Tongue Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠲⢦⣄⣀⡀⠀⠀⣀⣠⡴⠶⠛⠻⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⢀⠀⠁⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣠⡤⣀⠈⠶⢤⣀⡀⠀⠀⠀⢀⣀⣤⡶⠂⠶⠶⢁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⠖⠋⠘⠃⠀⠀⡀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠈⢦⠊⠀⢢⡝⠢⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣠⣾⣿⣦⣤⣦⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⣄⣨⣦⡀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣤⣤⣤⣤⣴⣦⣤⣤⣤⣴⣾⣶⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢻⣿⣿⡿⠋⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠻⣿⣿⡟⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⡏⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡇⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠤⠤⠤⠶⠖⠚⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⠉⠛⠦⣤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢺⠗⠛⠲⣄⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⢀⣠⡴⠚⠉⢰⠏⠀⡀⠀⠘⢿⡏⠁⠀⠀⠀⠀⢀⡏⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⢸⠳⢤⣄⣀⡟⠀⠀⢻⠀⠀⠘⢿⣶⣤⣤⣄⣀⣼⡁⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠸⡆⠀⠈⠻⣇⠀⠀⠈⢧⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣿⣿⣄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠳⢦⣄⡈⢧⡀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠿⠿⣿⣿⣿⣦⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠙⠳⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣄⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣹⣿⡿⠿⠒⠒⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠙⠓⠲⠦⠤⠴⠞⠋⠉⠉⠙⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⢶⡶⠶⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣀⣤⡖⠋⠉⠙⡇⠀⠀⠀⠘⡇⠀⠀⠀⢸⠋⠉⠙⢲⣤⣀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣴⠋⠁⠀⣇⠀⠀⠀⣧⣀⣀⣀⣴⣧⣀⣀⣀⣼⠀⠀⠀⡸⠀⠈⠙⣦⡀⠀⠀⠹⡄
⠀⠀⠀⠀⢠⠏⠀⢀⣴⠋⠈⡄⠀⣠⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⣀⠀⢠⠁⠙⣦⡀⠀⠹⡄
⠀⠀⠀⠀⡾⠀⢠⢏⠀⢆⣠⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣷⣄⡰⠀⡿⡄⠀⢷
⠀⠀⠀⠀⡇⢠⣏⢦⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⣹⡄⢸
⠀⠀⠀⠀⣇⠈⠻⣿⠻⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⡟⣿⠟⠀⣸
⠀⠀⠀⠀⢹⡀⠀⠈⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠳⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠙⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠦⠶⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠾⠿⠶⢶⣤⣤⣀⣠⣤⣴⣶⠶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠍⠉⠉⠉⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⢶⡿⠛⠻⠶⢶⣦⣤⣤⣤⡶⠶⠶⠶⣶⢶⣤⡀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣁⣐⣀⣀⣤⣤⣴⣶⣿⣯⣄⣀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣯⣀⣈⣉⣳⣦⣤⣀⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣠⣿⣤⣀⣀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⡿⠋⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠘⣿⣿⣿⣿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠙⠒⠤⣀⠀⢀⡠⠔⠒⠉⠉⠑⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀
⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀
⣠⣖⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠔⠒⠉⠀⢸⠀⠉⠑⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣈⣑⣦
⠘⣟⢿⣿⣿⣿⣿⣭⣭⣉⣹⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣸⣭⣭⣽⣿⣿⣿⣿⠟⣡⠋
⠀⠈⢆⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣶⣤⣤⣤⣤⣼⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡴⠁
⠀⠀⠈⢆⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⠞
⠀⠀⠀⠈⢧⠀⠀⠈⠻⣿⣿⣿⠿⠛⠋⠉⠉⠙⠻⣿⠿⠛⠋⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⡿⠋⠀⠀⣠⠋
⠀⠀⠀⠀⠈⢣⠀⠀⠀⢈⠟⠁⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣽⠟⠁⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⢣⡀⢠⠏⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⢁⠔⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠳⡎⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡴⠋⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠋⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠔⠚⠉
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠘⠦⣀⡀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋
⣤⣤⣤⣤⣤⣤⣤⣭⣿⣶⣶⣶⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠈⠻⣦⠀⣠⡶⠛⠉⠁⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣠⡴⠞⠛⠛⠳⢦⣀⠀⠀⢀⣠⣤⠶⠞⠛⠶⢦⣀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⣀⣴⣿⣏⣀⣠⡄⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⣀⡴⠟⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣠⣶⣄⠀⠀⠀⢀⣴⠶⣤⣀⣹⣆⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠈⠻⣄⠀⢺⣿⣿⣿⣿⣿⠿⠋⠁⠀⠈⠉⢉⣿⠟⠋⠉⠛⠛⠛⠋⠁⠀⠀⠉⠉⠙⠳⢦⣤⡄⠀⠀⠀⣹⡗
⠀⠀⠀⠀⠀⠙⢧⡀⠹⣿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠈⢷⣤⠟⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣰⠏
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣰⠏
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣰⠏
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠋
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣠⡞⠁
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⣴⠞⠁
⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠚⠉
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⡀⠀⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠉⠀⠉⠓⢤⡴⠋⠁⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣠⡤⠤⣄⣀⣀⣤⠤⣤⣀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣠⠴⠋⢹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡏⠓⢦⣀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⢀⣠⣴⣋⣡⣤⣶⣾⣯⣀⣀⣀⣼⡀⠀⠀⠀⣸⡇⠀⠀⢀⣀⣧⣀⣀⣈⣽⣶⣦⣤⣈⣓⣤⣀⡀
⠀⠀⠀⠀⠀⠻⣍⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⣽⡟
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠙⠿⣿⣿⠿⠟⠛⠛⠛⠛⠻⢿⡿⠛⠛⠛⠛⠿⣿⣿⣿⣿⡿⠋⠁⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢿⠉⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣶⣶⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⢶⣄⣀⣤⠶⠛⠛⠛⠳⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀
⠀⠀⠀⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣄⡀
⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤
⢿⠷⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠾⠷⠶⣴⠾⠿⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠖⢻
⠸⣇⠀⠀⠉⠻⣿⣍⡉⡉⡉⣹⡇⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠉⠉⣿⡛⠛⠛⠛⢛⣿⣭⣭⣭⣽⢇⣴⠟⠁⠀⠀⣾
⠀⢻⡄⠀⠀⠀⠈⣻⡽⠟⠋⠉⠛⠶⠶⠶⠶⣿⠟⠳⠶⠶⠶⠶⠾⠋⠙⠛⠻⢿⣋⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⢰⡏
⠀⠀⢿⡀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⣤⠞⠋⠀⠀⠀⠀⢀⡿
⠀⠀⠈⢷⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠞⠋
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⠟⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠠⣿⡷⠶⠶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⠟⠛⠉⠁⠀⠀⠀⠈⠙⠻⢷⣦⡀
⠀⠀⠀⠀⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⢻⡏⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠘⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠙⠛⢻⡿⠛⠛⠛⠛⠛⢻⣿⠷⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀
⠀⠀⠀⠀⠀⢻⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠉⠛⣿⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠘⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣧⣀⣀⠀⠀⣸⣿⣄⣈⠙⠛⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⠻⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠛⠉⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡿⠛⠉⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠾⠟⠋⠁⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣁⣀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠔⡃⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠉⡱⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰
⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠖⠀⠀⠀⠀⠀⠄⢢⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⡁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⣿⣿⣿⡇⢀⣀⣀⣀⠀⠀⣀⣀⣄⠀⠉
⠀⠀⠀⠀⠀⣠⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⠀⠀⢰⣿⣿⣿⣿⢠⣿⣿⡿⡿⠀⠀⠀⢀⣴⠿⠂
⠀⠀⠀⠀⠀⣿⠿⠀⢿⣿⣿⣤⣤⣀⠀⠀⣿⣿⡇⢸⣿⣿⣶⣿⣿⣿⠇⣿⣿⣷⠆⢻⣿⣿⡁⠀⠈⢿⣿⣶⣤⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⢀⠈⠉⢹⣿⣿⣷⡀⣿⣿⡇⢸⣿⣿⢿⣿⡏⠁⠀⣿⣿⡇⠀⠀⠙⢿⣿⣶⡄⠀⠉⠉⠛⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⣿⠃⣿⣿⡇⢸⣿⣿⠘⣿⣿⡄⠀⣿⣿⣷⣶⣶⡄⠈⢿⣿⣿⣠⣶⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠙⢿⡇⢸⣿⣿⠀⠸⣿⣿⣦⣈⣉⣉⣉⣉⣁⣤⣿⣿⣿⢻⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠦⣤
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠘⠙⡀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣶⣶⡶⠀⠀⢀⠄⠀⡤⠀⠀⠀⠀⠀⠀⠀⣸⣤⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠁⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⣽⡿⠇⠀⠀⠀⠀⡀⠀⠀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠒⠒⠋⠉⠉⠉⠉⠉⠉⠓⠒⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡆⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡤⠤⠖⠋⠁⠀⠀⠹⣄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡞⠀⣀⡀⠀⠀⠀⢀⣀⠈⢧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡤⡼⠁⢛⣛⠛⢦⠀⠀⠘⣛⠛⢺⡠⢤⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⢻⠀⠀⠁⠀⢸⠀⠀⠀⠈⠀⢸⠁⣸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⠛⣆⠀⠀⠀⠙⠒⠀⠀⠀⠀⢸⠗⠃⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣠⠼⢆⠀⠀⠀⠛⠀⠀⠀⣠⠯⣀⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⢷⡚⠉⠀⠀⠀⠙⠦⣤⣤⣤⠴⠚⠁⠀⠀⠉⢓⡶⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠉⠓⠦⢤⣀⣀⡤⣤⣤⡤⣤⣀⣀⡠⠴⠚⠉⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢳⡘⣞⢷⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⣣⡑⣌⢢⠳⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⡄⠀⠀⡞⠀⠀⠹⣝⠎⠀⠀⠀⠘⡆⠀⠀⢀⡄⠀⠀⠀⠀⠀⢧
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡼⠀⡠⢼⣁⠀⠀⣠⠼⠓⢤⡀⠀⠀⣹⠤⡀⠀⢧⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢠⡷⠊⠀⠀⠈⠙⡿⠀⠀⠀⠀⠸⣟⠉⠀⠀⠈⠲⣜⡆⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢣⡀⠀⠀⣀⠴⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⢤⣀⠀⠀⣠⠇⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⣧⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⣤⠤⠤⣼⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠤⠴⠧⣤⠤⠧⢤⡿⣧⡤⠼⠤⠤⢤⡿⠤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⡏⠀⠀⢸⡇⢸⠀⠀⠀⠀⠈⣇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⢸⠁⠀⠀⡼⠁⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠸⡄⠀⠀⣇⠀⠀⠀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢾⣀⢀⡼⠁⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠙⣆⣀⣹⠤⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣒⣒⣠⣼⣧⣼⣤⣤⣤⣀⣒⣒⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣶⡶⠀⠀⠀⠀⣰⣶⢄⠀⠀⠀⢠⣶⡀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⣠⣶⢆⡀⠀⠀⠀⣴⣦⡀
⠀⠀⢰⣿⣿⡆⠀⠀⢰⣿⣿⠚⠂⠀⠀⣿⣿⠛⠂⠀⠀⣾⣿⡟⠃⠀⠀⢺⣿⣿⠓⠀⠀⠀⠿⣿⡿⠃⠀⠀⢸⣿⣿⠛
⠀⠀⢻⣿⣿⡗⠀⠀⢀⣿⣿⡄⠀⠀⢸⣿⣿⡆⠀⠀⠀⣿⣿⣇⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⣸⣿⣧⠀⠀⠀⢼⣿⣿⡀
⠀⠀⠈⣿⣿⠁⠀⠀⠈⣿⣿⠁⠀⠀⠀⢹⣿⠁⠀⠀⠀⢹⣿⡏⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠩⣿⡏⠀⠀⠀⠈⣿⣿⠁
⠀⠀⠀⠛⠛⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣤⡀
⠀⠀⠀⣴⣯⡿⠃⠀⠀⣿⣯⡀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣯⡀⠀⠀⠀⣼⣿⡅⠀⠀⢸⣿⣧
⠀⠀⢀⣿⣿⢧⡀⠀⠀⢳⣿⠁⠀⠀⣠⣾⣿⡀⠀⠀⢀⣤⣤⣾⣿⣶⠀⠀⣸⣿⡏⠙⠦⠀⠀⣿⣿⡇⠀⠀⢸⣿⣟
⠀⠀⠛⢻⡇⠀⠀⠀⠀⢿⡿⣆⠀⠠⡿⠿⢿⡇⠀⠀⠺⠿⠿⣿⠁⠀⠀⠀⢻⡿⡇⠀⠀⠀⠘⣿⣿⠃⠀⠀⠺⣿⡿
⠀⠀⠀⠸⡇⠀⠀⠀⠠⡞⠁⢻⠄⠀⠃⠐⠌⡧⠀⠀⠘⠀⠐⠻⠀⠀⠀⠀⢸⠇⡷⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⡿⡇

⠀⠀⠀⣶⣦⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⣴⡦⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⢀⣴⣦⠀⠀⠀⢀⣾⣇
⠀⠀⢰⣿⣿⠇⠀⠀⢰⣿⡿⡇⠀⠀⠀⣼⣿⣿⠀⠀⠀⣞⣿⣿⣳⠄⠀⠀⣻⣿⣷⠀⠀⠀⠸⣿⣿⠇⠀⠀⠈⣿⣟
⠀⠀⢸⣿⣿⡄⠀⠀⢸⣿⣧⡙⠂⠀⠀⣿⣿⣏⠀⠀⠀⢨⣿⣿⡅⠀⠀⠈⣿⣿⡄⠀⠀⠀⢠⣿⣿⡄⠀⠀⢰⣿⣿⡄
⠀⠀⠀⣿⣿⠀⠀⠀⢈⡏⢹⡅⠀⠀⠀⢩⡏⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣾⠈⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠉⠉⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠉⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡤⠀⠤⠖⠀⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠑⠄⡀⠉⢉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠤⠀⠠⠤⠤⠤⠤⠀⢀
⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠠⠄⠐⠂⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡆⠀⠀⠀⠀⠈⢀⡀⠠⠀⢂⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠐⠂⠆⡓⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠼⠤⠄⠀⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠄⠀⠀⠀⠀⠀⡀⠼⠄⠈⠁⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⢊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠒⠈⠀⠀⠠⠀⠀⠁⠀⠄⠀⣀⠀⠀⠀⠐⠆⠤⠀⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠢
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠒⠲⢼
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡇⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣷⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠤⣀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠞⠚⠀⠋⠛⠋⠁⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠳⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠔⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⢹⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠇⠀⠀⢠⣿⠆⢸⠋⠉⠊⠀⠀⠀⠀⠈⠙⠲⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠀⢸⡿⢀⠜⠀⠀⠀⠀⣀⠀⣀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣥⣤⣤⡼⢿⣷⣦⡤⠤⠔⠊⢉⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠟⠁⡾⠵⠜⠓⢀⢘⠐⢢⡟⡆⣀⣀⠴⡅⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠒⡞⠺⠶⠷⠯⠴⠿⠶⠖⠛⠉⡎⠉⠀⠀⠀⠙⣄⠀⣀⠤⠒⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠈⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠕⠀⠀⡠⠊⠈⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠄⣈⠷⣀⣀⠀⠀⠀⠀⣀⣴⡊⠥⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣖⡀⣀⣄⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢀⡀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣼⡿⢀⡇⠀⣼⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣟⣿⡇⠈⠀⠀⣿⣿⣿⣻⣿⡆
⠀⠀⠀⠀⣸⡄⠀⠸⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⡟⢢⢀⠀⢀⣠⣤⣠⣀⠀⡤⠘⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠄⢠⣿⣿⣿⣿⣿⣿⢿⡇
⠀⠀⢀⣸⣷⣾⣸⣦⣾⣿⣿⣿⣿⡄⡀⠀⠀⠀⢠⣄⠀⠀⠐⠂⠤⢀⢸⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠰⣚⣛⣙⣿⣻⣿⠿⢿⣥⣌⣉⠹⣿⣟⢲⣀⣀⠠⠙⠿⣦⡄⠀⠀⠀⠸⣿⣿⣧⣣⡿⠿⠛⠛⠛⠛⠿⣿⣿⣧
⠀⣿⠉⡭⠩⣿⣿⣴⣾⠿⢿⣿⣿⣿⣿⣿⠟⠻⢶⡗⢦⣼⣿⡆⠀⠀⠀⢹⣿⣿⣿⠀⣠⣤⠆⠲⣴⣤⣄⣘⣻
⢨⣿⠀⠃⠀⠈⠙⠋⢁⡀⠀⣸⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⠀⢸⣿⣿⣿⣾⠋⠀⠀⢰⣿⣿⢿⡿⠿
⢸⣿⠀⠒⠀⢀⡒⠀⠒⠀⠀⢻⠒⠒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣇⠀⢀⠄⣾⣿⣿⣾⣿⣿
⢸⣿⠀⠀⠀⠘⠂⠀⠀⠀⠀⣾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⢻⣄⡌⠀⣿⣿⣿⣿⣿⣿
⡿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⡂⠂⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⠀⠀⢸⣿⣿⣿⣿⣿⣳⣠⣿⣿⣿⣿⣿⣿
⠘⡿⠀⠁⠀⢠⠄⠀⠀⠀⠀⢼⠅⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠺⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡿
⢸⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⡃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠸⣿⣿⣿⣷⣶⣶⣶⣿⣩⣭⣽⣿⣿
⢸⣿⠀⢀⣀⣁⣀⣀⣀⣀⣠⣿⣍⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣿
⠸⣿⣀⣻⣿⣿⣿⣿⣿⣿⣟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⣿⣿⣟
⠀⠉⠛⠛⠻⠿⠿⠿⠿⣿⠯⢤⣤⣼⣿⣿⣿⣿⣿⣛⣯⣭⣿⣿⣿⣿⣶⣿⣿⡿⢿⣿⣿⣿⡿⢿⠿⣯⣿⡉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣬⣭⣭⣿⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣤⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⡤⠴⠶⠶⠞⠛⠛⠛⠋⠉⠉⠉⢻⡆
⠀⠀⣸⠋⠀⠀⠀⠈⠙⠛⠻⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⠇
⠀⠀⠸⢦⡀⠀⠀⠀⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠈⠉⠃⠀⠀⠀⢻⡆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣉⣉⠉⠀⢀⣀⣀⣀⡀⠀⢀⣾⠃
⠀⠀⠀⠀⣾⠀⠀⢰⡖⠒⠒⠒⠲⣶⠶⠒⠒⠒⠶⣦⠤⠤⠤⠤⢶⣶⠶⠶⠒⠲⣞⠋⠉⠉⢹⡏⠉⠉⠀⠈⣷⡾⠟⠁
⠀⠀⠀⠀⠙⠶⠶⢾⡇⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⢿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⢻⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⢀⣽⡀⠀⠈⠀⠀⣸⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⣧⡀⠀⢀⣼⣷⣤⣤⠾⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠙⢿⠟⠶⠶⠶⠚⢿⣷⡶⠶⠶⢾⡿⠶⠶⠶⠒⠛⣿⠛⠛⠛⠙⣿⢀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⣀⣠⡗⠀⠄⡀⠀⢸⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠆⠀⠘⡿⠛⢷⡄
⠀⠀⠀⠀⠀⢸⠋⠉⢿⣀⣀⣀⣀⣼⡀⠀⠀⢀⣀⣠⣿⡀⠀⠀⠀⣇⡀⠈⠀⠀⢀⣸⣆⣀⠀⢀⣸⣀⣀⣀⡴⠃⠀⠈⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠙⠛⠛⠋⠉⠉⠓⠒⠛⠉⠀⠀⠉⠉⠉⠁⠉⠉⠁⣀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠛⠛⠛⠒⠶⠦⢤⣄⣀⣀⣀⣠⠴⣄⠀⠀⠀⠀⠀⠀⠰⠛⠳⣄⢀⣠⠴⠒⠖⠛⠁⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠘⠻⠶⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠘⠲⠋⠀⠰⣤⠆⠀⠀⠉⠉⠁⠀⢀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠷⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣙⣫⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⡉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⣤⠀⠀⠀⠀⠀⠶⠒⡆⠀⠀⠀⠀⠀⡀⢀⢄⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠛⠀⠓⠀⠈⠉⠉⠀⢸⣶⡇⠀⠀⠀⠀⠐⠀⠉⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣄⡄⢦⠀⣀⣀⣀⠀⢸⣿⡇⢀⣀⣀⣀⢠⣀⠐⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠁⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⡄⠶⠀⢀⣀⣀⠀⢸⣿⡇⢀⣀⡀⡀⢀⣦⣠⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠈⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠁⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠐⠢⠀⠀⠀⠀⡇⠀⣈⢄⣉⠀⠀⠠⠤⠀⢸⣿⡇⠠⠤⠤⠄⠀⣉⢆⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣜⠂⠀⠤⠤⠤⠀⢸⣿⡇⠠⠤⠄⠄⠀⠰⣘⠆⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠁⠀⠀⠈⠉⠲⣄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡄⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢲⣶⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⣆⡹⠀⠒⠒⠒⠀⢸⣿⡇⠐⠒⠒⠒⠀⠀⣈⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠇⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠱⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⢔⡂⠁⠀⠀⠀⡇⠀⠰⠢⠟⠀⠚⠒⠒⠀⢸⣿⡇⠀⠐⠀⠀⠀⠀⠐⠿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠆⠰⠆⠀⠀⠀⣥⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣴⠀⠀⠀⠀⣾⠁⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠌⠀⠀⠀⣼⠃⠀⢡⠀⠀⠀⡇⠀⠀⡀⢀⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡀⢀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠐⠒⣤⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠸⠀⠀⠀⡇⠈⠐⠂⠈⠁⠉⠉⠉⠀⢸⣿⡇⠈⠉⠉⠉⠈⠀⠒⠘⠃⢰
⠀⠀⠀⠀⠀⠀⠓⠐⣌⠳⣝⠷⡩⢔⡒⠤⠄⣀⣀⠀⡁⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠳⣝⠢⡉⠲⢄⡀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠈⠑⢮⡢⡀⠀⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣦⣏⣹⣿⣿⣿⣳⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡢⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣾⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⡳⣄⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢞⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣳⣄⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠐⣂⣀⣻⣏⣴⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣷⣆⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⣀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⢻⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢎⡵⣻⣣⡏⣩⢻⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⢳⣿⡟⣿⣿⣾⣿⣿⣿⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⢿⢸⣿⠷⠛⠿⠿⠛⠙⣿⠇⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠜⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠉⠉⠉⠉⠉⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠿⠳⠄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢤⡆⠠⠒⠋⠀⠀⡌⢧⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠐⠦⢤⣄⣀⣀⠀⠀⡀⠀⣀⠴⠃
⠀⠀⣀⠀⠠⠶⣯⡀⠃⠀⠀⠀⠀⠀⢳⠀⠀⢀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⡤⠞⠁
⢠⠏⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠐⣄⠀⠠⠚⠈⢷⡀⡆⠀⠠⠤⠒⠚⠉⠁
⣷⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⢻⡁
⠘⣆⠀⠀⠀⠀⠀⠀⠀⢹⡜⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⣷⡀
⠀⢹⢧⡀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⢻⣀⣀⣀⣠⡴⠋⢷⡀
⠀⠈⠃⠱⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⡏⠉⠉⠁⠀⠀⠈⣷
⠀⠀⣾⠛⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹
⣀⣀⣘⣂⣑⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣔⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⠿⠛⠉⠉⠳⠦⣤⠴⠚⠉⠮⢭⣛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⣀⣤⣵⣦⣀⡀⠀⢀⣴⣥⡤⢤⣤⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⣤⡾⠛⠉⠀⠀⠈⠉⠉⠛⠉⠉⠀⣀⢀⣼⣿⣿⡷⣾⡆
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠳⣶⣶⣿⣿⣦⣠⣾⠶⠶⠶⢶⣶⣶⣶⣿⣿⣿⣿⣿⠋⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⠟⠋⠉⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠉⠻⣅⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠘⢧⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠈⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⣀⡀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣛⡛⢿⣛⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣻⣿⣟⣛⣛⣛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⣥⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡍⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⢃⣦⣙⢻⣿⣿⣿⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⡿⢋⣾⣿⣿⣦⠹⣿⣿⡿⢿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⢋⣴⣿⣿⣿⣿⣿⡇⣿⢁⣶⣶⡈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇⣼⣿⣿⠇⣈⢻⣿⣿⣿⢸⡇⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣧⠹⣿⢡⣾⣿⡆⣿⣿⣿⢸⡇⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢘⣿⣿⣦⣍⠈⠻⠟⠁⣋⣴⣿⢸⡇⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣸⡇⢸⣇⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣙⠛⠛⠛⠛⠛⠛⢻⣿⢃⣾⢋⣤⣦⡙⢷⡀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣾⣿⣿⠇⣼⠃⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠞⠁⠀⠸⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇



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

⠀⠀⠀⠀⠀⠀⡞⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠙⡆
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠃⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠙⢦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠞⠁⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡎⠀⠀⠀⠘⠋⠉⠳⡄⠀⢀⣀⣀⠀⠀⣀⣀⡀⠀⡴⠋⠉⠙⠀⠀⠀⠀⣆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⢀⡾⡇⠀⠀⣠⣦⠀⠀⠀⠹⡞⠉⠀⠈⢳⠏⠁⠀⠙⠾⠁⠀⠀⢀⣦⣀⠀⠀⣻⣆⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⡼⠀⠳⠖⠋⠁⠸⡄⠀⠀⢀⣦⠀⠀⠀⣠⡀⠀⠀⢀⣆⠀⠀⠀⣸⠁⠈⠓⠶⠃⠸⡄⠀⢸
⠀⠀⠀⠀⠀⠸⡇⣸⠃⡀⠀⠀⠀⠀⠀⠙⠦⠖⠋⠈⠳⠴⠚⠁⠙⠲⠴⠋⠈⠓⠦⠞⠁⠀⠀⠀⠀⠀⡀⢳⡀⡿
⠀⠀⠀⠀⠀⠀⣧⡏⠀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⠈⣧⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠳⡄⠀⢀⣠⡤⠤⠴⠶⠖⠒⠒⠶⠦⠤⠤⣄⣀⠀⠀⣰⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠙⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡞⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⣿⠉⠙⢲⡤⠴⠤⣄⡤⠴⠤⣤⠚⠉⢉⣟⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠈⠳⠤⠔⠲⢤⡤⠞⠦⣤⠴⠒⠦⠤⠋⠈⠛⠚⠋⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠉⠁⠑⢦⠈⠹⡕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠈⣿⠄⠀⣼⡏⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠐⠲⢤⠤⠲⢄⠴⠚⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣤⠠⠤⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡠⠤⠀⠒⠀⠀⠀⠁⠒⠒⠒⠂⠀⠀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡏⠒⠶⠤⠤⠤⠤⠤⠄⠠⠀⠀⠒⡈⣇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠉⠓⠲⠶⠶⠶⠶⠂⠁⠀⡼⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⢓⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⠤⠒⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣨⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢁⣄⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡼⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡿⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣠⠁⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⡄⠀⠀⠀⠀⢱⠈⠳⢄⡀⠀⠀⠀⠀⠀⣀⡀⠈⠁⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢫⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠀⢠⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠠⠇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠰⠷⠂⠀⠘⠀⠀⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢀⠃⠀⠀⢀⢤⡀⢤⡖⠚⢀⠉⡆⠉
⠀⠀⠀⠀⠀⡎⠐⠐⠐⢀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⡸⠀⠀⠀⠀⠀⢧⡀⠀⡘⠀⠀⠀⢠⡀⠊⠄⣟⠡⠖⣂⢀⠀⠐⠢
⠀⠀⠀⢠⠴⠀⠀⠀⠀⠀⠑⠢⢤⣀⡈⠀⠃⢠⡄⠐⢀⡀⠤⠤⣼⡜⠀⠀⠀⠀⠀⠀⠀⠙⡀⣇⠄⠐⠒⠢⠉⠂⠁⠀⠀⠠⡅⣂⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠈⠀⠀⠁⠀⣈⠁⠒⠐⠒⠒⢀⣤⣈⣀⣈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠚⠛⠋⠁⠀⢠⣴⣄⣍⣥⣤⠄⠦⠝⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⣹⣿⣦⣄⠀⠀⠀⠀⠊⠀⠀⠀⢐⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⣠⣾⠟⠁⠉⠻⣷⡄⠀⠀⠀⠀⠀⠔⠋⠁
⠀⠀⠺⢷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⣠⣾⠟⠁⢀⣀⣀⡀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣆
⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣦⣄⣀⣴⣾⠟⠋⣠⣴⡿⠛⠁⠀⣴⡿⠛⠛⢿⣆⠀⢻⣇⠀⠀⠀⠀⠒⠒⠚⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣯⣤⣶⠿⠛⠉⠀⠀⠀⠀⣿⣇⠀⢀⣼⡿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣄⡀⠀⠀⠈⠛⠿⠿⠛⠁⠀⢸⣿⠀⠀⠀⠲⢤⣀⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠈⠋⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣬⣍⣉⣙⣛⣛⣛⣉⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠈⠉⠙⠛⠛⠛⠛⠛⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣤⡀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠠⢤⣀⠀⠀⢀⣠⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠒⠂⠀⠀⠨⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡠⠀⠀⠠⠠⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠰⣤⣴⠄⠀⠀⠀⠀⠀⠀⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠂⠒⠀⢠⠀⡀⠀⠀⠀⠀⠛⢄⠀⠀⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡆⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡄⠁⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⢾⣿⣿⣿⣧⠀⠀⠀⠠⡀⠀⠠⠤⠄⠈⠸⣿⣆⣰⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⢀⠀⠙⣿⣿⣿⡇⠀⠀⠀⣨⣤⠀⠀⢐⡁⡀⢻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⣀⡄⠀⠈⠉⠷⣦⣽⡁⠀⠐⠏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠠⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢾⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⣸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠶⠩⢷⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠤⠴⠒⠂⠀⡈⠀⢠⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠉⡩⠤⠜⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠸⣷⣶⣶⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠂⠀⠉⠉⠀⠑⠛⠃⠀⠀⠀⠙⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣄
⠀⠀⢀⣴⣶⣶⣮⠁⠀⠀⠀⠀⠀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣿⡆⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⢸⣷⣿⣿⠿⣦⡤⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠙⠋⠀⠀⠀⠀⠀⣠⡸⢿⡿⠃
⢀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠂⠀⡉⠀⠀⠀⠀⣿⣿⣷⣶⣦
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⡟⢸⣿⠀⠀⠀⠀⠀⠀⢀⣻⣿⣇⣽⣿⠀⠀⠁
⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠟⠀⠀⠀⠀⠀⠀⠛⠋⠀⠙⠟⠀⠀⠀⠀⠀⠀⠻⠿⠛⠋⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⠀⢠⡶⢸⣿⣿⠄
⠀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣭⣤⠀⠀⠀⠀⠀⠀⣠⣬⣭⣥⡀⠀⠀⠀⠀⢸⣧⣤⣭⣥⡄
⠀⠀⢠⣴⣮⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⣿⣿⣿⡇
⠀⢰⣿⣿⣿⣀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠠⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣠⣰⣿⣿⣿⣿⣷⣠⣀⠀⠀⠀⠀⠀⢸⣿⣻⣿⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⡇
⢠⣬⣭⣭⡙⣿⡆⠉⠋⠀⠀⠀⠀⠀⣾⣿⢹⣿⡟⠛⣻⣿⠛⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⣼⣿⣿⣿⣇⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣷⢠⣿⡏⠀⣿⡇⠀⠀⠀⠀⢸⣿⢾⣿⠀⠀⠀⠀⠀⠀⢸⣿⢼⣿⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⡇
⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢃⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣀
⠀⢀⣼⣿⣿⣥⡀⠀⠀⠀⠀⠀⢾⣥⣾⣿⣷⣬⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠸⣷⣦⣿⣶⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⡿
⠀⢸⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡅
⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠇
⠀⠀⣿⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿
⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⡿⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⡀⠀⡠⡀⠀⠤⠀⠤⠐⠁⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡁⠀⠛⠀⠀⠀⠰⠄⠀⡀⠴⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠠⡀⠀⠀⡀⢄⠀⢰⢏⣠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⠀⢀⠄⠀⢈⠱⠖⢓⠷⢖⣣⡀⡄⠀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⢐⡤⠐⠁⡠⠊⡡⠒⠉⠇⠀⠈⠄⠀⠈⢢⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣈⠉⠐⠺⡀⡌⠀⠀⠘⠓⠆⠀⠞⠀⠀⠀⢂⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⠐⡦⡈⠉⠀⠂⡄⠀⠰⠖⠬⠀⠀⠀⠈⡄⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢁⠈⢢⠀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⠀⠀⠀⠑⢌⠓⠓⠏⣐⠂⠠⠄⢀⣀⡀⠠⠜⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠠⡵⠂⠄⡀⠈⠁⠐⠒⠀⠀⠐⠒⠒⠀⠈⠉⢉⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠀⠀⠀⠀⠉⠁⠀⠐⠒⠒⠂⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡐⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠁

⠀⠀⠀⠀⣀⠤⠤⠤⠶⠶⠶⠶⠶⠦⠤⠤⠤⢤⣤⣀⡀
⠀⠀⠀⢰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣙⣛⠒⠶⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠈⠛⡮⢭⡵⣖⣒⣒⣒⣶⣶⣶⣒⣒⡯⡽⢶⠒⠒⠫⠭⠝⣛⣒⠶⠦⠭⣭⣍⣛⣛⣒⠲⠶⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠖⠚⢛⣧
⠀⠀⠀⣀⢀⠗⠘⠇⣰⣧⡆⠉⠉⠙⣦⠀⣗⠉⠙⢺⣤⠴⠖⠒⠶⠦⣄⡉⠉⠙⠒⠒⠢⠭⠭⢭⣉⣛⣛⡛⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⢉⡟
⠀⢠⠋⠀⠸⣄⠀⡼⠁⢀⠀⢀⠀⢰⣿⠀⠈⡀⠒⢬⡇⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠒⠶⠶⠦⠤⠤⢤⣤⣤⣤⣤⡤⠶⠋
⠀⢧⡀⠀⠀⠀⣿⡇⠀⠀⢸⡁⠀⠀⠉⠃⠈⢵⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⣸⠿⣶⣤⣤⡼⠿⣆⣀⣀⠽⢶⠀⠀⠀⢀⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⡿
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⢀⣠⠤⠊⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⣷⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡟
⠀⠀⠀⠘⠧⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠓⡆⠀⠀⠜⣀⣠⠤⣤⠶⠒⠋⠉⠉⠉⠉⠓⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠤⡄⢀⡸⠔⠒⢉⣡⠖⠛⠒⠒⠒⠒⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡠⠗⠛⢤⠴⠚⠉⡏⠀⢐⣁⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡮⠀⠀⠀⠙⣅⠀⠀⢻⣰⠋⠈⠹⣄⠀⠈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠸⣀⡶⢀⣠⣄⣵⠀⠀⠀⣿⠀⠀⠀⢹⡶⠋⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⠀⢋⣀⣸⣿⡆⠀⠀⣿⠀⠀⠀⠀⡷⠖⠉⠉⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⠞⣩⠥⣌⢻⠃⠀⠀⢹⡀⠀⠀⢀⡟⠒⠶⣏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠙⠀⠉⠃⠀⠀⣿⣿⣿⠁⠙⢿⣿⣿⣷⣄⠀⠀⠀⠙⠒⠤⣤⠙⠈⠀⠀⠀⠀⢙⠲⣾⡟⢡⡄⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⣠⠔⠲⠤⠼⢿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣷⣶⣤⣦⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠦⣄⡀⠀⠀⠀⡀⠀⠀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⠔⢛⣥⣤⠄⢀⣈⣶⠤⠴⠒⠏⠛⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⠴⡖⠲⣤⡀⠀⠀⠀⠀⠀⠀⠉⢹⠖⠶⠦⠤⠥⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠳⠤⠋⠸⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⣠⢺⠇⢸⠁⣠⡃⠉⠢⣄⠀⠄⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠳⠾⠔⠛⠉⠁⠈⠀⠀⠈⠋⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⢤⣴⣶⡞⠛⠉⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⡆⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡏
⠀⢀⡴⡺⢷⣛⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⢄⡀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢸⣿⣿⠁
⣠⢋⠊⠠⣶⣼⡇⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠏⠈⠉⠒⠢⠤⣄⣠⠞⠀⠀⣾⣿⣿
⡇⡞⠉⠉⠳⡽⡇⠇⠃⠀⢀⢀⠀⠀⠀⢀⡴⢋⡴⠁⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢹⣿⣿
⠳⣧⡀⠀⣰⠇⠙⢄⠀⠀⠀⢉⣹⠖⠒⠿⡴⢏⣀⡀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠸⣿⢿⣣⠤⡄
⠀⠀⠉⠉⠁⠀⠀⠀⠙⠒⠚⠉⠀⠀⢀⡞⠁⠀⠙⠩⠙⠂⠀⡝⠀⠀⠀⠀⠀⠀⠀⢠⢛⠊⠱⠯⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣗⡒⢦⣤⡤⣤⡶⢳⠞⠛⠓⣄⠀⠀⡠⠚⢹⠃⢠⣼⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⠿⢿⣶⡫⠤⠧⣤⣤⣖⡟⠀⠸⣀⠄⠧⣀⣈⣉⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠻⣤⣠⡋⠉⣉⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣼⣿⣷⠀⠀⣠⣄⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠘⢿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠉⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠈⠄⢨⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠊⠁⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠠⢸⣿⣿⠀⠀⠈⠙⠿⣿⠗⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡿⠀⣴⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢴⣿⣿⠀⠀⠀⠀⠀⠖⠀⠀⣠⣶⡄⠹⣧
⠀⠀⠀⠀⢀⠞⢤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⣿⡆
⠀⠀⠀⠀⠰⣤⣶⣇⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⢻⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⠃⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠙⢿⣿⣿⡇⠀⠀⢸⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⡠⠙⣿⣿⣄⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠈⠛⣿⠆⠸⡿⢷⡄⠀⠀⠀⢸⣿⣿⡏⠀⠘⣿⣿⣿⡇⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣾⣿⡟⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣧⣠⣄⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⢰⣿⣿⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠙⠿⣿⡿⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣿⡟⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣄⣙⣠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡆⢠⣿⣿⡇⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠀⠀⠈⠀⠈⠉⠉⠉⠀⠁⠐⠤⢄⡀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠈⠉⠉⠁⠀⠁⠐⠒⠂⠤⢀⣀
⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠤⢀⡀
⠀⠀⠀⣴⠊⢤⠄⠀⢤⠆⠀⢤⢤⣤⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⣤⡀⡤⠠⠤⡤⠤⠤⡬⠒⣦
⠀⠀⠀⠹⡑⢆⡀⠀⡎⠀⠀⠰⡏⠀⠀⠈⠆⠠⠚⠛⠒⢶⠀⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠄⡶⠒⠛⠓⢄⡠⠉⠀⠀⢸⠆⠀⠀⢱⠀⠀⣰⡾⠃
⠀⠀⠀⠀⠑⡀⠙⢢⡅⠀⠀⢠⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢃⠔⠉⠀⠀⠈⠑⡄⢠⠊⠁⠀⠀⠉⠢⡘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⢸⡤⠊⡰⠁
⠀⠀⠀⠀⠀⠐⡄⠀⠈⠢⣄⣼⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣧⣀⡠⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠈⠙⢄⡀⠤⠚⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠒⠤⢀⡠⠟⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠲⢄⡣⠄⢀⣀⣀⣰⠁⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⣆⣀⣀⡀⠠⢜⡠⠔⠈⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡰⠀⢀⡀⠄⠊⠁⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠬⠉⣀⡐⠒⠀⠁⠈⠐⢒⠀⠀⠨⠍⠒⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠄⣀⠀⠀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠤⢀⡀
⠀⠀⠀⠀⢀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⡀
⠀⠀⠀⣾⡉⣚⣀⡀⠻⠃⠐⠛⡰⠖⠶⢤⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⣤⠄⠲⢄⠒⠐⠒⡖⢒⣒⡒⢉⡿
⠀⠀⠀⠘⡌⠻⢕⠛⣧⠄⣀⡘⠇⠀⠀⠀⢣⠔⠉⠉⠉⠻⡀⠒⡲⠤⠤⢤⡤⠤⠤⢤⡤⠤⠴⢖⠒⢀⠟⠉⠉⠉⠢⡐⠀⠀⠀⠸⢃⣀⠤⣼⠛⢊⠝⡟⠁
⠀⠀⠀⠀⠈⠄⠈⠑⢏⠉⠚⢹⢖⠒⠰⣄⡸⠀⠀⠀⠀⠀⣡⠊⠀⠀⠀⠀⠈⢆⡰⠁⠀⠀⠀⠀⠑⣌⠀⠀⠀⠀⠀⢇⣠⠆⠖⡲⡏⠃⠉⢹⠖⢁⠌
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⠦⣼⠈⠀⠙⢁⡟⡎⡑⠒⢲⣀⡏⢀⣤⠀⠀⣀⠀⠘⠇⠀⡀⠀⠀⣠⡀⢩⣀⡖⠒⢊⢱⢻⡈⠉⠀⠁⣷⡤⠒⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠈⠲⢤⠂⠉⡇⠀⠀⠙⠂⠀⡍⢙⢀⡉⢉⠁⠦⠰⠆⠴⠈⡉⢉⣀⡏⢩⠀⠑⠋⠀⠀⢠⠉⠐⣠⠔⠋⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠙⠢⢕⠂⠠⠤⠤⠼⠀⠀⠁⠀⠈⠉⠀⢠⡄⠀⠉⠁⠀⠈⠀⠀⠧⠤⠤⠄⢐⡪⠔⠊⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠣⢀⣀⠀⠀⠀⠀⡘⢃⠀⠀⠀⠀⣀⡀⠜⢀⠠⠔⠂⠁⠀⠀⠀⠀⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠠⠤⠀⠀⠠⠀⠀⠀⠤⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠠⠤⢀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠐⠂⠉⠁

⣶⣶⣶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣷⣶⣾⣿⣷⣶⣶⣶⣿⣿⣿⡿⣶⠿⠶⠷⠾⣶⡾⠷⠷⠾⠷⠶⠶⡶⠷⠶⠶⠷⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡤⠖⠛⠓⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢠⠖⠛⠒⠚⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠳⣄⠹⣤⣀⣀⣀⡴⠚⣁⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡄⠀⠸⡆⠀⠉⠉⠁⢦⡀⣈⠳⡄⠀⠀⠀⢸⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢳⠀⠀⢹⡀⠀⠀⠀⠈⣇⠸⡆⠹⡆⠀⠀⢸⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⡼⢧⠀⠀⠷⠤⠤⠤⠤⠤⠤⢤⡀⢹⠀⠀⢸⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣀⠀⢀⡴⠋⠀⠘⢦⣀⣀⣀⡀⢀⣀⣀⣀⣠⡇⣀⣀⡀⣸⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⢳⡋⠀⠀⠀⠀⠀⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣉⣉⣉⣀⠀⠀⠀⢀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠼⠆⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⣿
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠨⠀⠸⠰⠁⢘⠀⠀⠘⠀⠈⠀⠈⠸⠂⠂⠀⠒⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⣠⡶⣿⡿⢿⣿⣿⣶⣦⡀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠹⣷⡘⣿⡌⠻⣯⡻⣿⡻⣷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣿⣷⡘⣿⡄⠹⣷⡘⢿⣎⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠸⣷⠀⠹⣷⠈⢻⣆⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢻⡇⠀⢻⣇⠀⢿⣆⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⠀⠈⣿⡀⠈⣿⡄⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠿⠆⠀⠻⠇⠀⠹⠇⠀⠸⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⡀⢠⣿⢁⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣿⡟⠀⡿⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣷⣿⣿⣿⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⢸⣿⣿⣿⡇⠈⠀⠀⢀⡿⢛⠛⠛⠛⣛⠛⠛⠛⠛⠻⣿⣿⣿
⠀⠀⠀⢸⣿⠏⢿⣿⣼⠀⠀⠀⣠⣦⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⡇⢠⣸⡀⠸⠃⣿⣿⣿⠟⠙⣿⣿⣿⣿⢠⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠈⢸⡏⠀⢀⣼⡯⣾⣇⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣷⡇⢸⣿⡿⠃⢸⠁⠹⣿⣿⡇⣸⣿⣿⣿
⠀⠀⠀⠀⢻⡀⠀⢸⣇⣀⣛⣛⣛⣛⣛⣀⣀⣾⠁⠀⠀⠀⢸⣿⣿⣿⣿⡌⣿⣿⡇⠾⠿⠤⠤⠤⠤⠤⠿⠿⠁⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢳⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⢀⣴⣿⣿⣿⣯⣭⣭⣽⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠶⠶⠖⠂⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠰⠶
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠐⠖
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⠛
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⣿⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⣠⣿⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠈⠛⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⡙⠿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣀⣀⣘⠟
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⣿⠓⠆
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢻⠁⠀⡟
⠐⠉⡟⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣶⠛⢩⡇⢀⡼⠀⠀⡇
⠀⠀⣧⠀⠀⣧⠀⠉⢹⠛⠒⢶⡤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⡾⠛⠉⠀⠀⣿⠀⢠⡷⠋⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠘⠳⢤⣼⠀⠀⢸⠀⠀⠀⠈⣿⠉⠉⠉⠛⠛⡟⠛⠛⠛⠛⢻⠛⠛⠉⠉⠉⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠶⠋⠀⠀⠀⠀⢸⠃
⠀⠀⢹⠀⠀⠀⠀⠀⠈⠳⠦⣼⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣇⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣿⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⣤⣤⡤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠛⠛⠒⠷⢤⡤⠤⠤⠾⠲⡞⠛⠋⠉⠁⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠋⠀⠀⠀⠀⣀⣀⣤⡤⠿⠶⠶⠶⠶⠶⠶⠦⠤⣤⣼⣁
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⢀⣠⠴⠒⠋⠉⠉⠉⠉⠉⠁⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⣰⠞⠁⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠟⠁⣀⣰⣋⣀⣤⠤⠴⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⠤⠤⠴⢶⡞⠛⠛⠛⠛⣿⠉⠉⠉⢹⠛⠋⠉⢹⡖⠛⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣟⠀⠀⠀⠘⡇⠀⠀⠀⠀⢻⠀⠀⠀⢸⡆⠀⠀⢸⡇⠀⢀⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣷⠀⠀⠀⠀⢸⡄⠀⠀⢈⣇⣀⣤⡼⠷⠛⠉⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣤⣤⣤⣤⣤⡤⠶⠖⠋⠉
⣿⣿⡟⠛⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠹⣿⣦
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⣿⣿
⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣿⠇⠀⠀⢻⣿⣇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄⠀⠀⠀⢿⣿⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠈⠛⠁⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣤⣀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣀⣀⣀⡀⠀⠀⣀⣀⠀⠈⠙⠻⢿⣷⣄⠀⠙⢿⣷⡄
⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⣿⠀⠀⠿⠿⣿⣷⣦⣄⠀⠙⣿⣷⡀⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠘⣿⣷⠀⠘⣿⣷
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢹⣿⡆⠀⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⠛⠃⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣤⡄⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢸⣿⠂
⠀⠀⠀⠀⠸⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠸⠿⠇⠀⠸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣦⣄⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⢟⣛⣭⣭⣭⣭⣭⣛⡻⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣛⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⡻⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⣫⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣂⣙⠿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢟⣵⣾⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣮⡻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣶⣿⣿⣿⡿⣫⣴⣾⣿⣿⣶⣶⣭⡟⣫⣵⣶⣾⣿⣿⣶⣮⡻⣿⣿⣿⣶⣭⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣭⡻⢿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⠟⣫⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢨⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⢦⣄⠀⠀⠀⠀⢀⣀
⠀⠀⣀⣤⣴⣾⣿⡅⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡷⠶⠟⠃⠀⠀⢀⣿⣿⣇
⠀⠈⢿⣄⣿⣿⣿⢿⡀⠀⠀⠀⠐⢿⣽⣿⣿⣏⣿⠆⠀⠀⠀⢠⣾⣿⣿⣆⠀⠀⠀⢀⣴⠟⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣟⣷⡀
⠀⠀⠀⠉⣿⣿⣿⡈⢿⠄⠀⠀⠀⠀⢹⡿⣿⡏⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⣿⡿⣿⠀⠀⠀⠀⠀⠈⠙⣿⣿⡏⠉
⠀⠀⠀⠀⢸⣷⠹⣷⡀⠀⠀⠀⠀⠀⣿⠇⢹⣧⠀⠀⠀⠀⠀⢘⣿⠃⢻⡟⠀⠀⠀⠀⠀⠀⣿⡇⢿⡇⠀⠀⠀⠀⠀⢨⣿⣿⡇
⠀⠀⠀⢀⣾⠏⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣆⣿⠇⠀⠀⠀⠀⠀⣴⡟⠁⢸⣧⠀⠀⠀⠀⢀⣾⠏⠘⣿⡄
⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣠⣴⢦⣤⡴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣋⡀⠀⠀⠀⠘⠻⣦⣘⣿⣣⣴⠟⠁⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⢀⠀⠀⢀⣹⣿⣁
⠀⠀⢀⣼⣿⣯⡀⠀⠀⠀⠀⣀⣤⡾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⡅⠀⠀⠀⠘⢷⣶⣿⣿⣿⡏
⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠈⠉⠁⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠉⣿⣿⡇
⠀⠀⠹⣿⡟⣿⡟⠀⠀⠀⠀⠀⠀⢀⣿⢻⣿⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⡄⠀⠀⠀⠀⠀⣿⡟⣿⣾⠃⠀⠀⠀⠀⠀⠀⢸⡿⢸⡇
⠀⠀⢠⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⠀⢠⣿⠇⢹⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣷
⠀⠀⠿⠃⠀⠹⠇⠀⠀⠀⠀⠀⠀⠘⠟⠘⠿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠸⠇⠀⠀⠀⠀⠿⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠿⠂

⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣿⣿⣩⡿⠇⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢴⣿⡆⠀⠀⠀⠀⠀⠀⠐⣿⡿⢠⣄⠀⠀⠀⠀⠀⠀⠘⣿⡟
⠀⠀⣰⣿⣿⣟⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⢷⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠈⠻⢿⣿⣿⠀⠀⠀⠀⠀⣾⠃⣿⣿⣿⣠⡿⠂⠀⠀⠀⠘⣯⣿⣿⣿⣿⠂⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟
⠀⠀⠀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢘⣿⢻⣿⠁⠀⠀⠀⠀⠀⠸⢻⡿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂
⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⢀⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⣿⠁⢻⠇⠀⠀⠀⠀⠀⢸⠏⠸⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⠼⡿⠀⠀⠀⠀⠀⠀⠀⢿⠇⢿⠇⠀⠀⠀⠀⠀⠠⡿⠃⠹⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣾⣿⢿⡿⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣼⣿⡝⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣺⣷⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⣿⣽⣿⣫⣷⣶⣾⣵⣶⣾⣽⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢻⣿⣿⢫⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡓⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠀⣾⢋⢭⣿⣿⣷⣽⣛⣻⣿⣿⣿⣿⣿⣿⣎⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠏⣿⡟⣿⣿⣿⣿⣿⢷⣍⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣺⠀⢸⣷⣻⣿⢟⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣈⣿⣿⡷⢧⣟⢿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡼⢟⣋⣾⣿⣷⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣿⣿⣿⢿⣟⣿⣯⣽⣭⣯⣍⣭⣽⣿⣿⣿⢏⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠾⢹⣾⣿⣿⣿⣿⣿⣛⣽⣿⣿⣿⣿⡗⠷⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣻⣼⣿⣿⣣⣍⣿⠽⠉⢹⣯⣼⣿⣿⣏⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣗⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠯⡖⣽⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⢿⡗⠀⠙⣋⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⣀⣿⣷⣾⡿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣅⣀⠄⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠺⠋⣽⣭⣿⣵⣭⣭⣿⣿⣿⣿⣿⣯⣭⡥⠹⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣹⣇⡣⠶⣼⣾⣦⣭⣤⣽⣿⣿⣿⣿⣾⣯⣧⣿⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠄⠀⠀⠉⠓⠶⠤⠶⠚⠉⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠑⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣀⣤⠒⠒⠘⠏⠉⠉⠐⠀⢲⠒⠊⠉⠉⢉⡉⠑⠺⣄⣀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⣠⣴⣿⣿⣿⣶⣦⣴⣇⡀⠀⠀⠀⢠⠀⠀⠀⠀⢸⣧⣤⣴⣿⣿⣿⣦⣄⠀⢀⠈⠳⣤⡀
⠀⠀⠀⠀⣴⠋⠀⢀⣤⣾⣿⣿⡿⠋⠉⠉⠉⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠙⢿⣿⣶⣤⣀⠀⠙⣦
⠀⠀⠀⠀⠹⡄⠈⠹⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠁⢠⡟
⠀⠀⠀⠀⠀⢻⡀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⡾
⠀⠀⠀⠀⠀⠈⣧⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠐⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢂⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠜⠇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠙⡀⠐⢀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠂⠀⠑⠉⠂⠃⠄⠀⠐⠉⢱⠐⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠈⠀⠈⠀⠀⠀⠁⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠐⠨⡀⡀⠀⠀⠀⠘⢠⠈⠀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠘⢀⠀⠌⠀⠄⠀⠐⠀⠀⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠈⠑⠀⠑⠀⠈⠂⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠀⣀⣤⣶
⢁⠠⡄⠀⠀⠀⠀⣀⠀⠄⠐⠉⠙⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡀⠀⠀⠀⠀⠀⡤⠈⠉⠉⠛
⠀⠑⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠐⡄⠀⠁⠤⠐⠂⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠂⠄⡀
⠀⠀⠀⠰⠀⠀⠀⠠⠀⢀⡀⠀⡀⠀⠀⠀⢀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠁⠄⠀⠀⠡⡤⠀⠈⠁⠀⠀⠠
⠀⢀⠤⠚⣀⡤⠒⠈⠈⠀⠀⠀⠁⠁⠂⠄⠀⠠⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠑⠀⠐⠀⠁⢀⠆
⠀⠂⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠤⠀⠠⠐⠁
⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⣸⣯⣛⣿⣫⣫⣟⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⠶⠶⠶⠶⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣀⣤⡴⠿⠿⠛⠛⠛⠛⠻⠿⢶⣦⣤⣤⡶⠖⠲⠶⠶⠶⠦⡤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⣠⡶⠟⠉⠁⠀⠀⡀⠀⠀⠒⢦⡀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠋⠀⠀⠀⠀⠴⣚⠅⠀⠀⢠⣤⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⣈⣭⣤⣤⣤⣄⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⢏⠉⠁⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⠀⠀⠀⠀⠀⠸⣯⣀⠀⠀⢀⠀⠀⠀⠀⠀⣦⣠⡿⠋⠀⠀⠀⠀⠀⠤⣿⡷⠶⠶⠦⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠷⠶⠶⠶⠿⠛⠉⣠⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⠋⠉⠉⢿⡄⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⣀⠀⠀⢀⡤⣼⠁⠀⠀⠀⠀⠀⢠⣾⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠄⠀⠀⡀⠃⠀⠳⣤⠴⠋⠁⠱⣄⡞⠀⠘⣆⠀⠀⠀⠀⣠⣿⣏⠀⠀⠉⠓⠤⡀
⠀⠀⠀⣠⠤⠶⠶⠤⣄⡀⠀⠀⠀⠀⣠⠞⠻⣦⡀⠀⠙⠂⠀⠀⠀⠀⠠⠲⠦⠀⠀⠀⠀⠈⠑⢀⣤⡾⠿⡅⠙⣧
⠀⢠⠏⠁⠀⠀⠀⠀⠈⠹⣄⠀⠀⠐⠁⠀⢰⡟⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⠀⠘⢦⠘⣧
⠀⣿⠀⢠⠖⠒⠒⢦⡀⠀⢹⡄⠀⠀⠀⢀⡿⠀⠀⠀⠀⠈⠉⠂⠀⠀⠠⠴⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠸⡇
⠀⢿⠀⣿⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡄⠸⡄⠀⠀⣸⠃⢀⡟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠈⡇⠀⢻⡀⠀⣇⠀⠈⠳⢤⣀⠀⢸⡇⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠘⣧
⠀⠀⡇⠀⠀⢷⠀⠈⠓⠲⡄⠀⠈⡇⣿⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⢀⣤⠤⢤⣀⣀⡀⠀⠀⠀⠀⣀⣴⠟⠁⠀⢰⠀⠀⣿
⢀⡼⠁⠀⠀⢸⠀⠀⢠⠞⠁⡠⠚⠁⣿⠀⠀⠰⡄⠀⠀⠀⠈⠉⠛⠻⠁⠀⠈⣿⠈⠙⠶⠶⠶⠛⠉⠀⠀⠀⢀⡟⠀⠀⣿
⣿⡀⠀⠀⣠⠟⠀⠀⢻⡀⠀⠳⠤⣤⡏⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠔⢻⡤⠄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣿
⠈⠛⠛⠛⠁⠀⠀⠀⠈⠓⠦⢤⣤⣤⣧⠀⠀⠀⠀⠈⠻⢦⣀⣀⠀⠀⢀⣀⣠⣾⣁⡀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠉⠻⣄⣀⣠⡿⠹⣏⣉⣀⡴⠒⠚⠛⠉⠁⠀⠀⠀⠀⢀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣶⣤⣤⣄⣀⣀⣈⣉⣉⣀⣀⣈⣉⣉⣀⣀⣀⣀⣤⣤⣤⣶⠶⠿⠛⠉⠁

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠋⠛⠻⣶⣄⠀⠀⠀⣠⣴⠾⠛⠛⠛⠛⠻⢷⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⣀⣤⣴⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠉⠛⢷⣤⣤⣠⣤⡶⠾⠛⠉⠉⠀⠈⠉⠛⢷⣄⠀⠀⠀⠀⠀⠈⢿⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢀⣴⣾⣿⣷⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠻⣧⡀
⣿⡇⠀⠀⠀⠀⢀⣴⡾⠋⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⠀⣠⣾⢶⣄⣀⠀⣻⡆⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⡇⠀⠀⠀⠰⣿⡁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠈⠙⠛⠿⢿⣿⡿⠟⠛⠷⢶⣶⣶⠾⠛⠁⠀⠉⠛⠛⠛⠻⣦⣤⣀⣀⡀⠀⠀⠀⠈⠻⣶⡄
⣿⡇⠀⠀⠀⠀⠈⠻⣦⠀⠘⢿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠋⠀⠀⠀⣠⡾⠋
⣿⡇⠀⠀⠀⠀⠀⠀⠙⣷⡀⠈⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⣠⡾⠋
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⢀⣼⠟
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣰⠟⠁
⣿⡇⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⣼⠏
⣿⡇⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣼⠏
⣿⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⣼⠏
⣿⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣼⡏
⣿⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣼⡏
⣿⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⣼⠟
⣿⡇⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣼⠏
⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⣾⠋
⣿⡇⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣴⠟⠁
⣿⡇⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣠⣴⠟⠁
⣿⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣤⣶⠟⠋
⣿⡇⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠉
⣿⡇⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠾⠿⠟⠛⠋⠁
⣿⡇
⣿⡇
⣿⡇
⣿⡇
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⢠⢐⠆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠁⠁⠀⠉⠉⢸⣿⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠤⠀⠤⠤⢸⣿⠀⠤⠤⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⣀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠀⠁⠉⢨⣿⠀⠁⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠶⠀⠀⠀⢘⣿⠀⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠀⠀⠀⢨⣿⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢸⠀⠐⠒⠀⠂⠂⢐⣿⠀⠒⠒⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⠀⠀⠀⢈⠀⠰⠐⠀⠀⠀⠐⣿⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠢⡀⢸⠀⢀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠆⠀⠘⢠⠀⠈⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠐⠀⠀⠀⠀⠀⢸⠀⠰⠒⠀⠒⠒⠀⣿⠀⠂⠒⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⠀⣀⣀⠀⣿⠀⣀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡅⠀⠀⢀⡀⠀⠀⢐⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠩⠁⠀⣁⠀⠀⢘⠀⠐⠄⠀⠂⠂⠀⣿⠀⠂⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⢰⠋⡄⠀⢸⠀⠀⢠⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠻⡳⡠⢐⠠⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠚⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠢⡢⡁⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠶⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠢⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠘⠿⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⣄⣠⣮⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄⠀⢨⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠬⣟⣛⣛⣛⣛⢛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣣⠎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⣋⠞
⠀⠀⢀⠀⠀⠀⣀⣀⣀⠀⢠⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⣀⠠⢄⡀⢄⣠⠎⡠⠇⠹⡷⠆
⡀⠀⠀⣢⠖⠉⠀⠀⠀⠑⢼⡠⢦⠤⡀⢀⣀⠤⢦⣀⣀⠀⡴⠉⠁⢢⣀⠤⠚⠉⠀⠀⠀⢀⡷⠊⢡⢻⠤⢷⠦⡇
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠐⢇⡃⣰⠋⠉⠀⣀⠁⠀⠸⡀⠘⠤⠀⢻⣧⠀⠀⠀⠀⢀⠴⠋⠀⣰⡿⠁
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⢤⠀⠀⠀⠀⠄⠀⣏⠀⠀⠘⠙⠻⠒⠒⠒⠈⠀⠀⠀⠜⢋⣉⠙⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⣎⣀⠷⢄⠀⠀⠉⠐⠂⠀⢜⣀⣬⡷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣁⠜
⠀⠀⢳⡀⠀⠀⠀⠀⠀⣪⠖⠉⠉⢆⠘⡕⢮⡐⢄⠀⠢⡎⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍
⠀⠀⠀⠙⠦⣤⡤⠔⠊⠁⠀⠀⠀⠈⢆⠘⣄⠙⢦⡀⢚⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⢲⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠣⡀⠙⠉⢺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⣱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠲⢄⡴⢿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢠⠎⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢀⠔⠁⠀⠀⠀⢀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⠀⠀⢀⡠⠚⠁⠀⡠⠊⠀⢀⠀⠀⠀⠀⠱⡀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⢤⣓⣄⢋⠠⣀⣀⠞⠀⠀⠀⠘⡀⠀⠀⢀⣀⠼⠀⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣏⠙⢦⡄⠁⠀⠀⠀⠀⠀⠓⢲⡿⠿⢇⠀⢀⡴⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⡞⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣤⡤⠄⠒⠒⠈⠁⢣⠀⠳⢄⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢢⡱⣄⠀⠀⠀⠀⠘⢆⡀⣐⣒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠽⠮⣷⢶⣀⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⠒⢷⡆⠤⣬⠦⠤⠤⠤⠤⣶⡶⠋⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢢⣈⠋⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠻⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣴⠟⢡⣾⠟⣹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢷⡀⢠⡟⠁⣴⠟⢁⡶⢋⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⡿⢤⣼⠃⣰⠟⣠⠟⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢿⡀⠈⠙⢦⡉⠛⢧⣴⠏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡇⠀⠀⠀⢱⡞⠳⣝⣾⠃⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⡇⠀⠀⠀⠸⣇⠀⢻⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢘⡇⣤⡀⠀⠀⠹⣆⠀⢷⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠈⠙⠛⠶⠆⣿⠀⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡎⢷⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⡟⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⠛⠛⠛⠳⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⢧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠋⠁⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⣴⠞⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣰⡏⢰⣶⢿⣿⣦⣄⠀⠀⠀⠀⠺⣯⡿⣦⡌⠇⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠛⣿⠀⠀⢠⣶⡄⠀⠹⣇⠀⠀⠀⠀⣴⣦⠁⢸⣷⠞⠉⣦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣷⠀⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠘⢧⣼⡆⠀⠀⠀⠀⠀⠸⣇⣤⠀⠀⠀⠀⠀⠀⠈⣷⣤⡾⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣀⡼⠿⣄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣰⠿⣄⡀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣤⣤⠞⠛⠉⠀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠈⠙⠛⢦⣤⣀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠉⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠟⠉⠙⠳⢶⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠈⠙⠳⠶⣄⣀⡀⠀⣠⢦⣤⣤⣤⣤⣴⣄⠀⠀⣀⣀⣤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣄⠹⣯⠻⣏⣠⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⠹⣆⠙⢧⡹⣧⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢡⣿⢷⡘⣧⠈⢳⡌⢷⡌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠙⣮⡳⣌⠻⠆⠁⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⠀⢀⡟⠀⠀⠀⠀⠈⠳⣌⠃⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣼⡃⠀⠀⠀⠀⣠⡴⠟⠳⢦⣄⠀⠀⠀⠀⢘⣧⣤⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣁⡶⠋⠀⠈⠛⠳⠶⣴⡟⠉⠀⠀⠀⠀⠈⢻⣦⠶⠞⠛⠁⠀⠙⢶⣀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠙⢷⣿⡄⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⢻⣄⠀⠀⠀⠀⠀⣠⡴⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⢦⣄⠀⠀⠀⠀⠀⣠
⠀⠙⠳⠶⠶⠶⠛⠁⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠉⠛⠶⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⣿⡗⠶⠶⠶⣶⡶⠶⢶⣤⠶⠶⠶⢶⡶⠚⠛⠛⠻⣿⠛⠛⠛⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣿⣤⣤⣤⣤⣶⣤⣄⣸⣿⣄⣀⣠⣼⣧⣤⣤⣤⣤⣿⣤⣤⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⡏⠀⢹⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣤⣤⣀⣤⣄⣠⣀⣤⣠⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣠⣤⣤⣄⣠
⣿⣿⣿⣿⠿⠛⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⣤⢀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣠⢔⠊⠀⢱⠀⠀⠰⠀⠉⡖⠂⠶⠊⠁⡆⠀⠀⡀⠀⠈⠑⣤⡀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⣠⡎⠀⠈⢆⠀⠀⢣⠀⠀⣇⣀⣧⠀⠬⠀⣰⣀⡀⢠⠁⠀⢀⠞⠀⠈⣢⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡰⠁⠈⠢⢄⠀⢱⠤⠚⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠐⠲⢅⢀⠤⠊⠀⠑⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠤⡀⠀⢀⠗⠡⠀⠀⡆⢀⡠⠊⠀⠀⠀⠀⠀⠈⠒⢄⠀⡀⠀⠙⢄⣀⠤⠒⠙⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⣀⠀⠈⢱⠃⠀⠂⢀⡼⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡱⡄⢀⠆⠀⢣⣀⣀⡀⢧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⠉⠐⡎⠀⠀⣀⡌⡠⠔⢊⡥⠒⡉⠉⠉⢹⠓⠢⣄⠀⠈⠻⣎⠀⠀⠀⣇⣀⠀⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⢻⠤⢄⣀⠀⡇⢠⠀⢸⠋⠀⡰⢇⠀⠀⠇⠀⠀⠸⠀⢀⠋⠳⡀⠀⠘⣀⠔⠁⡇⠀⠀⢀⠋⠐⠢⠤⡀
⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠘⣄⠀⠀⠈⢃⠸⡀⠘⠀⢰⠁⠀⢢⠀⠸⠀⠀⡇⠀⡘⠀⠀⣵⠀⢢⡟⠀⠀⡏⠀⠀⡏⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢩⠈⠉⠁⠻⡀⠑⡆⠀⡗⢤⡀⠀⢣⠀⣃⢀⡅⢰⠁⡠⠊⠀⡆⠀⡇⠀⡸⠁⠒⢲⠁⠀⠀⠀⠀⠀⠀⠀⠈⣢
⠀⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⢓⠒⠒⠀⢣⠀⠆⠀⣇⡀⠈⡲⠊⠁⠀⠈⠁⠣⡜⠁⠀⡠⢇⢠⠁⢰⠓⠢⣠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠘⡆⠤⠄⠀⡇⡀⢰⡀⠈⠹⠀⠀⠀⠀⠀⠀⠀⢱⡔⠉⠀⢸⠘⠀⠏⠢⣀⡎⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠰⡄⢀⣀⣸⢠⢸⡉⢑⠇⠀⠀⠀⠀⠀⠀⠀⠀⣆⡠⠊⢹⡆⠸⢄⡀⡘⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢣⡀⣀⣀⡃⢸⢈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠔⠋⡇⣄⠀⢨⠃⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⠣⣀⣈⣽⣆⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⠠⣷⠀⡱⠃⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠑⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠛⠉⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⢄⠀⢠⠀⠀⠀⠂⠀⠀⢄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠠⠄⠒⠁⡰
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⢀⣀⠀⠀⠠⠤⠤⠀⠈⡀
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠐⠀⠈⣀⡠⠃⠀⠀⠀⠀⣀⣀⡠⠤⠤⠔⠲⠒⠚⠁⢀⠀⢈⡀⢀⠀⠀⠄⠀⠂⡸
⠀⠀⠀⠐⠀⠀⠈⠐⢒⣈⡭⠥⠴⠒⠒⠊⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⠤⠤⠴⠖⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⣀⣠⠤⠤⠤⠤⠖⠒⠒⠒⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢀⣈⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢚⠄⠀⠈⠉⠉⢉⣛⡭⠉⠀⠀⠈⠙⠲⡄⠀⢠⠖⠋⠉⠀⠈⠉⠉⢙⣉⠭⠀⠀⠈⠉⠳⣄
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢹⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠸⡆⠀⠀⢀⡉⣀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⢸⠃⡇⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣧⠀⡐⠉⠀⠀⠈⠀⡠⠊⠀⠀⠀⠉⠀⠀⣸⠀⢷⠀⡐⠈⠀⠀⠈⠀⣀⠊⠀⠀⠀⠑⠄⠀⢸⠁
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠰⣷⠆⡁⠀⠀⠀⣷⡆⢈⢀⡏⠀⠸⡆⠀⢾⡦⠀⠀⠀⡁⢾⡧⠀⠀⠀⢈⠀⡟
⠀⠀⠀⠀⠀⢧⠡⣀⠀⠀⢀⡄⠉⢄⡀⠀⠀⣠⠂⡼⠀⠀⠀⢷⠠⣀⠀⠀⢀⠐⠉⢀⡀⠀⠀⣀⠂⣸⠁
⠀⠀⠀⠀⠀⠸⡄⠈⠉⠉⠀⠈⠛⠁⠈⠉⠉⠀⢰⠃⢀⡀⠀⠘⡆⠀⠉⠉⠀⠈⠉⠀⠈⠉⠁⠀⢠⠇⢠⡦
⠀⠀⠀⠀⠀⠀⣷⢀⣴⠋⠀⢀⣀⡀⠀⠀⠀⠀⡏⢀⡾⠁⠀⢀⣿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣾⣴⠏
⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⢠⠏⠀⠹⡄⠀⠀⢀⡟⠋⠀⠀⣰⠟⢹⡀⠀⠀⢠⠏⠀⠹⡄⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⢳⠀⠀⢸⡇⠀⠀⠘⠁⠀⢸⡇⠀⠀⡾⠀⠀⠀⢹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⠀⠀⠈⡇⠀⢰⠇⠀⠀⠀⠈⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡟⠀⠀⠀⠀⠀⢳⠀⣼⠀⠀⠀⠀⠀⠀⠀⣧⠀⡼⠀⠀⠀⠀⠀⢹⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠙⠞⠁⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⠀⠀⠀⠀⠀⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣭⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢣⣶⣶⣭⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡎⢻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣩⣶⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣍⡻⠿⣿⣿⣿⣿⠿⢡⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠷⠂⠀⠀⠀⠀⢹⣿⣿⣿⣟⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣩⣶⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢻⣦⢻⣿⣷⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣼⣿⣿⡟⣩⣭⣝⢿⣿⣆⠀⠀⠀⠀⢻⣿⣿⣦⡹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢰⣿⣿⡿⣸⣿⣿⠀⠀⠀⠀⠀⠙⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢡⣿⣿⣿⢡⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⣿⣿⣿⠃⢿⣿⣿⣿⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣷⣦⣍⠛⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣭⣙⠻⢿⣿⡿⠀⠀⠻⠿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⡇⠰⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢸⣿⣷⣾⣿⠀⠀⢸⣿⣯⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢀⣄⠀⠸⠟⠁⠸⡏⠀⠀⠿⠛⠉⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⡿⣿⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣴⣶⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣴⣾⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃



⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣶⣄⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢛⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣫⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣫⣾⣿⣿⡘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣛⣡⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⡅⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣷⢸⡿⣱⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠣⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠜⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠛⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⡀⠀⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡿⠛⠛⣻⠍⠀⠀⠀⠀⠙⣓⠖⠂⠀⠈⠁⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠶⣯⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⠀⠀⠈⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣇⠀⠀⠀⠀⠸⣤⡤⠄⣠⡤⢤⡀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢀⡞⠛⠓⠶⣞⢁⡴⢦⣻⣼⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣾⠃⠀⠀⠀⠈⠛⠁⠸⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣿⣿⢧⣄⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⡿⠁⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄⡀⠀⠀⠀⠈⠻⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⠻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠀⠀⠀⢀⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁⣸⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉