣿⣿⣷⡔⠀⠀⠀⠀⠀⠀⢯⣿⣿⡏⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡞⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡙⣿⣿⣿⣿⢏⠁⠀⠀⠀⠀⢸⢰⣷⣾⡆⣾⣶⣦⢈⠀⠀⠀⠀⠀⣿⣷⣶⡶
⠀⠀⠀⠘⡒⠒⢲⠒⠒⡞⠰⠒⠒⡖⠃⢒⠒⠁⠀⠀⠀⠀⠘⠙⡏⠑⠀⠀⠀⠀⠀⠀⢸⠙⠛⠛⠛⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⣀⣉⣉⣉⡱⠀⠀⠀⠀⠈⠉⠉⢉⣽⣍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⡞⠁⠈⢳⠄
⠀⠀⠀⠀⠳⣤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⣤⣄⢒⣤⣤⡐⡄⠀⠀⠀⢀⡀⢤⢰⢀⠄⣀⠀⠀⠀⠀⢀⣤⣤⣠⣤⣄⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⢣⣿⠟⣴⣿⣾⠂⠀⠀⠨⣿⣿⣿⢸⣿⣿⡯⡇⠀⠀⠀⠠⣹⣾⡿⣿⣿⡡⠀⠀⠀⠀⢨⣿⣿⢼⣿⡯⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠣⠿⠟⠼⠿⣳⠁⠀⠀⠀⢀⣼⣿⣯⢠⣿⣿⣄⡇⠀⠀⠘⢛⢿⣿⣄⣼⣿⢗⠛⠀⠀⠀⢰⣿⣷⣼⣿⡇⣿⣿⡦
⠀⠀⠀⠀⠀⣀⣿⣿⣱⣿⣟⣼⣿⡿⠁⠀⠀⠀⠀⠐⠿⣿⡿⠸⣿⣿⠗⡇⠀⠀⠀⠠⠞⡙⢻⠛⡛⠦⠀⠀⠀⠐⠚⢛⡗⠛⣟⠓⣻⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢇⣤⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⢠⠟⠙⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⡀⢠⡆⠀⠀⠀⠈⣧⠄⠐⠸⠀⡤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⠀⡰⠉⠷⠀⠐⠑⠀⠃⠀⣤⡠⠞⡷⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠸⢤⡇⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠐⡁⠘⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠈⠁⡐⠂⡰⠁⠀⠀⠀⠤⠂⡳⠀⠇⠆⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣦⡱⡄⠲⠇⠘⠀⠀⠀⠀⠀⠀⢀⠀⠞⠀⠔⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠌⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠊⠐⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠈⡤⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢥⡀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠮⠴⠖⠖⢤⣼⢶⡿⣷⣾⣷⠋⢻⣿⣷⡖⠦⢤⡄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣤⣤⣴⠞⠋⠀⣸⠁⢀⣿⢻⣆⠀⠙⢯⣟⠉⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢹⣁⣀⣠⣶⡇⠀⠸⣿⠄⣻⡆⠀⠈⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠈⣿⠷⠏⠛⠉⠘⠶⠶⠞

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⡤⠐⠂⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⢤⣿⢻⢿⣳⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⣦⣴⣿⣿⣿⣯⣯⢿⣶⢢⣎⠄⠀⠀⠁⠀⠒⠆⠐⡂⠠⢀⡄⠀⠀⣠⠟⡿⠄
⠀⠁⠀⠀⠉⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣟⢵⣷⢛⠽⣩⢟⢒⠮⡴⢀⣀⠀⠀⠀⠈⠀⠁⣾⡗⠒⠐⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠿⣗⠿⠻⡳⢢⡜⡽⡣⢂⠀⢡⠆⡐⠁⢀⡼⠀⢀⡞⠹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠅⣊⠞⠖⠔⡜⢁⠞⡠⣦⣿⣯⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠪⢔⡉⣨⡟⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⣠⡇⠀⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠋⠀⢀⣾⠟⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣴⣿⡏⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⢳⣿⢀⠠⠾⢻⣿⠀⠀⢠⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⣿⡿⣱⣿⡿⠃⠀⠀⣼⣿⣼⠠⠄⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣽⣿⣿⣿⣿⣆⣠⣾⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢟⣿⡿⣿⣿⣿⣿⣿⢣⣼⣿⡎⢷⣇⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⢏⣾⡟⣸⣿⣿⣿⣿⡇⡾⣿⣿⢻⡌⠻⣆⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢠⠁⣿⠟⣿⡿⣰⣿⣿⣿⣿⣿⡘⣇⢸⣿⣿⣿⠀⠙⣷⣄⠠⡱⣄
⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣾⣿⡇⣿⢸⣿⣿⣿⡿⠧⠀⣼⡈⣿⣿⡇⢢⠘⣿⣧⠙⣿⣦
⠀⠀⠀⠀⠀⠀⢸⡀⣼⢿⣿⣿⠀⣿⣼⠳⠏⢠⣷⢀⣼⣿⠃⣸⢹⡇⣸⡄⠸⣿⡇⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠘⣧⢹⡜⣿⣿⡄⢹⣿⠀⠀⢸⣾⡈⠻⣿⢀⡟⣹⠇⣿⣥⠀⣿⣷⠀⢻⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⣿⣿⣿⣦⡿⣷⣄⡈⠻⠏⠀⡹⣾⣱⠏⣼⣿⣧⠀⣿⣿⠀⢸⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣻⣯⣛⣿⣿⡝⢷⣂⠠⣼⣷⣿⢏⠼⠁⢸⡇⢰⣿⡟⠀⣸⢄
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠈⠋⣉⣿⣿⣿⣷⡙⠿⠿⠯⠁⠀⢀⠴⠋⣴⣿⠟⠁⣰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⣿⣿⣿⣿⣷⣦⣤⣤⣤⣷⣼⣿⣿⠗⢀⡴⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣹⣿⣿⣿⣿⣿⣿⣿⠿⢛⣡⠴⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣧⣴⣿⡭⠤⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠿⠟⢻⠟⢿⠿⢻⡿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣴⠀⠀⠀⣰⡿⠃⠀⢀⡄⠀⠀⢀⡴⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⠏⢠⣾⣿⡿⣿⣿⣿⡿⢻⣿⣿
⠀⠀⢀⣾⣧⡤⠀⠀⣿⠟⠀⢀⣾⣤⠀⠰⢿⡧⠀⠀⢸⣿⣿⡟⠁⠘⢻⣿⣿⠀⣼⣿⡟⠐⢻⣿⣋⠀⢻⣿⣿
⠀⠀⠉⢹⠟⠀⠀⠀⡿⠁⠀⠈⡽⠁⠀⠀⢹⡟⠁⠀⢸⣿⣿⣶⠆⣰⣿⣿⣷⣠⣿⣿⣷⢠⣾⣿⣷⠆⣠⣿⣿
⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⢀⠀⠀⢰⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣟⡀⠀⠀⣴⠀⠀⠀⣼⣿⡃⠀⠀⣠⡟⠀⠀⢸⣿⣿⠇⠰⢿⣿⣿⢫⣿⣿⣿⠁⠀⣾⣿⣿⠏⣸⣿⣿
⠀⠀⢛⡟⠁⠀⠨⣿⠁⠀⠀⣾⣟⠀⠀⠴⣿⣿⠃⠀⢸⣿⣿⡤⢠⣿⣿⣇⠀⣿⣿⡿⠀⢸⣿⣿⣃⠀⢈⣿⣿
⠀⠀⠸⠁⠀⠀⢠⠋⠀⠀⠀⡞⠁⠀⠀⠀⡿⠁⠀⠀⢸⣿⣿⣷⣿⣿⣿⣟⣼⣿⣿⡿⣰⣿⣿⣿⡿⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⡆⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⣤⣿⣿⣤⣶⣶⣶⣯⣴⣷⣭⣿⡆⠀⠛⢲⡀⢛⣒⣶
⠀⠀⢀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⡏⢿⣿⣿⠀⢀⢀⡐⢾⢈⣦⣠⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣰⣶⠟⣤⢿⡏⢈⡷
⠀⢀⣾⣿⣿⣧⣷⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠀⠀⠋⠀⢀⡌⣦⣠⢷⣏⣿⣯⣯⣧⡐⠀⠀⠉⢈⣍⣉⣩⣍⣭⣥⣤⡄⠀⣜⣿⣶⣼⠟⢹⣏⣸⡅
⠀⣼⣿⠏⠀⢿⣿⣇⠀⠀⠸⣿⣿⢿⢿⣿⣿⠃⠀⠀⢀⣜⣾⣷⣿⣿⣿⣛⣿⣿⣼⣿⣿⣷⣦⡰⣼⣿⣍⠓⢺⣟⡋⠉⠉⠀⠘⠿⠞⢿⣶⣿⠿⠛⠁
⠀⠻⢧⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⣁⣸⣿⣿⡟⠛⠈⠑⠀⠀⠀⠀⡀⠀⠘⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡀⣴⢠⡀⠀⠀⠀⠀⠀⠀⠆⡐⠂⡆⠐⠀⠀⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⣸⢼⣠⢧⣟⣳⢼⡰⣅⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠉⠁⡄⣑⣘⣄⠀⣀⣙⣦⡴⣃⠀⠀⠀⢠⡀
⠀⠀⠀⢸⡆⠀⠀⣯⣻⣾⣾⣿⣿⣿⣾⣷⣿⣷⣿⡄⠀⠀⠀⠀⠀⢀⣼⣧⣶⡤⣄⠀⠀⠀⠀⢀⠙⠐⠀⠑⠿⠟⠀⢠⣞⣿⡻⣞⡽⠁⠀⢠⣤⣽⠆
⠀⣰⢠⡿⢁⡀⠀⠈⠛⠛⢉⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⢠⣼⣽⣿⣿⣿⣿⣿⣤⠀⠀⣀⡴⠛⢦⡞⠀⠀⠀⠀⠀⣹⣟⣿⣏⠀⠀⢰⣛⣦⣹⣦
⠀⢿⡈⢷⣼⣄⠀⠀⠀⣠⢿⣆⣤⠀⠀⠀⠀⣦⣷⡄⢣⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣞⠀⡄⡟⢷⡜⣮⣷⣴⠁⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⢈⣽⣿⠁
⠀⢸⡿⢸⣿⣿⠇⠀⣰⣯⢾⣿⣏⣦⠀⠀⠲⣬⡟⣷⣦⡙⣷⠀⠁⢸⣿⣿⣿⣿⡟⠃⠸⣧⣿⣿⣵⣿⣟⣿⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⣿⡟⠋
⠀⣾⣷⣾⣿⣿⠀⠀⣿⡇⠀⠋⢹⡿⠀⠈⣧⣿⣷⣿⣼⣷⣡⣧⠀⠻⣿⡟⢽⣿⡅⠀⠀⣽⣯⣿⣿⣿⣿⣻⡇⠀⠀⣀⣤⣴⣆⡀⠀⠀⠀⠉⢻⣿⣦
⠀⠈⠛⠛⠛⠋⠀⠀⠈⠛⠀⠐⠋⠁⠀⠀⠙⠛⠉⠋⠋⠙⠛⠋⠀⠀⠘⠀⠘⠋⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠃⠀⠾⠿⠿⠿⠿⠟⠛⠗⠀⠚⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠟⣁⡴⠚⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⠚⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡴⠋⠀⠀⠉⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠀⣠⡶⠋⠀⠀⠀⢀⡄⠀⠀⣠⣿⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡼⣡⡞⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣼⡷⠃⠀⣠⡖⢀⣴⡿⠃⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇⠀⠀⣠⠞⠁⠀⠀⠋⢀⣠⡾⠋⣰⢋⡾⠁⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡞⠁⣸⠁⣠⠞⠁⠀⠀⠀⠀⡰⣫⠏⠀⡼⣡⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣷⠏⠀⠀⣿⠞⠁⠀⣀⡄⢀⡤⢊⡼⠁⣠⢞⡼⠁⣠⡞⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠸⣃⣀⠀⠀⠁⠀⣠⢾⣯⠖⠉⠀⠈⠁⠔⠁⠚⣡⣾⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣡⠴⠋⠁⠀⠀⠀⠤⠞⠁⠋⠁⠀⠀⠀⠀⠀⠀⡠⠞⠉⠁⠀⢀⣴⡷⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⣫⠴⠖⠒⠒⠛⠛⠲⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⢡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⢺⡏⠀⠴⣄⠀⠀⠀⠰⡄⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⣰⢏⠜⣡⠞⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠖⢸⡇⠀⠀⠰⠋⣠⠟⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⡏⡞⣼⠁⠀⡄⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⠀⣰⠋⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⡼⣱⢡⠟⠀⠀⠃⠀⠀⠀⣄⠀⠗⠀⠀⠀⠀⢴⠋⢀⡼⠁⠀⣠⠃⠀⠀⠀⣠⠞
⠀⠀⠀⢀⡞⢁⣿⡏⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⡾⠀⠀⠀⠁⠀⠀⠀⡴⠃
⠀⠀⠀⡞⠀⣾⠀⢳⡄⠀⢿⡀⠀⠁⠀⠀⠀⠀⠀⢀⠰⢋⣀⡼⠃⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢸⡇⠀⠸⡆⠀⢹⠀⠀⠉⠀⠀⠀⠀⠀⣀⡬⠁⢰⠏⠁⢀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢷⡀⠀⠀⠀⠘⣦⡀⠀⠀⠀⣈⣽⠿⠭⠤⠴⠋⣠⠴⠃⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠹⢦⣀⠀⠀⣀⣉⠛⠛⠉⠉⠀⣀⣤⣤⠴⠚⠁⢀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠈⠙⠓⠶⠖⠋⠁⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠶⠖⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⡀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠼⠶⠆⠐⠠⠐⣀⣠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢨⠂⠀⠀⠀⡆⢠⢻⣗⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣰⡡⠀⠀⢀⡏⠀⠀⠀⡘⢀⠆⠀⠹⣔⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠤⠦⣄⠀⠀⠀⢠⡁⠉⢢⢐⢊⠠⠠⠤⠴⢁⡎⠀⠀⠀⠹⡧⠜
⠀⠀⢀⠀⢤⢼⡤⠣⢴⡤⠺⠇⠀⠐⠀⡜⠐⠀⠈⢰⠁⠀⠀⢨⠂⡜⠀⠀⠀⠀⠀⢹⡌⠡
⠀⠀⠀⠁⠠⣭⠇⠀⠈⠀⠠⣐⡲⣤⡴⣅⣀⡀⣠⡁⠁⠀⢀⠆⡼⠀⠀⠀⠀⠀⠀⢸⠿⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⣧⡈⠉⠉⠐⠊⠡⠭⠱⠒⠎⡰⡇⠀⠀⠀⠀⠀⠀⢸⡠⢀⣨⠯⠦⠄
⠀⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣄⣤⠶⠚⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡴⠶⣤⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣰⠟⠁⠀⠀⠀⠈⢷⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠻⣆⠀⠀⠀⠀⢀⣼⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⠶⠶⠾⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡍⠉⠉⠉⠛⠛⡟⠛⠻⠿⠿⠿⠷⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀⠉⠀⠀⠀⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠉⠉⠹⡍⠙⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠉⠉⠉⠛⠛⢻⡖⠒⠒⠒⠢⠤⠾⣦⠤⠤⢤⣀⣀⣵⣄⣀⣀⣀⠀⢹⣧
⣴⣶⢦⣤⣤⣤⣤⣀⣀⣀⣀⡀⠈⣿⣿⣧⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢻⠀⠈⠉⠉⠉⢻⣧
⠹⣿⣆⠀⠀⠈⡄⠈⠉⠉⠹⡉⠛⠛⣿⣿⣟⠙⠓⠒⠒⠚⢿⠖⠒⠶⠤⠤⠤⢷⣤⠤⠤⢄⣀⣠⣧⣀⣀⣀⣀⡀⣿⣆
⠀⢻⣿⡄⠉⠉⠙⡃⠀⠒⠒⠳⠒⠂⠺⣿⣿⣆⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠉⠉⢿⡆
⠀⠀⢻⣿⡄⠀⠀⠶⡄⠀⠤⠤⢧⡄⠀⢹⣿⣿⡖⠒⠒⠒⠢⠾⣶⠤⠤⠤⠤⠤⠬⣷⣤⢄⣀⣀⣀⣸⣦⣀⣀⣀⣀⣘⣿⡄
⠀⠀⠈⢿⣷⡀⡀⢀⣰⣀⡀⠀⠀⣂⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠙⡅⠀⠀⠉⠉⠙⣿⡀
⠀⠀⠀⠈⣿⣧⠀⠀⠀⢣⠀⠀⠀⠉⠏⠉⠉⢿⣿⣷⡒⠒⠒⠶⠶⢿⣦⠤⠤⠤⠤⠤⢼⣦⡤⠤⠤⢤⣄⣽⣄⣀⣀⣀⣀⣹⣷⡀
⠀⠀⠀⠀⠘⣿⣏⠉⠉⠈⢛⠀⠀⠀⠚⡖⠐⠘⣿⣿⣧⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠹⣿⣦⣤⣤⣬⣦⣤⣤⣤⣴⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢤⣤⣿⢤⣬⣭⣭⠉⠉⠉⠉⠁⠉⠁⠉⠉⠉⢿⡉⠈⠉⠈⡏⠈⠁⠉⠁⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠗⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠿⣿⣛⣿⣛⣳⣶⣶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠶⠶⠖⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠐⠄⠐⠆⠉⠀⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠊⠁⠀⠀⡀⠀⠐⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠀⠀⠀⡀
⣰⠀⠀⣀⣀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⣀⢀⡀⡀⢀⠀⡀⡀⢀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠤
⢹⡇⠈⠀⠀⠊⢀⡤⠔⠈⠈⠉⡐⣺⠳⣧⠉⢄⢟⣤⠈⠨⣢⢤⠀⠚⢳⣆⢔⡉⠀⣆⣁⠑⠉⡄⠀⢀⠀⣔
⠸⡇⠀⠀⠀⠀⠉⠀⠠⠄⠀⠀⠀⠀⠐⠋⡀⠀⠀⢀⢀⣀⣀⣀⣈⢠⢀⣠⠌⠀⠄⠠⢀⠂⠂⢡⠀⠀⢠⠅
⠈⡿⠀⢉⠈⠈⠐⠀⠛⠹⠋⠝⠉⠝⣉⠋⡧⠉⠠⠪⢀⠁⠒⢁⠖⠀⡈⠁⡰⢃⣀⠈⠈⡰⠀⠈⡖⡡⠋⠀⠀⠀⠀⠦
⠀⢣⡇⠈⠀⠀⠐⠀⠀⠘⠀⠀⠀⠈⠂⣤⣧⠈⠀⠂⠋⠀⠀⠀⠈⠐⢁⣀⡀⠉⠃⢧⠀⡀⠌⠀⠘⠁
⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣀⡀⢤⣤⠀⠀⠐⠂⢀⠽⢃⠌⠋⡃⢀⢄⡀⠀⢀⠐
⠀⠀⣽⠀⠰⠒⠂⠉⠉⠁⠸⠋⠍⠉⠉⡀⢄⣘⠑⠀⢀⡇⠀⠈⢐⠺⠀⠀⠀⠀⠙⠔⢇⠀⢈⡀⢀
⠀⠀⠧⡇⠠⠀⠀⠀⠀⢠⣥⡆⠀⠀⠀⠀⠾⣇⠀⠀⠈⠸⢀⡀⣀⠀⠁⠘⡶⠂⢀⠄⠈⠀⠠
⠀⠀⢸⢰⠀⠀⠀⠀⠀⠐⠰⢱⡀⢀⠠⠤⠄⠀⠘⠲⢛⡵⠄⠄⠀⣲⡷⣶⠆⠐⠳⢶⣶⠦⠐⢴⣶⡶⣶
⠀⠀⠘⣴⠄⢐⡖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠧⢾⠀⠀⠙⠠⣤⠰⠀⠀⠀⣀⠠⠤⣼⣾⣏⢻⡆
⠀⠀⠀⡇⡇⠈⠁⠀⠀⠀⠀⢔⢲⠀⠀⠀⠊⠀⠨⠠⠀⠀⠈⠂⢠⠠⠤⠶⠖⠶⢶⠶⠶⡶⡖⢿⠿⢿⡾⠿
⠀⠀⠀⢱⢰⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠄⠀⠋⠙⡾⠁⠰⠂⠀⡀⠂⢀⠀⠀⠈⠋⢀⠀⠀⠀⠃⠁
⠀⠀⠀⠈⡾⡄⠀⠀⡤⢀⠐⢂⠈⢙⠁⠀⡰⠂⢐⠜⠀⠀⠀⠠⡄⠄⠀⢁⠀⠀⠀⠐
⠀⠀⠀⠀⢿⠅⠀⠆⠀⠀⠀⠀⢠⠈⡆⠀⠀⠀⠫⠺⠄⣀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣵⠀⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠘⢯⡄
⠀⠀⠀⣀⡀⢸⡅⠀⠁

⠀⠀⠀⣠⡤⠤⠶⢶⠄⠀⠀⠀⠀⠀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠉⡕⠀⠀⠀⠀⠀⠀⢀⡔⡆
⠀⠀⢰⡇⢔⠂⢀⣾⠀⠀⠀⠀⠀⠀⢀⡴⢣⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⠃⠀⠀⠀⠀⢀⡴⠋⡜
⠀⠀⢸⠃⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⠞⠀⢸⣡⡤⠤⣤⠀⠀⠀⣸⠀⠀⠀⠿⢤⡀⠀⠀⡰⠋⠀⠀⠁⠀⣲⠆
⠀⠀⢸⠀⠀⠀⠀⠧⢶⡄⠀⠀⢠⡏⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣟⣀⠀⠀⠀⡾⠀⠀⠐⠳⠒⣲⠂⠀⡴⠃
⠀⠀⢸⡤⣤⠀⠀⢀⡞⠀⠀⠀⣾⡴⠖⠛⡇⠀⣼⠃⠀⠀⠀⠀⠀⢸⠀⠀⣸⠁⠀⠀⠀⢀⡜⠁⢀⣞⡁
⠀⠀⠀⠀⣼⠀⢀⡞⠀⠀⠀⠀⠉⠀⠀⢰⡇⡸⠃⠀⠀⠀⠀⠀⠀⡜⠀⠐⠗⡦⠀⠀⠀⣾⣀⡀⠀⣹⠋
⠀⠀⠀⠀⣿⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢧⣤⠀⣰⠁⠀⠀⠀⠀⢠⡇⡴⠃
⠀⠀⠀⠀⡟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⠃⠀⠀⠀⠀⠀⣸⡾⠁
⠀⠀⠀⠀⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⡖⠚⠛⣻⠀⠀⠀⠀⠀⡷⡀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⣤⠼⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷⠹⡄⠀⠀⠀⠀⠸⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⢀⡶⠋
⠀⠀⠀⠀⣿⠀⠀⠀⡖⠋⠀⠀⠀⣠⠞⠁⠀⠘⡄⠀⠀⠀⡇⠀⠀⣸⠁⠀⠀⠀⠀⢠⠞⠀⠀⠀⣰⠟
⠀⠀⠐⣏⠁⠀⠀⢸⡇⠀⠀⢠⠞⠁⠀⢀⡴⠋⠀⠀⠀⢀⠀⠀⢠⡏⠀⠀⠀⠀⣠⠟⠀⠀⠀⠸⠯⠴⡶
⠀⠀⠀⢻⠀⠀⢸⠉⠁⠀⠀⠈⢇⠀⠀⠸⡀⠀⠀⠀⠀⢸⠀⠀⢸⣀⣀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠐⣎⠀⢀⡼⠀⠀⠀⠀⠀⠈⢣⡀⠀⠙⡆⠀⠀⠀⢸⣀⣄⠀⡔⠁⠀⠀⠿⠒⠛⡿⠀⢀⡼⠁
⠀⠀⠀⠸⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⢁⠀⠀⠀⠀⢀⢏⠞⠀⠀⠀⠀⠀⠀⢰⡇⢠⠎
⠀⠀⠀⠀⠘⣆⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣻⠀⠀⠀⠀⣸⡞⠀⠀⠀⠀⠀⠀⠀⣼⣴⠋
⠀⠀⠀⠀⠀⠈⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣛⣿⣿⣿

⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣤⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣄
⠀⠀⢰⣷⣿⠇⠀⢻⣷⡆⠀⠀⢰⣷⣿⠿⣿⣿⣆⡄⠀⠀⠀⠀⢻⣿⣿⣿⣶⣇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣶⠀⠀⠀⠀⡄⣿⣿⠏⢿⣿⡆
⠀⠀⠸⣿⠁⣰⣦⠈⣿⡇⠀⠀⢸⣿⠿⠀⠘⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⣶⡿⠁⡀⠛⣿⠀⠀⠀⠀⣿⡿⠁⠀⢸⢿⡿
⠀⠀⠀⠙⠦⡙⢛⠴⠋⠀⠀⠀⠀⠻⠄⠀⠀⠠⠟⠀⠀⠀⠀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠹⠄⢾⡿⠀⠋⠀⠀⠀⠀⠙⠧⠀⠀⠀⠜⠁

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣆⢸⣿⡄⡄⠀⠀⠀⠀⠀⠀⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⠀⢠⡄⣾⣿⢿⣿⣀⡄⠀⠀⠀⠀⣶⣻⣿⣷⢀⡄
⠀⠀⠀⢸⣿⣿⣿⣇⣷⠀⠀⠀⢈⣿⣿⠏⠻⣿⣿⣶⠀⠀⠀⣼⣿⣿⠋⢻⣿⣧⠀⠀⠀⣿⣿⣿⠟⠈⣿⣿⣿⠀⠀⢰⣦⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣷⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⡇⢀⣦⠀⣿⠇⠀⠀⠀⢻⣿⠁⠀⣼⢿⡟⠀⠀⠀⠸⣿⠉⢀⣆⠉⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠈⠁⠘⠟⠁⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠛⠟⠀⠉⠀⠀⠀⠀⠈⠙⠚⠛⠛⠋

⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⢀⢀⣼⣿⣷⡄⠀⠀⠀⠀⡀⠈⣿⣧⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣿⠀⡀
⠀⠀⢀⣿⣿⣿⢿⣿⣿⡄⠀⠀⢀⣿⣄⣽⣿⡟⢀⡀⠀⠀⠀⡀⢻⣿⠛⢿⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⡀⣿⣿⣿⣾⣿
⠀⠀⠸⣿⡟⠉⠀⠹⣿⡇⠀⠀⢸⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⣿⣾⠋⢠⡀⢻⣿⠀⠀⠀⢠⣸⣿⡏⠿⣷⣾⡆⠀⠀⢸⣿⣿⣿⠛⢿⣿⣿
⠀⠀⠀⠻⣧⡀⠀⣰⠟⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⢿⣄⣿⣧⡼⠃⠀⠀⠀⠀⠻⡏⠁⠐⢻⡟⠀⠀⠀⠈⢿⡿⠷⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⣠⢦⣄⣀⡀
⠀⠀⢠⣶⣶⢴⣿⣿⣿⢶⣶⣦⠀⠀⠀⣾⠀⠀⠈⡇⠀⠀⠀⠀⣿⡟⣿⣿⣿⡄⠀⠀⠰⣯⣯⣞⡾⠉
⠀⠀⠚⢻⠛⠸⠿⡿⠿⠞⢻⠛⠃⠀⠀⡈⠓⠶⠚⢁⠀⠀⠀⠐⠛⢓⡻⠓⠛⠓⠀⠀⢸⣏⣿⣮⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⠀⠘⠀⠀⠀⠀⠤⠤⠤⣶⣶⢢⠀⠀⠀⠀⠉⠛

⠀⠀⠀⢸⣿⢾⣷⢾⡷⠀⠀⠀⠀⡠⠤⠠⠄⡄⠄⠀⠀⠀⠀⢀⣤⠶⠤⣄⠀⠀⠀⢠⣶⣴⣶⣶⣶
⠀⠀⠀⠸⣿⢾⡿⢿⡿⠀⠀⠀⠀⣃⣙⣘⣀⣇⣀⢀⠀⠀⠀⣼⠁⠀⠀⢹⠆⠀⠀⣸⣟⣿⢷⢿⡿
⠀⠀⠀⠸⠿⠻⠿⢻⢿⠛⡆⠀⠀⠄⠧⠼⠤⠧⠬⠠⠀⠀⠀⠈⠷⠤⡴⠛⠀⠀⠀⠛⠿⠿⡹⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⡅⠀⠀⡀⠀⠀⠀⢐⣾⣿⣿⣖⠀⠀⠀⠀⠸⣿⣿⢿⣿⡿⠀⠀⠀⠀⣸⡟
⠀⠀⢀⣀⣀⣀⣀⡜⣀⣀⡰⠀⡀⠀⠀⠀⢻⢿⠿⠃⠀⠀⠀⠀⡷⣿⣿⣾⣿⣷⡄⠀⠀⠀⠿⣿⡟
⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⢀⣈⣀⣀⡄⠀⠀⠀⠓⠒⢒⣖⠛⠛⠃⠀⠀⠀⠠⠏
⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠉⠁⣤⡆⣤⢄⣤⣴⠀⠀⢰⣿⣿⢾⣿⣷⠀⠀⠀⢘⣾⣾⣾⣞⠀⠀⠀⢸⣿⣿⣿⣻⣿⡀
⠀⠀⠀⠀⢀⣾⢟⣾⢛⣾⡳⠁⠀⠀⢠⣿⣿⣼⣿⣧⠀⠀⠀⠻⣿⣦⣿⡿⠃⠀⠀⣸⣿⣾⣿⣾⣿⡆
⠀⠀⠀⠀⠚⠛⠚⠛⠚⠛⠁⠀⠀⠀⠨⠛⠛⠘⠛⠫⠀⠀⠀⠈⠙⠹⠙⠉⠀⠀⠀⠉⠹⠥⠿⠼⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡁⣠⣄⡾⡠⢤⢠⡀⠀⠊⣿⢸⢦⢤⢠⣤⡄⡠⢸⢧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠋⠃⠋⠓⠓⠛⠈⠃⠀⠀⠋⠀⠘⠚⠚⠁⠋⠓⠘⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⠳⠶⠶⠶⠀⠶⠶⠆⠶⠶⠷⠾⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣯⣩⣩⣍⣍⣿⣁⣁⣉⣉⣽⣅⣈⣀⣀⣀⣀⣿⣁⣁⣈⣁⣹⣍⣉⣉⣌⣹⣧
⠀⠀⠀⠀⠀⢠⣟⣀⣀⣀⣀⣰⣏⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣈⣷⣀⣀⣀⣀⣘⣧
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⣧
⠀⠀⠀⢠⠏⠉⠉⠉⠉⠉⣹⠏⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢿⡉⠉⠉⠉⠉⠙⣧
⠀⠀⢠⣿⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⡼⣧⣤⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣼⣇
⠀⠀⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣀⣀⣀⡀⠀⠀⠾⣿⡇⠰⠀⠀⢀⣀⣀⣀⠀⠀⣤⣤⣤⣤⣤⣶⣶⣶⡆
⠀⢀⣮⣽⣯⣽⣤⣼⣯⣽⣭⣧⠐⠛⢻⠛⠓⠀⠀⠀⣿⡇⠀⠀⠀⠚⠛⠟⠛⠃⣴⣯⣿⣽⣯⣤⣿⣬⣯⣽⡄
⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣆⣉⣻⣇⣈⣀⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢂⠔⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣡⠖⠁⠀⡴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠔⠁⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠔⠁⠀⡠⡢⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⢊⠔⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡠⠊⠀⠀⠀⢀⠔⠈⡠⠃⢀⠔⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠂⠈⠀⠀⠀⠠⠈⠁⠀⠊⠀⠀⠊⢈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⡅⠀⠠⠊⠀⡠⠊⠨⠀⠁⠀⢀⠔⠁⠀⠀⠀⣀⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠀⠘⠐⣁⠠⠒⠁⠀⣀⡀⠀⠀⠠⠆⢒⠄⠀⠀⠀⡡⠊
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠎⡠⠒⠆⠄⠂⢉⡀⠤⠐⠊⠁⠀⡩⠃⠀⠀⡠⠃⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠰⠈⠔⡡⠊⢀⠠⠀⠒⠈⠉⠐⠒⢄⠀⠀⢐⠆⠀⡠⠊⠀⡠⠒⠁
⠀⠀⠀⠀⠠⠁⢠⠊⡠⢊⡡⠀⠠⠀⠀⠀⠀⠢⡀⠡⡠⠂⡠⠊⠀⠔⠉
⠀⠀⢸⠑⠁⡰⢁⠎⡔⠁⠀⢀⠌⡠⠀⠀⠌⠀⢡⠀⡇⢌⠀⠰⠥⢤
⠀⠀⢘⠀⢠⠁⠆⠈⠀⢀⠔⠡⠊⢀⠀⠈⠀⠀⠠⢀⠃⠌⡀⠀⢠⠂
⠀⠀⠘⡀⠀⠀⡄⠐⠔⠁⠀⠑⠒⠊⠀⠈⠢⠐⠁⠌⠀⡔⠁⡠⠁
⠀⠀⠀⠡⠰⡀⠰⡀⠀⠔⠈⠉⠁⠈⠑⢂⠀⢀⠜⡠⠊⠀⠊
⠀⠀⠀⠀⠡⡈⠢⡈⠢⡑⠠⠄⠀⠤⠐⢁⠠⡢⠊⡠⠒⠁
⠀⠀⠀⠀⠀⠈⠂⢄⡑⠂⠅⢀⣀⣂⠨⠕⣊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠘⡆⢀⠀⢤⠀⠠⠀⢠⠃⢀⠌⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⠠⡌⡇⢸⠀⢰⠀⠘⢀⡄⣰⠃⠠⠊⠀⢀
⠀⠀⠀⡀⠀⠢⣀⠀⠳⢀⠙⡄⠳⠹⠘⠀⠘⠀⠃⠜⡰⢀⠔⠀⠀⠄⠉
⠀⠀⠀⢈⠓⠆⢀⠐⢤⡈⠃⢀⡤⠖⠚⠉⠉⠙⠒⠦⣄⠉⠠⠞⠁⠠⠖⠋
⠀⢀⡀⠈⠉⠀⠦⣅⡠⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠚⣁⡤⠴⠂⢀⣀
⠀⠀⠀⠈⠉⠃⠐⠤⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠱⠂⢈⣁⣁⡀
⠀⠀⠀⠉⠉⠙⠀⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⣉⡉
⠀⠀⠐⠒⠒⣀⡉⠩⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⣀⠉⡉⠁⠈⠁
⠀⠐⠒⠀⣉⠁⠖⠊⣠⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠲⠄⢀⠉⠉
⠀⠀⠀⠁⠀⠠⠖⠈⣠⠆⢀⠙⠦⣄⡀⠀⠀⢀⣀⡤⠞⢁⠐⢦⡀⠲⢬⡉⠓⠆
⠀⠀⠀⠀⠀⠀⠤⠈⢀⡄⢁⡖⠤⢀⠈⡉⢉⠉⡀⡄⠰⡈⠢⡀⠈⠃⡄⠈
⠀⠀⠀⠀⠐⠃⠀⠠⠎⢠⠌⡴⠀⡞⠀⠇⠸⠇⠧⠠⡀⠑⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⢀⠁⠠⠄⠀⡆⠐⠀⢳⠀⢈⢤⡤⣥⢤⠤⡤⣤⢤⠤⡤⣤⢤⡤⡤⢤⢤⡤⡤⢤⢤⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠷⠀⢀⡾⡴⠤⠦⠦⣼⢥⠧⠬⠴⢤⠯⠴⠴⠤⠆⡼⠴⠥⠦⡴⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⠖⢲⠒⡖⢒⡖⣲⠒⡞⠛⠗⣻⠚⡖⢻⠛⠺⠓⡿⢻⠚⠳⠓⡞⢺⢷⠆⡖⠰⢢⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⡞⢒⠓⠲⠓⡾⢲⠓⡺⠒⡞⢲⠟⡾⠒⠞⢲⠓⣾⢓⠖⢲⠃⡾⢒⡟⠞⠺⠲⠓⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡼⠠⡞⢠⠇⣼⠣⠞⢰⠇⡼⢠⡿⠰⠃⡾⢠⠆⢴⠇⡾⢠⠇⢴⠃⡞⠙⢰⠃⠎⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢴⠧⡼⢤⠮⣴⠧⡼⢤⠧⣴⠥⡾⢤⠧⣴⠥⡾⢤⡯⡴⠤⡾⢤⠧⣼⠻⢁⠋⡘⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢥⠧⣴⠥⡼⢠⡯⣴⢥⡮⢤⠧⣼⢥⡮⢤⠧⣼⢤⡾⢤⠥⡼⢤⡮⣴⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣃⣎⣠⡇⣰⢁⣾⣠⣅⣼⢀⡎⣰⣇⣼⢀⡆⣠⢃⣼⢡⡇⣰⢁⣼⢠⡏
⠀⠀⠀⠀⠀⠀⢠⣇⣸⣀⣎⣠⣃⣼⣁⣆⣰⣁⣜⣀⣏⣰⣁⣜⣀⣇⣸⣃⣌⣠⣃⣰⣁⡞

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠈⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⢀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠰⠳⣄⡎⠀⠀⠁⠠⠀⡜⢆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠈⠆⠀⠀⢀⠀⠰⠁⢸⠈⠰⠃⢰⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡏⠲⢦⠀⠀⠀⠀⠀⠈⢄⠁⠀⢸⠀⠀⠀⡌⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⡘⠘⡐⢚⡇⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⡀⠀⠳⠉⠀⠌⡰⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢤⣄⡀⠀⠀⠀⠀⠂⠄⠐⠂⠀⠀⠁⠄⠂⠀⠀⠤⠊⠉⠈
⠀⠀⠀⠀⠀⣼⠹⣭⢍⣠⢴⠚⢠⣀⣤⡤⡖⠢⣤⢼⣐⠒⣦⠀⢲⢢⡀⠘⠛⣻⣻⡄⢠
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠻⠼⠛⠛⠊⠳⣾⡴⠃⠰⣌⣠⡼⠷⣤⣸⡖⠲⠮⠯⠟⠛⠛⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⠀⠀⠀⠀⠀⠈⢻⠋⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠙⡿⠁⠀⠀⠀⠀⠀⠈⢿⠋⠀⠀⠀⠀⠀⠈⢻
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣦⣀⣀⣀⣀⣀⣤⣿⣷⣄⣀⣀⣀⣀⣠⣾⣷⣄⣀⣀⣀⣀⣀⣴⣿⣦⣀⣀⣀⣀⣀⣴⣿⣦⣀⣀⣀⣀⣀⣠⣾
⣿⣿⠋⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠈⠙⡿⠋⠀⠀⠀⠀⠀⠙⢿⠋⠁⠀⠀⠀⠀⠈⢻
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣄⣀⢀⣀⣀⡀⣠⣾⣦⣀⢀⣀⣀⣀⣀⣼⣷⣄⢀⣀⣀⡀⢀⣴⣿⣄⡀⣀⣀⣀⢀⣠⣾⣦⡀⡀⣀⣀⢀⣀⣼
⣿⣿⠟⠉⠉⠉⠉⠉⠙⢿⠟⠉⠉⠉⠉⠉⠙⢿⡿⠋⠉⠉⠉⠉⠉⠻⣿⠟⠉⠉⠉⠉⠉⠙⣿⠟⠉⠉⠉⠉⠉⠙⢿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣄⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⣠⣷⣄⠀⠀⠀⠀⠀⢀⣾⣄⠀⠀⠀⠀⠀⢀⣼
⣿⣿⠟⠛⠛⠛⠛⠛⠻⣿⡿⠛⠛⠛⠛⠛⠛⢿⡿⠛⠛⠛⠛⠛⠛⢿⣿⠟⠛⠛⠛⠛⠛⠻⣿⡿⠛⠛⠛⠛⠛⠛⢿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡀⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⢀⣼⣀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⡿⠒⠒⠒⠒⠒⠿⣿⣿⠓⠒⠒⠒⠒⠺⣿⣿⠗⠒⠒⠒⠒⠚⢿⣿⡿⠒⠒⠒⠒⠒⢿⣿⡿⠓⠒⠒⠒⠒⠺⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣀⠀⠀⠀⣀⣀⠀⠐⠛⠋⠙⠒⠂⠐⠶⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠸⣿⣧⠙⣧
⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢻⣿⡇⢹
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠙⠁⢀
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⣼
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⣳⠀⠀⠀⠀⣿⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠉⠙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣄⣀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⡿⠟⠋⠉⠉⠙⠻⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣻⣿⣿⣿⣿⣟⣛⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⢿⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⢦⣌⢷⣄⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⣆⠙⠷⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⡓⠦⡀⠈⢷⡀⠀⠀⠀⣿⠀⠀⠘⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡄⠀⠻⡄⠀⢰⡇⠀⠀⠀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⣠⠟⠀⠀⠀⠹⣄⡀⢻⠀⠸⣇⠀⠀⠀⠀⠀⢰⡇⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣠⠟⢰⡏⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠘⢷⣄⠀⠀⠀⠀⠻⣄⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣮⡉⠀⠀⠻⢦⣄⣀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠳⢦⣄⠀⠀⠈⠳⡄⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⡀⠀⠀⠀⠈⠉⢻⠓⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠃⠀⠀⠀⠀⢠⣸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⡞⠀⠀⠀⢀⣤⠟⣿⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⠀⠀⢹⡆⢀⡤⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢁⡖⠉⠀⣀⡴⠞⠋⠀⣰⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠘⡇⢸⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠘⢧⣠⠞⠁⠀⠀⠀⠘⠁⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢰⠇⢸⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⢠⢀⠞⠁⠀⣰⠋⣠⡾⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠃⢀⣠⠄⣀⣴⠆⢀⠀⠀⠀⠞⠀⠀⠀⠀⠟⠉⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠰⣶⣤⣛⠀⠈⢁⣾⣿⣷⣿⣿⠃⠀⠀⣀⠀⠖⢀⣀⡀⠀⠀⠀⠀⠀⣰⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣍⣻⣦⣄⡀⠀⣀⠐⣀⣈⠛⠻⣟⣻⣿⣿⡿⠟⣋⠀⠀⣠⣤⣤⣤⡶⠿⠛⠁⠀⠀⠀⣀⡼⠯⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⠶⠛⠻⢶⣤⣄⣈⣁⣰⣿⡿⣯⣥⣤⣀⡛⣿⣿⣶⣬⣍⠀⠻⠷⠶⢶⣆⣤⣴⣾⣿⣶⣶⣶⠤⠴⠶⠖⣶
⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣤⡤⠤⠶⠶⠚⠋⠉⠉⠉⠉⠁⣀⡤⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⠲⠶⣿⣿⣭⢤⣭⣍⣛⡛⠛⠶⠦⢤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠋⢑⣻⡿⠟⠋⢁⣀⡈⠉⠉⠉⠋⠉⠛⠒⠾⠭⣅⣀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣯⣉⣀⠤⠖⠚⠉⠉⠀⠠⠖⠛⢉⣀⡙⠚⠙⠛⠶⠶⢦⣄⣠⣤⡴⠶⠯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⠀⣠⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢀⣠⡤⠤⣤⡀⠴⠋⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠙⣆⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⢺⠀⠀⠀⠀⠀⠀⣿⠐⠒⠒⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣀⡀⠀⣠⡼⠃⠀⠲⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠩⠉⠉⡭⠉⠩⡍⠉⢩⠍⠉⢭⠍⠉⣭⠉⠉⡭⠉⠩⡝⡆⠁⡀⠙⠷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⡇⡇⠀⠏⠀⠠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⡇⣧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠒⠒⡗⠒⠒⡗⠒⢺⠒⠒⢺⠒⠒⣿⠒⠒⡗⠒⠒⡇⡇⢸⡗⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⡇⡟⠋⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣶⣶⣷⣶⣶⣷⣶⣾⣷⣶⣾⣶⣶⣿⣶⣶⣷⣶⡠⠴⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⡏⠉⠉⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠞⠋⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠷⠶⠶⠟⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠤⠤⠤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠐⡶⠣⠌⣁⠒⠠⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠄⠀⣠⢃⢀⠀⡜⡀⠀⡠⠁⠀⠉⡱⠒⠠⠤⡈⠁⠒⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠉⠐⠧⠹⢒⣢⢮⢄⡑⠰⢠⢀⠀⠜⠀⠀⢀⠎⠀⠈⠁⠖⠠⠨⣀⣂⣥⡒⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠂⠀⡠⠊⠀⢀⠌⠀⠈⡰⠊⠕⠂⠆⢮⣈⠲⠠⠂⠆⠀⠀⠎⠀⠀⠀⠠⠃⠉⠑⠲⠄⠤⣀⠈⠁⠒⠀⠄⡀
⠀⠀⠀⢀⠄⠒⠉⠧⣀⢀⠔⠡⡀⡠⢣⠀⢀⠞⠀⠀⢠⠂⠈⠁⠢⠍⣓⠢⢤⣁⠎⠸⠄⡀⠠⢁⠀⠀⠠⠁⠀⠀⣰⡅⠀⠀⠀⠀⠀⣩⡦
⠀⠀⠀⠈⠂⠢⢄⡀⠀⠉⠛⠒⠸⢅⡁⡠⢂⢁⠀⡔⡁⠀⠀⡔⠁⠀⠀⢉⠐⠠⢍⡐⠢⢤⣁⠈⠆⡠⠁⢄⠀⣠⢉⡿⠒⠀⢀⡤⠞⢉⠃
⠀⠀⠀⠀⢀⠀⢀⠈⠀⠂⠄⠐⠄⠀⠈⠉⠒⠤⣌⠔⠄⢀⢎⢀⠀⠀⠠⠃⠀⠀⠀⠁⠋⠐⠢⠍⠑⠣⢤⣈⣰⠏⠀⠀⣠⠞⠋⠁⠀⠈
⠀⠀⠀⠀⠀⢂⠀⢦⠄⢀⠀⠀⠈⠐⠨⢐⠀⠀⠀⠉⠑⠢⢌⡀⠃⠔⠁⠂⠀⠀⡐⠁⠀⠀⠀⣼⡡⣀⠀⠀⠀⣠⡴⠛⠍⠀⣀⠂⢠
⠀⠀⠀⠀⠀⠈⡀⠈⠄⠈⠗⠂⠴⣀⠀⠀⠈⠑⠢⠅⡂⠄⡀⠈⠙⠲⠤⣄⣀⠌⢢⢃⠄⢀⠎⠙⠃⠀⢀⡴⠛⠇⠐⢀⢠⠃⣍⠀⠆
⠀⠀⠀⠀⠀⠀⠐⡀⠈⠄⢈⡀⠀⠁⠈⠳⠤⣰⠀⠀⠀⠑⠠⢅⡂⠤⢀⠀⠈⠓⠦⢤⡠⠋⠁⢀⣤⣮⠋⠁⠈⢀⠖⠁⡀⢠⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠀⢤⡀⠰⠀⠈⠁⠂⢦⡀⠀⡀⠀⠑⠂⠬⡒⠠⢄⡀⠀⣠⡴⠽⠋⠀⠄⣠⠀⠁⠆⣠⠊⢰⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠰⠄⡄⠀⠄⠈⡖⠤⡅⠀⠀⠀⠑⡧⢀⡀⠄⠀⠀⠉⠑⠪⠵⠛⢁⠀⠌⡬⠂⠁⠀⡪⠀⠁⢀⣄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠁⠘⠙⢴⡀⠁⠀⠈⠉⠰⢄⠄⠀⠀⠀⠓⠠⢀⡀⠀⠀⠰⢀⢈⠄⠈⠐⢠⡧⢊⡁⢠⠆⠘⢨⠡⠄⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠁⠀⠀⠙⠂⢤⡀⠈⠀⠈⠓⠤⣂⠀⠀⠀⠁⠀⠀⢠⠀⠌⠊⠰⡀⢛⠀⢸⢄⡧⠀⢁⠂⠀⠀⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠉⠂⢥⡀⠀⠀⢀⠀⢔⡠⠚⢀⢎⠔⡋⠈⠀⢃⡜⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢁⠀⠀⠀⠀⠀⠀⢈⠀⡠⠠⠁⣦⠃⠈⠀⢀⠴⠋⠀⡐⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡜⣀⠀⠁⠢⣀⠉⠂⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠘⠐⢀⡁⠊⠀⠂⢀⡜⠉⠈⠀⠀⣀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⡂⠀⣆⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠠⢁⠁⠀⢀⡔⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠓⠃⠀⠈⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠂⠀⡴⠊⢀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⡇⠀⢀⠎⠁⠀⠀⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢶⢢⣤⠀⠀⠀⠁⠢⡀⠀⠁⡴⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠀⠘⠛⠛⠛⠛⠃⠀⠙⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠁⠀⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠟⠀⠀⠿⠿⠿⠿⠿⠿⠀⠀⠻⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣈⣉⣉⣉⣉⣉⣉⣁⣀⣀⣈⣉⣉⣉⣉⣉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣤⣤⣤







⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⡴⢣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢀⢴⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣴⣿⣁⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣠⣤⡄⠀⠀⠀⠀⠀⠼⠿⣿⣿⠟⠁⠀⠀⠀⠀⢠⣾⣿⣿⠟⠋⠀⠀⠀⠠⠆⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠞⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠴⠎
⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠠⠚⡠⠇⠀⠀⠀⠀⠀⠀⢀⠔⠃⢀⠔⠂⠀⠀⠀⠀⠀⠀⠊⠌⠀⢀⠀⠀⠀⠀⠀⠀⠄⢠⡤
⠀⠀⠀⠀⠀⠀⠀⢠⣁⣀⡀⠀⠀⠀⠀⢠⠄⣠⠀⡩⠚⠀⠀⠀⠀⠀⠄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠄⢤⠄⣠⠞⠁⠀⠀⠀⠀⢀⡀⠕⠈⠀⠀⠀⠀⠀⠀⢀⡴⠓⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁
⠀⠀⠀⠀⠀⡠⡢⠊⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⣤⢎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠠⢾⠖
⠀⠀⠀⠀⠀⠀⢀⢨⠏⠀⠀⠀⠀⠀⠀⢀⠜⠉⣩⠟⠁⠀⠀⠀⠀⡠⠊⠦⠠⡠⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⣠⣃⣚⢒⡻⠃⠀⠀⠀⠰⠧⣶⢄⠽⠋⠀⠀⠀⠀⠞⣲⢦⠗⠁⠀⠀⠀⠀⠀⠀⠉⡡⠋
⠀⠀⠀⠀⠀⢁⣜⡵⠋⠀⠀⠀⠀⠀⣀⡾⠛⠁⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠁⠀⠀⠈⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⠀⠀⠠⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⡠⢠⣾⡿⢡⣿⣿⢠⣿⣿⠘⣿⣷⡙⣿⣦⡑⠀⠀⠀⠀⠀⠐⣡⣿⡟⣱⣿⡟⢸⣿⣧⢸⣿⣧⠹⣿⣦⠠⡀
⠤⠴⠿⠿⠥⣾⠿⠯⠼⠿⠿⠤⠿⠿⡷⠼⠿⠿⠦⠄⠀⠀⠤⠾⠿⠿⠴⡿⠿⠧⠼⠿⠿⠬⠿⢿⡦⠽⠿⠷⠤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⢀⣶⣷⡖⢰⣶⣶⠆⣶⣶⣶⠰⣶⣶⡄⢷⣶⣦⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠛⠛⠛⠛⢛⠋⣰⣿⣿⡟⢠⣿⣿⡿⠀⣿⣿⣿⠀⣿⣿⣿⡄⢻⣿⣷⣆⠻⡛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣾⣿⣿⣯⣤⣿⣿⣿⣧⣴⣿⣿⣿⣦⣼⣿⣿⣿⣤⣿⣿⣿⣷⣬⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⡤
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⢸⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣔⣂⣰⣶⠖⠀⠀⠀⠀⡀⣴⡟⣻⣿⣿⣦⠀⣾⣭⣧⠀⠀⠀⠈⠀⠁
⠀⠀⠀⢤⣴⣾⠟⡛⠩⠁⠀⠀⠀⠀⠀⠀⠀⠼⠻⣿⣿⣿⣿⡇⠀⡹⢻⣿⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⢠⠀⠀⠀⠀⡠⢬⣿⣿⢟⠗⡁⢀⡼⠋⠀⢠⣤⣶⣤⡀⠀⠀⠀⠀⡎⣾⠀⣀⢀⡆⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠋⢀⣀⣆⠀⡔⠋⢱⡀⠀⠸⣬⣷⠶⡋⠀⠀⠠⣿⣿⣿⣿⡷⠄⠀⠀⠀⡟⣿⣆⣀⣾⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠑⠾⣵⣧⣴⡟⢳⣦⣴⣿⡿⠛⢿⣿⠀⠀⠙⢿⣿⠿⠃⠀⠀⠀⠀⡇⣿⣯⢨⣿⡇⡇
⠀⠀⠀⠀⢠⣀⣄⡀⠀⠀⠄⠰⠀⠀⠀⠀⠀⢸⣵⣸⣿⣿⡿⠖⠒⠚⢋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇⣿⣇⠀⣿⣇⡇
⠀⠀⣤⠀⠀⠉⠛⠷⣶⣄⡀⠀⠀⠀⠀⢰⠀⠀⠹⣯⣀⣿⡇⠀⢠⣴⣄⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡿⣇⢀⡿⡧⡇
⠀⠀⢀⡀⠀⣴⠂⠀⠀⠈⠙⠻⠦⣤⣤⣾⡀⣄⡀⠀⠁⠹⣿⡊⠉⣻⡟⢴⣔⣄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⡧⠀⡇⢳⡇
⠀⣠⢾⡽⠛⠿⣇⠀⠀⠑⢤⣤⣤⣶⠟⠉⠙⠛⠣⠄⠀⠀⠹⣷⣂⢩⡝⢾⣾⡟⠀⠀⠀⠀⠀⠀⢀⡴⣣⣶⢣⣤⠷⣶⡝⣦
⠀⠈⣻⣇⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠗⠈⡟⠇⠀⠀⠀⠀⠀⠀⠺⢛⡟⣧⣼⣺⣆⡟⣿⠻⠃
⠀⠴⠿⠛⠳⢤⡀⢀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢰⣸⠠⣀⠀⠀⠀⠀⠀⠈⣶⡟⠹⠿⠉⢷⡎
⠀⠀⠀⠀⠀⠀⠙⠛⠷⢤⣄⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠛⠶⣄⡶
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠳⠦⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠊⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠈⠙⠲⢬⣢⡀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠀⠀⠀⣰⠋⠀⠀⠋⠈⠉⠰⠂⣀⠈⠀⢰⡄
⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠠⠄⡄⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⢀⢌⠈⠀⠀⢠⠘⠁⠰⠆⠀⠀⠀⠂⣼⡟
⠀⠀⠀⠀⠀⠢⢀⣀⠀⢀⢀⣠⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣠⣴⣯⠞⢐⡂⠀⠈⢳⣄⡠⢠⢤⣏⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠷⠇⠀⠾⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠾⠛⠉⠀⣨⣴⣟⠁⠀⠀⠈⠻⠿⢿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⢀⠈⠀⠀⡀⠀⠀⠀⠀⠁⣀⣤⡴⠚⠉⠀⢀⣤⣶⠿⠛⠿⠿⠟⠺⠤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡰⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⢘⠄⠀⠀⢀⣜⠅⠄⢀⣠⣴⣿⣟⡭⠔⠒⠋⠉⠉⠉⠙⠉⠉⠀⣀⣀⣤⡤
⠀⠀⠀⠸⠀⢄⠀⡂⠀⠀⠀⡐⠀⠠⡘⠀⠀⣴⡟⢇⣠⣼⡿⠿⠛⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⣛⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠊⠀⡂⠀⠰⠈⠂⠊⠀⠀⠘⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠂

⠙⡖⠢⠤⣄⣀⠀⠀⡀
⠀⢈⡆⠀⠀⠀⠉⠒⠿⠑⢄
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀
⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡀⠀⠉⠒⠤⣄⡀⢠⣀
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢯⠑⠦⣀⠀⠀⠈⠙⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⡆⠀⠈⠑⠲⠒⠢⢄⡀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠉⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠦⠀⠀⠸⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⢠⡓⠀⠀⠀⠹⡑⠦⣀⠀⠀⠀⠀⠀⠈⠲⠒⠤⣀⠈⠑⢄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⢄⠀⠀⠀⠱⡄⠀⠙⠢⢄⡀⣄⣀⠀⠀⠀⠀⠙⠲⢄⡈⠛⠀⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠳⣄⠀⠀⠙⡄⠀⠀⠀⠈⠉⠀⠉⠒⠖⠠⣄⠀⠀⠈⠲⢄⠀⠀⠀⠀⠈⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡍⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣤⠤⠒⠊⢉⣉⠐⠒⠤⢄⡀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⢦⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⡤⠒⠉⣁⠠⠄⠀⠈⠀⠀⠉⠁⠀⢀⡈⠒⠢⣄⠀⠙⠋⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣵⡄⠀⢶⠊⠀⠀⠀⠀⠐⠉⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠆⠀⠈⠓⠤⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠙⣄⠀⠀⠳⡀⠀⣠⠎⢀⡠⠊⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠘⡆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢦⡀⠀⠈⡶⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠃⠀⠀⠘⡄⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠑⢄⣠⠃⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡹⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠤⡀⠀⠸⠤⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡆⠀⡇⠀⠓⠂⢰⡀⡄⠀⡀⠀⡀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⢱⠀⠠⠒⠂⠌⡀⠀⠃⠤⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡜⢀⠎⠈⠂⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡆⢰⠀⠀⠀⠀⡀⠀⠀⠐⠂⠒⣄⠀⠀⡈⠖⠒⠒⠶⠊⠀⡎⠀⠀⠀⠀⢸⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⡇⠀⡇⢠⠒⠒⠁⠀⠧⣀⣀⠀⢈⡆⡞⠀⠀⢂⠀⠠⠒⠄⠈⠱⠴⠃⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠙⠋⠀⡜⠉⠉⠑⠲⢄⠉⠉⠀⠈⠒⠊⠁⢠⡃⣀⠀⡠⢄⠀⠀⢰⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠳⣄⠀⠀⠣⡀⠀⠀⠀⠀⠱⠀⡴⠊⠁⠉⠢⢄⠉⢠⠊⠀⠀⠅⢀⠇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠑⢄⡀⠹⡄⠀⠀⠀⡜⠘⡄⠀⠀⠀⠀⠀⠇⠈⠑⠒⢀⡴⠋⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠙⠦⡈⠀⠀⠀⡡⠀⠈⢦⣀⣀⡀⠈⠀⣀⡠⠖⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡈⠑⠢⠌⣀⡀⠀⠀⢉⣁⠤⠔⠋⠀⠀⢀⡠⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣒⣤⣀⣠⣭⣭⣤⣤⣤⣀⣀⣒⣊⣁⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⢀⣛⡀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⠄⣴⠞⠛⠉⠙⠻⣦⡀⡴⠗⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⠀⠀⠘⣷⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⢹⡟⠉⠉⢹⡏⠉⠉⢹⡏⠉⠉⣿⠉⠉⢻⡆⠀⢀⡿⠈⠉⠁⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⠶⣾⠷⠶⠶⣿⠶⠶⠶⢾⡷⠶⠶⢿⡷⠶⠶⣿⣴⠟⠁⠶⡦⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⢀⣿⠀⠀⣀⣿⡀⠀⠀⢘⣇⠀⢀⢘⣷⡀⠀⢸⣧⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠛⢻⡟⠛⠛⠛⣿⠛⠛⠛⠛⣿⠛⠛⠛⢻⡟⠛⠛⢻⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⣤⣤⣿⣥⣤⣤⣼⣯⣤⣤⣤⣤⣿⣤⣤⣤⣼⣧⣤⣤⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⣀⣼⣇⣀⣀⣀⣸⣇⣀⣀⣀⣀⣹⣇⣀⣀⣀⣸⣇⣀⣀⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⣶⣶⣶⣶⡆⢠⣴⣶⣶⣶⡦⢀⣴⣶⣶⣶⣶⠀⣤⣶⣶⣶⣶⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠸⣿⣿⡿⡿⠏⠰⣿⣿⣿⣿⠟⠀⢿⣿⣿⣿⠿⠁⢾⣿⣿⣿⡿⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣶⣶⣶⣶⣶⠀⣴⣶⣶⣶⣶⠀⣠⣶⣶⣶⣶⡆⢠⣶⣶⣶⣶⡦⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣼⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠿⠿⠿⠿⠟⠀⠿⠿⠿⠿⠿⠃⠸⠿⠿⠿⠿⠃⠸⠿⠿⠿⠿⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⣶⣶⣶⣶⠆⢠⣶⣶⣶⣶⡆⢠⣶⣶⣶⣶⡶⠀⣴⣶⣶⣶⣶⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠺⠿⠿⠿⠿⠃⠸⠿⠿⠿⠿⠋⠐⠿⠿⠿⠿⠟⠀⠿⠿⠿⠿⠿⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⣾⣿⣿⣿⡷⢀⣶⣿⣿⣿⣷⠀⣴⣿⣿⣿⣿⠆⣰⣿⣿⣿⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⣿⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠘⠿⠿⠿⠿⠋⠀⠿⠿⠿⠿⠟⠀⠻⠿⠿⠿⠟⠃⠸⠿⠿⠿⠿⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣶⣿⣿⣿⣿⠀⣴⣾⣿⣿⣿⠆⢰⣾⣿⣿⣿⡗⢠⣾⣿⣿⣿⣷⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⡇⡌
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠿⠿⠿⠿⠟⠁⠸⠿⠿⠿⠿⠃⠘⠿⠿⠿⠿⠋⠀⠿⠿⠿⠿⠟⢠⠁
⠀⠀⠀⠀⠀⠀⠀⡌⣰⣿⣿⣿⣿⡇⢰⣾⣿⣿⣿⡷⠀⣾⣿⣿⣿⣿⠀⣴⣿⣿⣿⣿⠇⡎
⠀⠀⠀⠀⠀⠀⢠⢁⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⡏⢰⣿⣿⣿⣿⡿⢠⠁
⠀⠀⠀⠀⠀⠀⢎⠘⠟⠿⠟⠟⠋⠐⠛⠿⠟⠟⠋⠀⠛⠿⠛⠟⠛⠁⠚⠟⠻⠛⠟⢁⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢔⣀⡀⠀⠀⠀⡀⠈⡀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠈⠀⠠⠂⠀⠀⠀⠐⡀⠄⠐⠪⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⡀⠀⠀⠀⠐⠀⠀⠀⠢⡀⠀⠀⡀⠀⢀⠀⠤⠀⢀⠀⡠⠂⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⢀⠀⠤⣀⢀⡀⠀⢀⡒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠈⠁⠐⠜⡋⠈⠀⠌⠐⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠔⠉⠀⠈⠰⡀⠀⠈⢲⠚⠒⠂⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⡀⠀⠀⠀⢀⠃⠀⠀⠀⠳⡀⠀⠀⠡⡈⠀⠐⠀⠂⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠣⡀⠁⠢⠠⠔⠁⢐⠂⢄⠀⠀⠈⢂⠀⠀⢈⡶⡀⠀⠀⠐⠀⠀⠁⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⡑⠢⡀⠀⣱⠐⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠈⠒⠂⠤⣀⠀⠀⠈⠂⢌⠚⢄⠀⡴⠚⠅⠦⠀⠀⢀⢠⠀⠚⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠘⠀⠀⠐⠒⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠉⠐⠤⠤⠋⠑⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠠⢀⠀⠀⠀⠀⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⠁⠀⠀⠠⠠⠄⠀⠀⠁



⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣟⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠒⠒⠲⢦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣀⣠⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⠐⠈⠁⠀⠀⠀⢄⢀⠀⡐⠀⠀⠀⢀⣿⢀⣤⠶⠛⠉⠸⡏⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢠⠞⠃
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠘⠓⠶⡾⢛⡿⠋⠉⠉⠉⠙⠓⠠⣄⡀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣠⠞⠳⡇
⠀⠀⠀⠀⠀⠀⢻⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⢷⡀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⡄⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠄⣣⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⣇⠀⠘⢧⡀
⠀⠠⠄⠱⡄⠀⠀⠀⠈⠢⡀⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠉⠀⠦⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢷⡀
⠀⢰⠖⠇⠀⠀⠀⠀⠀⠀⠀⠙⢳⡷⢦⡄⠐⠀⠈⣷⠒⠂⠐⠀⠲⠒⠒⢦⡀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠸⡇⠘⠁⠀⠀⠀⢻⣄⣀⣠⢀⡄⠀⠀⠰⠉⠂⡖⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣟⠀⢻⣾⡆⠀⠘⠀⣼⠻⡄⠀⠀⠉⠙⠲⠶⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢣⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠈⣷⠀⠃⢠⡏⠀⢹⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡀⠘⢷⡀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡀⢶⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷⡀⠀⣿⠀⠀⠙⣆⠀⠀⠀⠀⢠⠄⠀⠀⣀⠀⠀⠀⢀⡾⠆⠉⠀⠖⠉⢿⣄⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢑⠠⡿⠂⠀⠀⠀⣸⠁⠀⠀⠘⡏⠰⡿⠀⠀⠀⠈⢷⡀⢀⠴⠐⠒⠢⠄⠀⠉⢂⢀⡞⠠⠐⠈⠀⠀⠀⠀⠻⢇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠾⠙⣧⠀⠀⠀⠀⣽⠄⠀⠀⠀⠹⣄⣧⠀⠀⠀⡠⠤⢋⠌⠁⠀⠀⠀⠀⢁⠀⣸⡋⠠⠄⠀⠀⠠⠤⢀⡀⠀⠃⠉⢰⡶⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⠇⠒⠈⠀⠀⠀⠀⠙⣆⠀⠀⠂⡴⠁⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢴⠖⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠳⣄⣠⠁⡂⠀⡀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⠜⣿⡀⠁⠀⠃⠘⠀⣴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⠀⡀⠀⠀⠀⠀⢀⡜⠃⠀⡠⣡⠊⠀⡿⣀⢀⡁⣀⣰⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢰⠆
⠀⠀⠀⢀⣠⠶⠛⠀⠐⠤⠀⡀⠢⡀⢀⡴⠋⠀⠀⢠⡜⠁⠀⢠⠃⠈⠉⠙⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⢈⠓
⠀⢰⣉⠉⢀⡀⠀⠀⠀⠀⠀⠈⣴⠟⠉⠀⠀⠀⢀⡿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡴⠊⠉⠁
⠀⠀⢉⡟⠁⠀⠀⠚⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢺
⠀⢀⡟⠀⡔⠁⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢿⡀⠀⠀⠀⠀⠀⠛⠁
⠀⢸⡅⠀⢀⠄⠀⠂⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀
⠀⠘⢧⣤⡥⢶⠱⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡀⠀⠀⠀⠀⣶⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⡀⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠰⡄⠂⠀⠁⠀⡀⠀⠘⣷⡀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠿⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠚⠁⠈⠀⠀⠈⢷⡄⠀⠀⠈⠳⣄⠀⠀⢀⡀⠄⣀⡔⠉⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⢀⠀⠀⢀⠀⠀⠘⣦⠀⠀⠀⠘⢯⣀⠀⠀⠚⠁⠀⠐⠉⠀⠴⠈⠲⡆⠀⠀⠀⠀⠀⠀⠠⠂⡀⠀⠀⠀⡿⣧
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢉⠀⠀⠀⠘⢷⡀⠀⠀⠀⠙⠢⣄⠀⠈⠀⠠⠀⠀⠀⡀⠀⠉⢲⡀⠁⠀⠄⠀⠁⠈⠃⠀⠀⡜⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠳⢆⠀⠀⡀⠄⠀⠀⣀⠄⢫⡝⡟⠁⠀⠀⠀⠀⠀⣤⠜⣡⡟
⠀⠀⠆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠙⠦⣤⣴⠶⠾⠉⠀⠈⢰⡟⠁⠀⠀⠐⢓⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠴⠊⣠⠞⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡂⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⣏⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠊⢤⡀⢰⡇⠀⠐⠊⣁⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣄⡁⠐⠀⢀⣠⠤⠂⠁⠀⠀⠜⠒⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡀⠄⠋⢉⡿⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⣄⠀⣉⣠⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣴⠀⠈⠈⠉⠀⢄⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠊⠀⠁⠉⢀⣠⠀⠁⠀⠀⣴⡖⢀⡀⢤⡵
⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⡄⡠⠀⠀⣾⠆⢸⠃⢀⣀⡀⠀⣨⣙⠟⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡠⣀⠈⠀⢄⠀⠀⠀⠀⠀⣠⠆⣀⠁⠋⢀⣀⣈⠀⠀⠀⠙⢉⣤⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⡂⠀⠐⣀⠀⠀⠀⠀⠉⠙⠗⢿⣷⠈⢻⡜⢿⣃⣨⣌⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣘⣥⣶⠩⠛⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠔⠡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠀⠀⠐⠅
⠀⠀⠀⠀⠀⣠⠔⠛⠃⠀⠁⠀⠀⠈⠛⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠁⠊
⠀⠀⠀⠀⡘⠁⠀⠀⢰⣶⠀⠠⣄⠀⢀⣴⣦⣵⡀⠄⠀⠀⠀⢠⠄⢇⠔⠊⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣯⠀⠀⢀⠀⠁⢀⢀⠃⣧⡀⠭⠀⠀⠵⢾⡀⠀⠈⠉⡶⠲⠉⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡴⠃⠀⠀⢈⠄⠐⠁
⠀⠀⠀⡏⠀⠀⣦⠀⠀⢀⢀⡀⠀⠈⠉⠀⣄⠀⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠠⢀⠄⠀⠀⢔⠅
⠀⠀⠀⢳⠀⢀⠀⠀⢸⣿⣿⠇⠀⢀⡻⢦⣨⢙⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠⠆⣾⣶⡦⠐⢀⠔⠀⠀⠀⠀⠁
⠀⠀⠀⠢⠀⠸⠇⠀⠈⠉⢁⡀⠓⠀⢸⣿⣿⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢀⡉⡵⠘⣋⡷⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠤⡤⠠⣄
⠀⠀⠀⠀⠙⣇⡀⣦⣷⠀⢈⡁⢀⣿⣾⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠡⣅⠈⠠⠴⢰⢫⣞⠰⠃⠀⠀⠀⠀⠀⠀⣀⡾⢀⢻⠞⣻⣻⣷
⠀⠀⠀⠀⠀⠈⠑⢉⣯⣼⣯⣿⣶⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣦⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣛⣝⣛⣩⣛⣻⣛⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⣐⣒⣒⠀⠠⠤⠤⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⠀⢀⠀⠀⠈⠀⢹⠈⠀⠏⠀⠐⡂⠒⠀⠄⠨⠍⠭⠴⠤⣀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠸⠀⠀⡇⠀⣨⠀⢰⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠐⠀⢠⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣃⠀⢀⠁⠀⠿⠀⡄⠀⠀⠘⠀⠸⡄⠀⠸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠚⠚⠛⡛⠣⠌⢈⠀⡇⠤⡤⠆⠠⠂⢇⠀⡄⠀⠀⡄⠀⠈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠃⠀⠀⠇⢠⠀⠀⠈⠇⠀⣦⠂⢘⠛⠲⠶⠗⢀⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⣸⠀⠈⠀⠀⢰⠀⢠⡞⠀⡈⠀⠀⢸⠠⡞⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣢⡬⠤⠀⣄⢀⡠⠃⡀⡈⠀⠀⠀⠀⡈⡇⠀⠃⠔⡊⣔⢠⡇⢸⠅⠀⠀⢀⢴⠤⠔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⡀⠈⠉⡈⠐⢂⠔⠀⠉⠤⠄⠛⠀⠁⠑⠚⠶⠤⣾⣥⠺⠁⣿⠀⠀⠀⢹⠁⠀⠈⠀⠀⠀⠀⠀⠀⣀⠤⠄⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠁⠀⢠⠀⠀⣮⠀⢠⠀⣀⠴⠀⢴⠠⡿⡅⢽⠡⠆⣲⡄⢰⡇⠀⠀⠀⢿⣆⡀⠀⠀⠀⠀⠀⡠⡌⠀⠀⢀⠨⡗⡒⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡘⠀⠀⡈⠀⢠⢹⠀⡈⠨⠂⣽⢂⡽⣿⠑⡨⠐⢨⠋⢰⡇⣾⠃⠀⠀⠀⠀⠑⠪⡟⡼⠶⠾⠟⢧⢿⡑⠀⠠⠀⡷⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠉⠁⠒⠂⠧⠶⠂⠱⠠⣇⣬⣸⡞⣩⠇⣯⠀⡇⡂⠟⢠⣸⢁⡟⠀⠀⠀⠀⠀⠀⡐⡠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣈⠀⡀⢀⠮⠬⣉⣑⣴⣖⢴⢲⢦⠭⢭⣉⠀⣉⠓⡓⠲⠦⠭⠝⢨⡇⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⡸⣀⠔⠪⢄⠢⣘⢌⣦⣿⠕⡹⣲⡆⡂⠀⣸⢸⢃⡄⣈⠩⡍⢚⡆⣿⠀⠀⠀⠀⡠⡮⠊
⠀⠀⠀⠀⠀⠀⢀⠁⣔⣚⡇⠗⣾⢀⠷⢥⡗⢅⣼⠙⢀⠡⠑⡏⣼⣄⠁⠐⢹⠤⢲⢡⡿⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠘⢠⣬⠍⢉⢛⣊⠐⠛⠘⠯⠡⠿⣔⣈⣂⣔⠃⣯⠚⢔⠂⡅⠈⡶⣼⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣏⠁⠃⡔⠅⠈⠍⡇⡴⠕⠀⡲⠆⠤⣤⡀⠀⣘⠛⠚⠣⠦⠷⠁⣿⠁
⠀⠀⠀⠀⠀⢀⠸⢅⠸⠀⡢⢠⠐⢨⠁⡯⠀⠆⠪⠀⡆⠢⡇⣾⠉⡀⡋⠉⠰⣶⢸⡟
⠀⠀⠀⠀⠀⠀⠺⣵⣀⣐⡄⡁⠐⡼⢰⡢⢸⠀⠄⣠⠐⢬⢁⡧⠐⣇⡆⡸⢉⣺⢸⡇
⠀⠀⠀⠀⠀⠀⠒⠂⠀⠩⠍⣁⣈⠁⠘⠃⠤⢤⣅⡄⠰⡸⢸⡇⠰⢻⠑⡅⡁⠂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠠⠤⠠⠀⣀⣉⠛⠐⠒⠷⠖⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠒⠈⠅⠒⡠⠄⣂⠠⠀⣂⠠⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠉⠒⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠀⢸⠇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠿⠀⠀⠀⠀⡆⢸⠇⠀⠀⢠⡀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠀⠀⠀⢰⠃⠉⠀⡼⠀⠀⣇⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢻⡀⠀⠀⠁⠀⢠⡏⠀⠙⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⣶⠀⠀⢰⡀⠈⠁⢠⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⡟⠀⠀⠈⣷⠀⠀⢸⡄⠀⠇⠀⠀⣀⢠⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠸⠇⢄⠀⡄⠀⠀⠀⠈⠁⠀⠀⢠⠀⠛⠈⠀⣧⣰⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⢀⠈⠀⠁⡀⠀⠀⠚⠀⠀⣆⠛⠀⠀⡇⢸⢿⠋⠀⡀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⠋⢸⠃⠀⠀⠃⠀⢰⣆⠑⡆⣼⠘⠀⠀⠙⠀⠀⠄⢠⠀⠈⠀⠠⡇⠸⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠈⣷⢈⡁⡀⠀⠀⢀⠘⠛⠀⠁⠻⠀⠀⢠⡀⠀⠀⣄⠀⠰⠀⠀⠀⠃⡿⠀⣆⠸⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⠀⠐⡋⢻⠃⣷⠀⠀⠚⡀⠀⠀⠀⠀⠀⢰⡌⡅⠏⢠⠟⡄⠀⠄⡀⠀⠀⣀⠠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢸⡸⠇⠑⠴⡄⢡⣲⠐⣄⡇⠀⢀⠀⡄⢈⠀⡀⠿⠀⡾⠠⣠⡇⠸⠇⢀⡜⠃⠀⠀⢰⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢸⠂⠓⡆⣠⡄⠀⢧⣴⣾⡿⣶⡔⡌⠇⠀⠘⢠⡇⠀⠀⠀⠀⠋⡠⡖⣠⣸⣧⡘⠁⠀⠈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡦⠘⣄⠀⠈⠛⠈⠃⠙⢟⠃⣿⠿⣦⠀⠶⠀⠈⠓⣦⠀⠀⠐⠈⣷⠏⣻⢁⣼⡿⠋⢀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣌⠀⡮⡄⢈⣗⣦⡼⢆⢠⡄⠻⠃⠀⠀⠊⡰⣿⠄⠈⠀⠰⢷⠠⠉⠈⠈⣴⢒⡊⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢈⣛⣠⠤⣿⣄⡧⢴⣾⣿⡹⠇⢸⣧⢱⣄⡶⠀⠆⠁⠁⠁⢠⣄⠀⢁⣈⡀⢻⣧⢀⣿⡌⠃⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠞⠁⠀⠀⠀⢹⣿⣆⡈⠯⠀⣀⣀⠀⠈⠛⢡⣿⣧⠤⠓⠠⢾⣿⣦⡈⠿⠃⢘⠡⢜⣿⡛⠁⠀⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⣀⣠⣾⡾⠁⠀⠀⠀⣨⡿⠂⠒⠒⢿⠏⠀⠀⠀⠀⠀⠙⢿⡟⠈⠁⠙⣄⠀⠈⠙⢿⣯⡭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⡽⠯⠽⠿⣵⣠⢤⣄⣾⡿⣇⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⣠⣿⣷⣤⣠⢔⣿⡆⠀⣠⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠐⠾⠶⠛⠿⠧⢯⡥⠿⣿⣓⠠⠄⠂⠾⠛⣋⠿⠷⠿⠿⠳⢿⠶⠾⠾⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀
⠀⠀⠀⠀⠀⠈⡀⠠⠄⠤⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⣠⣮⣀⠀⣠⡶⠋⠀⠀⣠⠆⠀⠀⢠⠄⠈⢄⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⣽⠏⠘⠶⢦⡀⢾⣋⡀⠀⡴⠁⠀⣨⡦⠀⣴⢄⠡⠀⠀⠠⠀⠀⠈⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⢶⠔⢿⣁⠀⢀⣤⠞⠈⠈⢉⡏⠀⠵⠖⠺⢋⡰⠊⠀⠈⢧⠐⡀⠄⠀⠀⠈⠀⠄⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⠄⠀⣠⠦⠈⠁⠉⣭⡉⢷⣤⡀⠴⠋⠀⠀⣤⠀⡠⠊⠀⣀⢦⠄⠀⠣⡈⢣⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣈⠙⠊⠡⣄⣀⡰⠞⠁⠀⢀⡼⠖⠈⢙⠒⠛⡡⠞⠀⠀⠀⠹⣸⠀⠀⠀⠙⢄⠱⡀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⢆⡀⢀⠀⠓⠲⠆⡋⠀⠀⣠⡾⢃⠞⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠣⡘⢆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠂⢥⢀⣄⡈⠙⢊⡕⡰⠋⠀⠀⠠⢀⠀⠀⠂⠐⢲⠄⠀⢸⣹⠀⢙⢜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠉⣬⠨⠀⠀⠐⡀⣀⣸⡆⠀⢴⣨⣼⠅⠀⠐⣼⠀⠈⣠⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠑⠲⣄⠀⢀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⡅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣽⠀⢐⡛⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⢂⢀⡀⠀⣯⠇⠀⡀⢈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠘⠳⢶⡸⠀⠂⠀⠀⠀⢠⠒⠒⡏⣱⠀⠀⠄⣠⣄⣫⡵⠆⠀⠇⠁⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⡀⠀⠀⠀⡄⢀⡂⠰⠀⠀⢸⠠⠮⠥⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡀⡸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⢁⠀⠀⠀⠀⠀⢸⠀⠀⣀⣇⣀⣀⣀⣤⠤⠤⠖⠒⠚⠓⠋⠁⠠⠤⠶⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣀⠂⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉

⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡗
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⡟⣷⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣷⠄⠀⠀⢸⣿⣿⣽⣿⣷⠀⣾⣿⣿⣽⣿
⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠘⢸⡿⢻⡇⠙⠀⠀⠀⢿⣿⡿⢿⣇⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠁⣷⣿⣿⣷⣿⠈⠁
⠈⠛⠻⣿⡿⠟⠛⠀⠀⠀⠀⠀⢺⠃⠘⡟⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⣤⠀⠀⠀⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢑⣶⣾⣶⣄⠀⠀⠀⠀⠀⢾⣿⣷⠄⣀⣠⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⣿⣦⣤⣶⣶⠤
⠀⠀⠀⠻⣿⣋⣿⡿⠃⠀⠀⠀⠀⠀⠙⢡⣾⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣶⣿⣿⣷⣊⣽⣷⠃
⠀⠀⠂⣸⣿⣿⣿⣿⡄⠂⠀⠀⠀⠀⠰⣝⠿⢋⣴⣿⣦⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣻⣧⣞⣹⠿⣿⠖⠁
⠐⠃⠀⠀⠀⠛⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠈⠒⠛⠛⠐⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢐⠉⡆⠀⠀⠀⠀⠀⠀⢀⢶⣿⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣿⣿⣿⠀⠀⠲⢦⡄⢀⣤⣶⣤⡀
⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⣾⡆⣻⣿⠿⣃⣠⢼⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠉⣾⣿⣿⣿⣿
⠀⣾⠿⣿⠿⣷⠀⠀⠀⠀⣾⣿⣿⡞⠛⠒⠛⢽⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠛⠼⢦
⠀⡏⠀⣿⠀⢹⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⣤⣀
⢠⣿⣿⣿⣽⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⡿⢷⣦⣀
⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⣴⣶⣯⣽⣹⣽⣷⣶⣤⡀⠀⠀⠀⠀⠀⢀⠋⠂
⢸⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⢀⣸⣟⠛⠟⠛⠁⠀⠀⠀⠈⢹⠟⠛⠻⡟⠛⠛⢿⠉⠀⠀⠀⠀⠀⢀⠂⠘⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⡤⠤⠀⢻⣿⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡆⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢙⣛⣛⣛⣛⢹⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣇⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⣿⣿⣿⣿⢘⣛⣛⣛⢘⣛⣛⣛⡃⣛⣻⣿⢟⣫⣭⣾⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢼⣿⣿⣿⡇⣿⣿⣿⡟⣾⣿⣿⣿⡇⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⣶⣶⣶⣾⡇⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⢾⣿⣿⣿⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣘⣛⣛⣛⣃⣛⣛⡛⣛⣃⣛⡛⠸⣿⣮⡥⣿⢮⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠃⣙⣛⣛⡁⠀⠘⣿⡇⣿⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⠀⢸⡇⠿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⠍⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⠖⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⠋⠀⠀⠀⠀⠀⠰⢿⣿⡿⠃⠀⠀⠀⠀⠴⠟⠛⣿⣿⡿⠋⠀⠀⠀⠀⣾⣿⣯⡴
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠀⢹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣥⠀⠀⠀⠀⠀⠀⢀⣼⣏⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠆⠀⠀⠀⠀⠀⠸⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⢩⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⠀⠀⠀⠀⠀⠀⣰⠿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡤⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⢟⡻⢻⣻⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢰⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠗⣀⣈⣁⣀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⣠⣾⣿⣿⣿⣿⣷⣄⠰⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⣿⣿⣿⣿⡆⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⣼⣿⣿⣿⢸⣿⣿⣿⣷⢸⣿⣿⣿⢸⣿⣿⣿⡸⣿⣿⣿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⢃⣛⣛⣛⡛⣘⣛⣛⣛⣛⢘⣛⣛⣛⡃⣛⣛⣛⣃⠻⠟⠁⠘⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣸⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⡆⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⡃⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⡉⣛⣛⣛⣛⡈⣛⣛⣛⣛⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢸⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣧⢻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⡋⣛⣛⣛⣛⣛⢉⣛⣛⣛⣛⣛⡃⣛⣛⣛⣛⣛⡘⣛⣛⣛⣛⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣈⣁⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⣴⠞⠛⠉⠉⠛⠳⣦⡀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠦⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠴⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠀⠀⠀⠈⣿⠉⠁⠀⠀⠀⠀⠀⠀⣿⠁⠁⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⣦⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠂⠀⠂⠀⠀⠐⠰⠐⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠄⡠⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠉⢀⣄⡴⠀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⠀⠌⠀⠀⠀⢠⡄⠀⠀⠓⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠂⠔⠀⢄⡂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠈⠓⠀⢀⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⡀⠉⠢⢄⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠐⠆⠀⠀⠀⠀⠑⢄⠀⠰⡄⠒⠀⠏⢂⢸⡤⢢⡀⠀⠀⡠⠄⣀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠑⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠑⠦⠀⣴⢊⠔⢁⡼⡤⠊⢀⠤⢀⠈⠁⠒⢠⣤⡄⠀⠰⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣈⡁⢡⢁⡎⢠⢋⠜⠀⠀⡇⠀⢈⠀⠀⡰⢿⠞⠉⠐⠤⡇⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠰⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠠⢧⠂⢀⢀⡀⠈⠀⠈⢀⡞⡷⠃⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠐⠂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⢣⠎⡜⡱⠀⢠⠛⠟⠀⠀⢀⣀⣀⣀⣀⡀⠀⠉⠢⡀⠀⠃⠀⠀⠄⠘⠤⠀⠀⠁⢀⠤⠠⠠⠄
⠀⠀⠀⠇⠆⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠂⢀⢡⠇⡞⡐⠀⢠⠿⠏⠀⣠⣾⠟⠓⠋⠙⠚⠿⣳⣄⠀⠈⠢⡄⠀⠀⠈⠐⠀⠀⠀⠀⠀⠁⠁⠐⠄
⠀⠀⠀⠀⠀⡀⠤⠤⠴⠀⠤⡁⠴⢲⠤⣀⡘⠀⢈⡜⢸⢡⠁⢀⢿⡟⠀⣮⠟⠠⠂⠁⠀⠀⠀⠀⠈⢻⣥⠀⠀⠈⢆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠂
⠀⠀⢖⠈⠁⠀⠀⡄⠒⠒⠓⠈⠇⡏⢰⠃⠁⠀⠀⠀⠉⠂⠀⣼⣶⠀⢨⡟⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⣟⡆⠀⠀⠀⠱⡀
⠀⠀⠀⠁⠢⢄⣀⡀⠁⣐⣂⠴⠀⡇⢸⠰⠀⠀⢀⠀⠀⠀⢀⣧⡄⠀⠘⣣⠀⢄⠀⠰⠆⠀⠒⠀⠀⠀⠿⠇⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠠⠔⠇⠧⠘⠺⠀⠰⠁⠈⠂⠀⢸⣭⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⠐⠀⢈⢼⠟⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⠐⠁⠀⢸⣹⠀⠀⠀⠀⠙⠛⣶⣤⡤⣤⣤⡰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⠄⡀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠦⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠐⠂⠁
⠠⠀⡌⠀⠀⢀⢀⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰⠄⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠰⠀⠀⠀⡀⠉⠀⠀⠀⠈⠐⠂⠀⠠⠤⠄⠀⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡔⠁⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠑⠀⠉⠉⠉⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠤⠄⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠑⠢⠄⣀⣀⠠⠔⠊⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠘⢄⠀⠀⠀⢀⠔⠁⠈⠉⠁⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡰⢁⣾⣿⡿⢁⣿⣿⡟⢘⣿⣿⣇⢹⣿⣿⣇⠻⣿⣿⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣼⣿⡿⢃⣿⣿⣿⢈⣿⣿⣟⠘⣿⣿⣏⠹⣿⣿⣆⠳⡄
⠀⢠⠊⣰⣿⣿⡟⢁⣾⣿⣿⠇⢸⣿⣿⣷⠀⣿⣿⣿⡆⠹⣿⣿⣦⡘⢆⠀⠀⠀⠀⠀⢀⠞⣠⣾⣿⡿⠁⣾⣿⣿⡇⢰⣿⣿⣿⠀⢿⣿⣿⣆⠙⣿⣿⣷⡈⢢
⣴⣡⣾⣿⣿⣿⣤⣾⣿⣿⣿⣤⣼⣿⣿⣿⣤⣼⣿⣿⣿⣤⣽⣿⣿⣿⣦⣱⠄⠀⠀⣴⣥⣾⣿⣿⣿⣥⣼⣿⣿⣿⣤⣼⣿⣿⣿⣤⣼⣿⣿⣿⣦⣼⣿⣿⣿⣦⣱
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣧⣠⡤⠤⣠⣤⣤⡠⠤⣤⣤⣤⡤⠤⣤⣤⣤⡤⠤⣧⣤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣬⣤⣤⣤⣤⣤⣤⣤⣤⠎⢠⣼⣿⣿⡿⠁⣼⣿⣿⣿⡇⢠⣿⣿⣿⣯⠀⣿⣿⣿⣿⡄⠹⣿⣿⣿⣤⠈⢢⣤⣤⣤⣤⣤⣬⣤
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠟⢁⣰⣿⣿⣿⡿⠁⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣷⡀⠘⣿⣿⣿⣷⣀⠙⢏⠙⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⣾⣿⣿⣿⡿⠁⢰⣿⣿⣿⣿⡏⠀⢼⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣦⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣄⣤⣤⣤⣄⣄⣀⣤⣤⣤⣤⣀⣤⣤⣤⣤⣅⣠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⡤⣤⡶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠉⠁⠀⠀⠉⠉⠀⠀⠾⠿⡟⠛⠓⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⢀⣤⣦⣄⠀⠀⠀⠀⠀⠀⡀⠀⢤⣤⣀⣠⣀⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠁⠀⠀⠀⠀⢸⣟⣻⣿⠇⠀⠀⠀⠀⠀⡀⠀⠈⠛⠻⣿⣷⣷⡌⢻⣯⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⢨⣶⠿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⡆⠁⠿⠊⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠖⠃⣽⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡤⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⡎⢷⡀
⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⠀⠀⠀⢺⣿⡗⠀⠀⠀⣼⣽⣶⣶⡄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⡁
⠀⠀⠀⠀⠀⠀⢸⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠿⠿⠿⠽⠏⠀⠀⠀⢤⡟⣿⣿⣮⡻⡆⠀⠀⠀⠀⠈⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⠿⠐⠀⠀⠀⠀⠀⠀⡄⢻⣿⣿⡇⣷
⠀⠀⠀⠀⠀⠀⢸⡁⠂⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⢿⣷⠞⠀⠈⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⣿⣿⣿⣿⢹⠇
⠀⠀⠀⠀⠀⠀⠘⣇⣄⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⠿⠟⣩⡾
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠃⠀⠘⢿⣿⣿⣿⣾⠀⠀⠀⠀⣟⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⡀⠂⢾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡄⠈⠛⠿⢿⣿⠧⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⣿⣿⠀⠀⡀⠈⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡔⠁⢠⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠛⠛⢯⡿⠏⠀⠀⣀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣔⠀⠙⠻⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠠⣿⣿⣤⣴⣶⣶⠦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠆⢀⠈⠛⠿⠿⠿⠛⠃⠀⠀⢀⠀⣡⣼⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠥⠴⠦⢶⣿⣿⡿⠿⠷⠞⠛⠉⠁

⠀⠀⠀⠀⠀⣴⣷⣷⠇⠀⠀⠀⠀⢀⣾⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣰⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⡗
⠀⠀⠀⠀⢠⣿⣿⠏⠀⣀⡀⠀⢀⣾⣿⣁⣠⣤⣤⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠀⣾⣿⣿⣾⣿⠏⠀⠀⡼⠿⠟⠛⣻⡿⠁⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⣷⡟⠀⠀⠀⣸⣿⣿⠃⠀⣀⡀
⠀⠀⠀⠸⠛⠋⣹⣿⠏⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⢀⣼⣿⣿⣷⣶⠖⠀⠀⠘⢉⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣾⣿⠏
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢀⣾⣋⣤⡤⣤⠀⠀⠛⠛⢹⣿⣿⠋⠀⠀⠀⠀⣾⣿⣿⡤⠀⠀⠀⢸⡿⠟⢩⡿⠃
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡴⠁⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠘⠋⣿⠟⠁⠀⠀⠀⠈⠀⢠⡟⠁
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠃