Raindrop Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠙⠻⣶⣦⣤⣀⣀⣤⣤⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⡀⠀⠀⢸⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢛⡍⠁⠀⠉⠻⠻⢿⣶⣦⣄
⠀⠀⠁⠠⠀⠘⢀⣀⣉⠁⠀⠀⠀⠀⣁⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⣒⣂⠀⠀⡶⡒⠊⠩⢔⣣⣄⡀⡀⠀⠈⢑⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣄⣿⡏⠉⠉⠀⠒⠖⠊⠁⠐⠂⠀⢦⡴⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠖⡉⠥⠒⢒⣒⡺⡂⠀⠀⠀⠉⠻⣟⢮⠒⡀⠀⠈⠔⠀⢀
⠀⠐⠒⠚⡳⠛⠹⢿⢦⡀⡀⠀⠀⠠⡄⠀⢀⡠⣠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠈⠀⠑⠆⠀⠀⢠⠀⠈⠈⢧⢑⣀⠀⠀⠀⠡⠚
⠀⠀⠀⠈⠀⢀⠀⠀⠁⠀⢨⠀⠀⠘⠂⠈⠁⠘⣯⠠⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⣀⠁⡀⠀⠀⠀⠀⢀⠀⠀⠸⢀⠆⠀⢀⡰⠂⠀⠐⠒
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⠀⠀⠣⡂⠀⠀⠙⠂⠀⠉⠉⠉⢭⠄⠀⠀⠔⠋⣠⠄⠀⠁⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⠀⣀⣀⣀⣠⣤⡤⠤⠶⣛⠵⠂⣠⠞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠒⢋⣡⡴⠚⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠌⢛⠩⠅⣀⣀⠀⢡⡎⠀⠐⠠⢤⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢈⠔⠉⠀⠠⣤⣤⠍⢡⣌⣉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢄⠀⠀⠀⢠⣤⠿⠋⠀⠀⠈⢳⡄⠀⡈⠄⠀⠐⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢦⡜⢾⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⡼⢃⡠⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠲⢝⣛⠷⢦⣤⣀⣀⢀⡄⢀⣂⣀⡤⢔⡒⠍⠐⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⡀⠀⠈⣐⣂⠉⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠂⠹⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⣰⠃⠀⠁⠀⠳⡀⠀⠀⠀⡰⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠀⠀⠀⠀⠀⡴⠁⡐⠀⠀⠀⠀⠹⣄⠀⠀⠳⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠄⢄⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠃⠀⠀⢀⡴⠋⠀⠀⢀⠂⠀⠀⠀⠀⢠⠀⠀⠙⢦⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⣀⢀⡐⠀⢠⠊⢦⠀⠀⠀⠳⣄⠀⠀⠀⡸⠳⡀
⠀⠀⠀⠀⠀⢀⠷⠀⠀⠙⠒⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢦⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠘⠴⠃⠀⠀⠀⢀⡼⠁⠀⠀⣠⣴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡉⠙⠳⣄⠀⢻⡀⠀⠀⢠⡀⠀⠁
⠀⠀⠀⢠⠋⡀⠀⠀⠀⢰⠃⠀⠀⢀⣴⣿⠛⠙⣿⣿⣦⡀⠀⠀⠀⠀⢠⣾⠟⠙⢿⣿⣷⣄⠈⠀⠀⢳⠀⠀⡜⢣
⠀⠀⠀⠀⠉⠀⠀⠀⢠⡏⠀⠀⠀⡜⣿⣿⣤⣤⣿⣿⣿⢣⠀⠀⠀⢀⢿⣿⣦⣠⣾⣿⣿⡏⡆⠀⠀⠘⡇⠀⠓⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⢇⠹⣿⣼⣿⣿⣿⠇⡼⠀⠀⠀⠘⡘⢿⣭⣿⣿⣿⡿⢁⡇⠀⠀⠀⣷
⠀⠀⠀⠀⠠⠆⠀⢀⣿⠀⠀⢀⠤⠼⢆⡈⠛⠛⠋⢁⡴⠃⠀⠀⠀⠀⠱⣄⠙⠛⠛⠉⣀⠾⠤⢤⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢠⠞⢸⡄⠀⠠⠊⠉⢢⠉⠑⠒⠚⠉⠀⠀⠀⠰⠔⠀⠀⠈⠉⠒⠒⠋⢡⠊⠈⠑⡄⠀⡏⢳⡀⠀⠀⣜⠄
⠀⠀⠀⠀⠀⠀⢸⡀⢀⣧⠀⠘⠄⡠⠜⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠘⠤⠀⠴⠁⣸⣃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠈⢧⡀⠀⠀⠐⠀⢢⠀⠀⠀⠀⠀⢺⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠎⢳⡀⠀⠱⢤⡀⠈⠒⠁⠀⠀⠀⠄⠠⠈⠙⠒⠋⠀⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠻⣄
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢱⠀⠀⠀⠙⠲⢤⣄⣀⡀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠋⢿⠀⠀⠀⠀⣇⠀⣸
⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠀⠀⠀⠀⠀⠀⢸⠉⢹⠋⠛⠓⠒⠒⠒⠛⠛⠋⠉⠉⠀⠸⣄⣀⡞⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⡄⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣠
⣿⠟⠀⠀⠀⠀⠘⠿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠰⣿⣷⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣷
⠀⢠⣾⣿⡆⠀⠀⠈⠀⠀⠀⢀⣼⣷⡀⠀⠀⠸⣿⣿⡗⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⢻⣿⣿⠇
⠀⠘⠻⠿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⡄⠀⠀⠀⢰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⡀⠀⠀⢀
⠟⠀⠀⠀⠀⠉⠁⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⣾⣿⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠈⠁
⠀⠀⢀⣴⡄⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⣾⣿⣷⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧
⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⣠⣆⠀⠀⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠇⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠘⠿⠿⠀⠀⠀⠉⠉

⡀⠰⣰⠀⠃⠃⠐⠄⠀⣉⠀⡌⠁⠐⠂⠠⠂⠸⡸⠰⣉⠀⢁⠀⠐⠀⠀⠤⠀⢇⠅⢐⢙⠈⠂⠘⠊⠀⣡
⡠⡀⢀⠆⠰⠙⠀⡰⡄⢀⢄⠈⣥⢠⢱⢀⠛⠀⣤⠀⣀⠀⡰⠀⡜⢃⢀⢢⠀⡰⡀⢀⠅⢠⢉⠀⣎⠀⠄
⠄⠅⠈⠂⠈⡉⠀⠒⠃⠣⠜⠐⠤⠀⡁⠀⢉⠀⠤⠰⣁⠇⠑⡁⠁⢁⠈⠊⠀⠤⠂⠘⠜⠀⡁⠀⡰⠀⡜
⡰⠀⠜⡄⢘⡡⢰⠡⠀⠶⠀⢠⡀⢈⡱⢠⠉⡆⢰⠂⠀⠆⠀⢙⠀⡊⡆⡌⡂⠴⠀⡐⠂⠸⡰⠀⠂⠁⢈
⠃⠃⢁⠁⠀⢤⠈⢁⠀⠒⡀⠀⠂⠀⣠⠀⡤⠀⢈⡁⠈⡊⠀⣄⠀⢀⠀⢈⡀⠒⠁⠑⡂⠀⣤⠀⠜⠀⢆
⡜⡀⢆⡇⠨⠠⠀⠧⠂⡎⣱⢀⠳⠰⡀⠂⠠⠀⢈⡁⢐⠡⠘⠬⠀⠍⠀⣂⡡⢀⢳⠠⡱⠀⠠⠀⠑⠁⡄
⠁⠁⠀⡰⡀⠠⠄⠀⡄⠀⢀⠈⠈⠀⠀⡴⠀⢢⠀⢀⠀⢠⡀⢠⠄⠀⡠⠀⢠⠀⠁⡀⠀⡴⡀⡔⢃⠘⠜
⡄⠋⠀⠂⠃⠐⠔⠐⠜⠀⢆⡇⢰⠉⠀⠒⠀⠉⠀⣎⡃⠣⠆⠀⠄⠀⠠⠂⠑⠃⢘⡰⠀⡁⠁⠈⠁⣤
⡀⠉⡀⠀⣖⠀⠔⠄⢠⡀⠀⣤⠀⣩⠀⡘⠂⡊⡆⣀⠀⢀⡄⠰⠆⢠⠒⠀⡰⡀⢀⢄⢠⢙⠀⡰⠀⠤⠂
⡁⠘⢙⠀⢉⠀⠒⠁⠂⠅⠸⠠⠂⠥⠃⠑⠁⠈⠀⣉⠄⠇⠸⠈⠁⠈⠒⠀⠓⠃⠣⠜⢀⠁⠀⠂⠃⠰⡆
⡀⠀⡄⠀⣉⠀⡔⠀⢠⠀⠠⠄⠀⢆⠀⠚⡄⡐⠆⢀⡀⢠⠀⠘⠃⢠⢣⢀⠒⠀⣄⢠⠊⡆⠰⢂⠀⢈⡁
⠄⠸⡰⠀⡀⠀⠓⠁⠇⠇⠀⠀⠀⠉⠀⠉⠁⠂⠂⠨⠅⠠⠄⠈⠁⠈⠊⠈⠊⠸⠨⠀⠉⣁⠐⠊⠀⣆⡇
⠄⢀⠆⠸⡸⠀⡔⠆⠀⡄⢠⠚⡄⠜⡀⠔⠃⢠⡀⢀⡄⠀⢄⠀⡴⠀⢈⡄⡠⠂⢠⠄⠀⣉⠀⡌⠆⢀
⠜⠘⠜⠀⡄⠀⠓⠂⠐⠔⠈⠀⠀⠁⠁⠁⠀⠣⠄⠠⠔⠘⠬⠀⠒⠀⢀⠀⠁⠂⠐⠂⠀⢀⠀⠈⠁⢈⠂
⡄⢀⢆⠨⡸⠀⠐⠃⠀⣄⠀⢦⠀⠎⠃⢠⠆⠀⣤⠀⢤⠀⠴⠀⡴⠀⡌⡂⢀⠆⠀⠚⡀⣃⡃⡜⡃⠀⡀
⠄⠘⠘⠀⢀⠄⠈⠁⠀⠊⠈⠚⠀⠉⡁⠈⡁⠀⠒⠘⠤⠀⠒⠀⠒⠀⠈⡀⠈⠊⠀⠉⠁⢀⡀⠈⡀⢐⢡
⠆⠀⠊⠆⠘⠂⡔⢡⢀⢢⠀⠎⡆⢰⢱⢰⢱⢀⠓⠀⡴⠀⠎⠂⠠⠄⡎⡡⠠⠂⢠⠊⡆⢆⠄⢰⢡⠀⠁
⠂⠀⢉⠁⠐⡄⠈⠁⠈⠚⠀⠁⢁⡀⠁⡀⠁⡀⠉⠀⠒⠁⠁⠁⠐⠂⡈⠀⠘⠊⠀⠉⠀⣤⠀⢀⠁⠰⢣
⠞⠀⡎⡄⠑⠃⡎⡄⡜⡆⢠⢂⠨⠅⢘⡁⠐⢙⠀⢶⠀⢦⠀⠛⡀⢐⢱⠀⠞⠀⡐⠆⠨⠠⠀⣎⡆⠈⡁
⡍⠀⡈⠀⡰⡀⠈⡀⠈⣁⠐⠂⠀⠠⡀⢠⡀⠁⡄⠉⡀⠉⣀⠉⢀⢆⠀⣠⠉⢠⠑⠂⡀⢀⠆⢀⡄⠐⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⡿⢟⣛⣯⣭⣭⣽⣛⡱⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣭⣭⣭⣝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢼⣿⣿⢟⣫⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣮⡝⠛⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠂⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⠂⠀⠀⠀⠀⢀⣶⣶⣶⣀⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡶⠀⠀⢀⣼⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠚⠛⢻⣿⡿⠋⠀⠀⣠⣦
⠀⠀⠀⣰⣿⡿⠀⠀⠀⠈⠉⠉⣽⣿⠏⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣾⠟⠁⠀⠀⣼⣿⡟
⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣴⣿⡇⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣼⠟⠁⠀⠀⣠⣾⡀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠋⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠿⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣆⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣿⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⢀⣿⡇⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⡤⠞⠁⠀⠀⢀⣴⡿⠟⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⣿⠁⢀⠜⠀⢀⣤⣤⣾⡟⠉⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀
⠀⠀⠀⣠⣤⣤⣤⣴⣶⡾⠟⠋⠁⠀⢸⡟⠀⠁⠀⠚⠁⠀⠀⢸⣧⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣧⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣇⣀⣀⡀
⠀⠀⢰⠟⠀⠀⠀⣠⡟⠁⠀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⢠⣾⣿⡟⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠈⠁⠈⢳
⠀⠀⡻⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⡤⡼⣷⣴⣶⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⢻⣷⣴⣶⣶⠶⠶⠶⣦⣀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠃
⡠⠞⠁⠀⠀⠀⢻⠀⠀⠀⢀⠞⠁⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠘⠀⠀⠎⠀⠀⢀⣀⣠⣤⡶⠶⠟⣿⡟⠋⠉⠙⣿⣿⣆⠀⠀⠀⠀⠙⠷⠶⣤⡀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠏⠀⠀⢠⣿⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠘⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠈⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣤⣤⠤⠤⢄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢹⣿⣇⠈⠉⠛⠿⢿⣧⣄⠀⠀⠓⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠀⠀⠀⠀⠀⠀⣰⠚⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣇⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠈⠿⢶⣶⣤⣤⣤⣄⣀⣤⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠉⢠⡞⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠀⢻⣆⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⣫⣿⣿⠟⠀⠀⣿⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠋⠁⣠⣾⣿⣿⠁⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣾⣿⠟⠁⢻⣇⠀⠀⠀⠈⠻⣆⣠⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⣴⣿⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠉⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠘⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣸⣿⠇⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠻⣆⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠙⠦⣀⠀⠀⠀⠀⠻⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠞⢻⣿⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠷⠴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃

⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣾⣿⡶
⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠈⠉⠉⣿⡿⠃⠀⠀⠀⠀⠘⠛⣿⣿⠟⠀⠀⠀⠀⠀⠸⢿⣿⠋
⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⡿⠃
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⣀⡀⠀⠀⠀⢰⣿⣿⡗⠀⠀⠀⠀⢀⣾⣿⣇⣀⣀
⠀⠀⠀⠀⠛⢿⣿⣷⣦⠀⠀⠀⠀⠘⣻⣿⣿⣟⡀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⣠⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠘⢻⣿⣿⠟⠁⠀⠀⠀⠈⢹⡟⠁⠀⠀⠀⠉⠁⣸⣿⡟⠁
⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠊⢸⣷⣶⣦⣤⣤⣄⡶⣞⣷⠸⣷⣜⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⣀⠄⠀⠀⠀⢿⣿⡿⣿⢿⠁⡅⡿⢻⡆⢿⣯⢿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡅⡊⠊⠀⠀⠀⠀⠀⠛⠀⣡⣼⠀⠀⡆⣼⢣⡘⣿⡷⣀⢺⡏⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠂⣿⠁⠀⡄⣣⢇⣾⡧⢸⣿⠗⢸⡃⡄⠈⡛⠂⠀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠁⠆⢋⠀⣿⡇⠘⡉⠒⠻⠿⢥⡆⠓⡤⠂⠐⢩⡷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⣼⣯⣇⢰⣿⣗⣱⣶⡆⢠⠎⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢸⢠⡿⢻⡞⢟⡧⡝⠛⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⣿⣻⡇⡆⢘⠰⠛⠁⠿⠃⠀⠁⣼⠖
⠀⠀⠗⢆⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣿⠾⠁⠀⠨⡊⠁⠊⠰⠀⠀⠀⠈
⠀⠀⠀⠏⠀⠀⠀⠉⣿⣷⣶⣶⣻⣵⣦⡤⢤⡤⠀⠀⠀⡂⢉⡴⠋⠘⠉⠀⠄⡀⠀⠀⢠⠀⠠⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⠫⣾⣿⢃⠀⢈⡄⢀⡠⠎⡔⠈⠀⠀⠀⠄⠎⣠⣜⠳⣷⢸⣄⡄⠀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠹⠺⢛⡄⢿⢿⡠⠜⠋⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣷⣌⢻⣇⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣗⠋⠈⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠐⡫⠘⠁⢹⡄⢻⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⢠⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⡀⢿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠁⢃⢘⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⣀⠔⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⢀⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⡶⠒⠛⠛⠙⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠏
⠀⠀⠀⢠⡇⡰⣊⠩⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⢀⡟
⠀⠀⠀⢸⡇⠁⠁⠀⠙⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠘⠒⠒⠲⢦⡄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⠛⠉⠉⣹⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣹⠇⠀⠀⠀⡜⠀⣀⣀⡀⠀⠀⠀⣴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠛⢉⡟⠀⠀⠀⠀⣼⠃⠀⠀⢀⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣯⣤⣄⠀⠀⠀⢲⡏⠀⠀⠀⠀⠉⠉⢉⡽⠃⢀⢀⡼⠁
⠀⠀⠀⣿⣀⣠⣤⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⣏⣴⡶⠟⢋⡏⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣢⡟
⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⣁⣀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠟⢛⡿
⠀⠀⠀⠀⠀⠰⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢠⠏⠀⠀⠀⠀⠿⠛⠒⡖⠀⢠⡟
⠀⠀⠀⠀⠀⢸⡧⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡤⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⠟
⠀⠀⠀⠀⠀⢸⡇⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋
⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠠⡇⢷⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⡴⠶⠖⠒⡒⣲⠆
⠀⠀⠀⠀⠀⢰⣶⠛⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢀⡇⠈⢣⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⡶⠛⠁⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⡾⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⢠⡶⠞⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡞⠉⠀⠀⢀⢂⡴⠛⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣰⢏⠀⠀⠀⠀⢠⣿⣃⣀⣀⡀
⠀⠀⠀⠀⣿⡄⠀⠀⠀⣠⣭⠇⠀⠀⠀⠘⣇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠐⠉⠉⠉⣩⠞⠁
⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧⣤⡄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠠⣞⠃⠀⠀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠓⢲⠀⠀⠀⠀⠀⣸⠀⢀⡀⠀⢠⠞⠀⠀⠀⢰⡯⠶⠖⠚⣿⠀⠀⠁⣴⠋
⠀⠀⠀⠀⠹⣆⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡜⡀⢸⠀⠀⠀⠀⠀⠙⠋⢹⡟⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡄⠀⠀⠀⠀⠀⢀⡟⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠹⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡇⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠒⠀⠀⠀⠀⠀⡴⠃⠀⠀⡄⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⣷⣤⠤⣤⣤⣶⣧⣰⣄⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⡀
⠀⠀⢀⣾⡇⢠⠎⠀⠘⠛⠻⠁⠰⢿⣿⢿⣿⣯⠀⠀⠁⠠⠤⠀⣀⠀⠀⠀⠠⣤⡄⠀⠀⢀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠁⠉⠛⡛⠉⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⢟⣿⣶⣶⣶⡾⠋⠈⠉⠠⣄⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠠⠀⠀⠀⠀⠰⡍⠓⠲⠶⠚⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣵⡾⣿⣿⣿⣿⠿⣶⣤⣠⣠⠉⠙⠛⠁⠀⠀⡰⠀⢤⣤⡤⠤⠀⠳⣅⡀⠀⠀⢀⡈⠻⣶⣶⣾⡿⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠈⠁⠞⠔⠋⠁⠀⠑⢦⣌⣒⣭⣽⣇⠀⠀⢶⣄⣀⣀⣤⣮⣿⠛⣻⣟⣤⣿⣿⡿⠋⠀⣀⡄
⠀⠀⠀⠞⠀⢲⣄⣉⣂⠀⡀⠀⠈⠃⠄⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣶⢿⣿⠿⢛⣿⣿⣿⣷⡖⣹⣿⣟⡿⠋⠱⠁⠉⢀⣼⠟⢋⡀⠀⠀⠁
⠀⠀⠀⠀⠂⠁⣄⠀⠀⠀⠳⠆⠀⠐⠀⢠⡘⠉⠉⢉⠀⠀⡀⠀⠀⠈⢙⠁⠀⣴⡂⠊⢛⣿⡿⢋⣾⣯⣿⡟⠁⠀⠀⠀⠀⠈⢀⡔⠁⡰⠚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢰⣆⠀⠰⣄⠀⠉⣓⡈⠁⢀⣌⢷⣤⢤⣶⡽⠂⡴⠛⡁⣰⣼⠟⣴⣿⡿⠟⠋⠀⠀⣴⡅⠀⠀⣰⣯⡀⠊⠀⠀⢀⠞⠁
⠀⠀⠘⣿⣷⣶⣆⣀⡴⠂⠀⠙⠛⠟⣹⣿⣿⣿⣿⣿⣿⣿⣷⣾⢫⡥⠀⠀⢀⢀⣰⣿⣧⡶⣠⢿⡃⠀⣠⣤⡾⢟⡖⠀⠀⢑⣏⠀⠀⠀⠀⠁⣠⠆
⠀⠀⠀⢋⡿⣯⠟⣵⠾⣠⡔⡡⢂⣼⣿⣿⠟⢻⣿⠿⣿⣿⣟⣽⣋⠠⢀⡴⢇⣭⣿⣿⢋⣴⡣⠈⣠⠊⠿⣩⣶⣿⡷⠀⢴⡿⠋⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠋⠀⢀⠞⢃⡿⠋⠀⢰⡾⣻⡿⠂⢠⡔⠂⠀⠀⠁⠭⠨⣻⡆⢈⣴⣿⣿⣿⣡⣿⣿⡿⡿⠛⠀⠘⠛⢻⠟⠂⠠⠍
⠀⠀⠀⠀⠀⣀⡰⠋⠐⠀⠀⠊⠀⠉⠀⠀⠀⢀⣊⠐⢛⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣚⢞⣁⡀⠀⡐⠀⢠⡜⡁⠈⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠛⡀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣾⣿⣷⣟⣴⣿⣿⣿⣯⣭⣿⣿⠟⣿⣿⣷⣖⣠⣥⣹⠞⡀⠈⠀⠀⠾⠻⠃⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⢀⠚⠿⠿⠁⠀⠀⠀⡠⠊⠁⠁⣰⣿⣿⣿⣿⣷⣽⣯⣼⣿⡿⠃⠾⢿⣿⢯⠿⢿⡿⣿⣿⣅⢠⠄⠀⠈⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠟⢻⣿⣷⣿⡿⣛⢿⣿⣿⣿⡟⣡⡞⣡⡯⠀⠈⠈⠉⠉⢱⣶⣴⣦⣿⣿⣿⣿⣷⣶⣶⣖⠃
⠀⠀⠀⢀⠂⠀⠀⢰⡇⠀⠀⠠⠀⠀⠀⠀⠠⡾⠿⢋⠜⠙⠁⣼⣿⣿⣏⣸⣿⡿⢈⣦⣾⣥⣤⣤⣴⡿⠟⣋⣩⣿⣿⣿⣿⣿⣿⣿⣯⣷⠀⠁
⠀⠀⠀⡤⠊⠀⠀⢼⣇⠀⠈⣆⢠⠀⠀⠀⠀⠀⠜⠃⠀⢀⣾⣾⣿⣿⣿⣿⣿⣧⣿⠛⡁⠾⢿⣿⣫⣵⣾⣿⣿⢟⣿⡛⣩⣷⣧⣍⣙⣷⣶⡄
⠀⠀⠀⠟⠀⠀⠀⣿⣟⠂⢼⡿⣿⡂⠀⠀⢀⡀⠀⠀⠀⢺⣿⣿⣭⣭⣽⣿⣿⡿⣡⠌⠑⠠⠘⠿⢻⣿⣿⣿⣁⣙⣻⣿⣿⣿⡏⠻⣿⣿⣟⣦
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣸⣿⣿⡇⢰⡄⣾⡆⠀⠀⠰⠃⢾⣿⣿⣿⣿⣟⡿⠈⠁⣀⠄⠀⠀⠀⠀⠀⠸⢿⠿⣿⣿⣿⣦⣼⡰⣿⣿⣷⣿⠁
⠀⠀⠀⡀⠀⠠⢾⣿⣿⢿⣿⢫⣿⣇⣸⣟⣿⣟⠀⠀⣀⢀⣐⣫⣽⣭⣩⣭⣤⣉⠛⢁⣀⣀⡀⠀⠀⠀⢀⡘⡀⡟⠃⠉⠿⢁⠔⠙⠛⠋⣁⣀⣀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣾⣿⢟⣿⣻⡧⣿⣿⢾⣾⣿⣿⣿⠿⡟⣿⣿⠟⢻⠻⣻⣶⢃⣿⣧⠻⢶⣿⣧⣿⣿⣿⣿⣿⣧⣥⣧⣶⡷⠘⢿⣿⣿⣿⡆
⠀⠀⠀⣉⣍⣵⣾⡿⣧⣌⣵⢿⣿⣟⣡⣿⣿⣷⣙⣉⠁⣤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠉⠉⠉⠉⠙⡇⠁⢹⡇⠉⠉⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⡽⠿⠟⠿⡛⠒⠙⠛⠻⠉⠬⠽⠷⠼⠿⣦⣬⣅⡀⠀⠀⠐⠛⠛⠛⠛⠻⠿⠛⠓⠈⠀⠀⠒⠂⠀⠈⠀⣿⡀⢸⡇⠠⠀⢴⣤⡤⠤⢤⡤
⠀⠀⠀⣷⣴⣶⣶⣶⡶⣶⣦⣤⣴⣦⣤⢀⣀⠀⠀⠉⠉⠉⠋⠉⠒⠐⠒⢴⣤⣤⣤⣄⠀⠀⠀⠀⠀⠤⠤⠶⠖⠚⠷⠚⠻⢿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⡻⠓⠚⠉⠋⠀⠀⠈⠁⠐⠒⠛⠛⠛⠛⠻⠿⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣽⣿⣾⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⡀⠠⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠑⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠉⠐⠀⠀⠀⠀⠠⠀⠀⠀⡀⠉⠀⠀⠅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⢀
⠀⠀⠀⠠⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⡄⠄⠃⠢⣀⠀⠀⠀⡂⣀⣀⠀⠀⠀⠉⠀⠒⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣂⠀⠈⠀⠙⠀⠀⠒⢲
⠀⠀⠀⠀⠀⣄⢸⠀⠀⠀⣶⠡⠤⢵⠀⣽⠒⠀⠀⣟⠁⢸⡀⣂⠂⠀⠀⠀⣰⡀⠠⠘⠢⣀⢁⢠⠄⠠⣄⠀⠙⣀⠀⣄⢠⠀⠰⣰⠀⡀⠈⠀⢄⠨
⠀⠀⠀⠄⠂⠨⠘⢃⠀⠀⠙⠚⠀⢸⣀⣉⠠⣤⠐⠛⠀⢸⠁⠹⠒⠀⠀⣆⢠⡀⢰⠄⠀⡟⠙⣦⠀⢸⡄⠀⢚⠈⠆⠙⡏⢱⢸⠹⡆⢸⠀⠀⠀⠀⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⡅⠙⠀⠿⠀⠀⠀⢸⠀⠀⡿⠀⠀⠛⠈⡄⠛⠀⡆⠍⢂⠉⠘⠀⠘⣯⠉⢠⣢⠀⠀⢸⢸⠀⡇⢸⡏⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠁⠁⠘⠂⠀⠀⠀⠉⠁⠈⠈⠈⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠐⠫⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠆⠀⠀⠀⠀⣰⣿⣿⡶⠛⠀⠀⢀⡄⣀
⠀⠀⠀⠀⠀⠀⠼⢿⣿⡿⠋⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢈⡽⠟⠁⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢀⠐⡁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠁⠌⠁⠀⠀⠀⠀⠀⠐⠁⢠⢌⠁⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⢃⠔⠃
⠀⠀⠀⠀⢀⢀⡘⠂⡰⠀⠀⠀⠀⠈⠀⡪⠐⠁⠀⠀⠀⠀⠈⣱⠃⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⢀⠔⠁⠈⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢴⡩⠇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠠⣸⣁⣀⡀⠀⠀⠀⡠⠋⢠⣎⠁⠀⠀⠀⣠⠊⢘⡂⠖⠀⠀⠀⠀⢠⠎⣠⠄
⠀⠀⠀⠀⠰⢓⢖⡴⠋⠀⠀⠀⠈⣩⡿⠒⠁⠀⠀⠀⠀⣩⠏⠋⠀⠀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠰⠎
⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣟⡆⠀⠀⠀⠀⠀⣸⣧⠀⢀⣿⡇⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⡇⠸⡆⠀⠀⣀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣀⠀⠀⠀⠀⠀⠉
⠀⡠⡄⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠻⠟⠀⠀⠉⠀⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⠙⠤⠃⠀⢰⣿⡆⠀⠛⠀⠀⠀⠀⠀⠀⢿⡷⠀⢠⠛⡆⠀⠀⠀⢀⡆
⠰⣧⠇⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠳⠼⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⡜⡄⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣆⠀⠀⠿⠇⠀⢀⡄⠀⢸⠁⡽⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠶⡄⠀⠀⠀⣿⡄⠀⠀⢀⠀⠀⠘⣿⡇⠀⠀⢰⣷⠀⠀⣰⡄
⠀⢾⡿⠀⠀⠀⠀⠀⣾⣷⠀⠘⠞⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡄⠀⠈⠳⠃⠀⠀⠈⠿⠇⠀⢀⡞⡆⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢿⡷
⡄⠀⠀⢀⡀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⣶⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣸⠀⡟⠀⠀⠀⣿⠀⠀⠀⢠⡀⠀⠀⠀⠀⣼
⡟⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⢰⣷⠀⠀⠀⢸⣿⡆⠀⠘⠚⠁⠀⢀⡀⠁⠀⠀⠀⢮⡳⠀⠀⠀⠀⠸
⠀⠀⠘⠿⠟⠀⠀⢠⡀⠀⠀⣸⣧⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⡞⢆⠀⠀⠀⠀⠘⠟⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⡏⣇⠀⠀⠛⠋⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⣇⢸⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⢠⡀⠀⠀⠀⠀⠸⠟
⣶⡀⠀⢀⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡎⢣⠀⠀⠀⢠⠀⠀⠈⠛⠀⠀⠀⡞⢡⠀⠀⠀⣼⡀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠸⠇⠀⢠⡆
⠿⠇⠀⢸⣿⠀⠀⣄⠀⠀⠀⠀⣴⡄⠀⠙⠋⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠧⠜⠀⠀⠰⣿⠇⠀⠀⠈⠉⠀⠀⠀⣰⣄⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠈⠉⠀⢰⠉⡆⠀⠀⠀⣿⠇⠀⠀⠀⢠⡀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⣦⠀⠀⠸⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⡀⠀⠀⢼⢹⠀⠀⣼⡆⠀⠀⠀⢀⠜⡄⠀⠀⠀⡇⡳⠀⠀⠀⠀⢠⢶⠀⠀⠀⠀⠈⠋⠀⢀
⠃⠀⠀⠿⠇⠀⠀⠈⠁⠀⠀⠀⡔⣇⠀⠀⠀⡄⠀⠀⢰⣿⠀⠀⠈⠉⠀⠀⠻⠏⠀⠀⠀⣮⠀⡇⠀⠀⠀⠉⠁⠀⠀⠀⢠⡇⢸⠀⠀⠀⢀⠀⠀⠀⠸
⠀⠀⢀⠀⠀⠀⠀⣰⡆⠀⠀⣼⠀⡇⠀⠀⣰⣿⡀⠀⠈⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢀⣦⠀⠀⠀⠀⡀⠀⠈⠧⠞⠀⠀⢰⢡⡄
⠀⢀⠟⡆⠀⠀⠀⠿⠇⠀⠀⠘⠚⠁⠀⠀⢻⣿⡇⠀⢀⡄⠀⠀⣸⣷⠀⠀⢰⡆⠀⢰⡀⠀⠀⠀⠸⠿⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢻⡴⠇⠀⣠
⠀⣾⢀⡇⠀⢠⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠉⠀⢀⠇⡇⠀⠀⠘⠛⠀⠀⠘⠁⠀⡎⢹⡀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣧
⠀⠈⠋⠀⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⣾⡆⠀⠀⠀⠘⠶⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⢳⣈⡇⠀⣰⡆⠀⠐⡿⠀⠀⠀⠀⠀⠀⡎⣇⠀⢀⣷⡀⠈⠻⠟
⠀⣤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⠁⠀⢠⡀⠀⠀⠀⠀⢀⣿⡆⠀⠀⢠⡀⠀⠀⠉⠀⢠⣿⣷⠀⠀⠀⠀⢀⠴⡀⠀⠀⠙⠃⠀⠘⠿⠇⠀⢀
⢸⣿⠆⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⣤⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠛⠁⠀⠀⢯⠇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠸⣼⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡞⡆
⠀⠁⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⢼⣸⠀⠀⠀⠈⠁⢠⣾⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⢠⣷⠀⠀⣰⣿⠀⠀⠀⠳⠃
⠀⣀⠀⠀⠻⠜⠀⠀⢀⡼⡀⠀⠈⠁⠀⢀⣤⠀⠀⠘⠟⠀⠀⣠⠀⠸⠏⠀⠀⠀⠀⠀⠸⣿⠆⠀⣤⠀⠘⠿⠁⠀⠀⠀⠘⠿⠁⠀⣿⣿⠇⠀⠀⣀
⢰⣿⡆⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⢠⡇⢣⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⢸⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢸⣿
⠈⠛⠁⠀⡀⠀⠀⠀⠹⠴⠁⠀⠀⢀⡀⠀⠁⠀⡜⡇⠀⠀⠈⢧⡸⠂⠀⠀⠈⠿⠃⠀⣠⡄⠀⠀⠉⠀⠀⣾⣿⠀⠀⢀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⢸⠁⡼⠀⠀⡄⠀⠀⠀⠀⣶⡄⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠈⠁⠀⠀⡎⢀⡇⠀⠀⡤⠀⠀⣾⣇
⠀⠀⢸⣿⡟⠀⠀⠀⠀⣿⡄⠀⠀⠻⠿⠃⠀⠈⠚⠁⠀⢸⣷⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠀⠀⣰⡆⠀⠀⠀⣄⠀⠀⠹⠞⠁⠀⣸⠘⡇⠀⠙⠋⠀⡰
⠀⠀⠀⠉⠀⠀⢀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⠸⢆⠀⠀⠀⠀⠷⠇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⢰⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⢀⠔⠉⠐⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⡠⠁⠈⠔⡠⢂⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠂⠄⠀⡠⠠⠂⠀⠀⠠⠊⠀⠀⠀⢀⠔⡡⡀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢀⢀⠁⠈⠈⠈⠉⡠⠁
⠀⠀⠀⠀⠀⠀⠃⢠⠀⡠⠀⠴⠀⠀⠖⠀⠰⠂⢀⠄⠀⠀⡐⠁⢀⠟⠉⠐⠁⠀⠤⠂⠀⠀⠀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠠⠂⠠⠀⠰⠀⠀⠃⡔⢀⠊⠀⠀⠠⠮⠄⠀⢲⣂⠀⡰⠂⠀⢈⡀⠀⠚
⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⢀⠀⢠⠀⠀⡰⠂⠀⠰⠇⠒⠒⠒⠒⠀⠀⠀⠄⠀⠊⠠⠆⠀⠈⡠⠀⠐
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠉⠀⠃⡤⠀⢀⠀⠀⠀⠰⠂⠠⠊⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠰⠁⡄⠀⠀⠊⠀⠸⠁⢀⠔⠁⠀⢀⠔⠁⡰⠀⡀⠀⠊⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠘⠀⠈⠀⠠⠂⠀⠔⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⣀⠀⠋⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢠⠇⠀⠀⠄⡠⠂⠀⡀⠈⠀⠀⠀⠋⢀⠀⠀⠈⠁⠀⠜
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢠⣊⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡨⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⠀⡔⠀⠀⠀⠀⡠⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣎⠁
⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀
⠀⠀⠀⠀⠐⠛⠛⠋⠉⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⡶⠾⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣀⣀⣀⡄⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠉⠉⢀⡇⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣿
⠀⡀⠀⣠⡶⢻⡄⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠙⣦⠄⠀⠀⠀⠀⠀⠘⣿⠙⠛⠳⠿
⠀⠱⠞⠁⠀⠈⢷⣀⣴⠟⠉⣷⠀⠀⣠⠔⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⢠⣤⣄⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠘⣧⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡇
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠤⠒⠛⠛⢙⡞⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⠈⠁⠸⠆⠈⢢⠀⡀⠀⠄
⠀⠀⠐⠀⠀⠀⢀⣀⡠⠖⠂⠐⠲⣤⢀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠿⢷⢤⣀⡀⠀⣀⣀⡨⠊
⠀⠀⠒⠉⠒⣤⣼⡉⠀⠰⣶⡀⠀⠀⠀⠀⠀⣾⢹⢹⡱⣅⠠⣀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢤⠀⠀⠦⠈⠀⠁⠀⠆⠀⠛⣤⡠⠔⠁⠀⠪⡢⢕⡛⠦⠭⠒
⠀⠈⠷⢬⡁⠀⠈⢀⠀⣠⠔⢈⠄⠀⠀⠀⠀⠀⠀⠁⣀⠁
⠀⠀⠀⠀⠉⠁⠀⠐⠒⠭⠒⠁⠀⠀⣠⣴⡶⠶⠒⠒⠓⠀⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠠⠀⢀⡖⢂⣰⠄⠀⣄⡀⢆⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢣⡘⢦⣀⠀⠀⠀⠀⠀⠈⠔⠀⠀⡞⠀⢀⣠⡤⠄⠠⣄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠉⠑⠏⠉⠉⠉⠀⠀⠈⠀⠀⠀⠉⠁⠀⣀⣤⡴⠙⠀⡆⢀⠐⠲⢄
⠀⠀⢀⣤⣴⣤⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠄⠁
⠀⠠⡜⢜⠎⢯⡳⠽⣶⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⠀⠀⠰⠂⠀⠰⠀⠠⠃
⠀⠀⠈⠒⠅⠊⠭⠓⢒⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢍⠫⠝⠒⠂

⠀⠉⠀⠀⢀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠸⠇⠀⠀⣀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠁⠀⠀⢸⡆⠀⠀⠘⠟
⣧⠀⠀⠀⠸⠂⠀⠀⠉⠀⠀⣸⡄⠀⠀⡀⠀⠀⠀⠰⠇⠀⠀⡄⠀⠀⣠⠀⠀⠀⠀⠉⠀⠀⠀⠶⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⡄
⠉⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⠠⠷⠀⠀⠀⡀⠀⠀⠸⠇⠀⠀⠉⠀⠀⠀⢸⡄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢀⠀⠀⠀⣷⠀⠈⠁⠀⠠⠷⠀⠀⠘⠁⠀⢀⣆⠀⠀⠀⠀⠀⣄⠀⠀⢠
⠀⣠⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠾⠀⠀⠀⢀⠀⠀⠀⠸⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠁⠀⣴⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠸⠂⠀⡀⠀⠀⠀⠀⢰⡆⠀⠀⠛⠀⠀⠀⠙⠀⠀⢠⣷⠀⠀⠈⠃⠀⠀⠀⠀⠀⣼
⠀⠀⡀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠄⠀⠀⠀⢠⣧⠀⠀⡀⠀⠘⠃⢰⡄⠀⠀⣰⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠸⠇
⠀⠘⠃⠀⠈⠋⠀⠀⠀⠀⠿⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠃⠀⠀⠙⠁⠀⠀⠛⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⠀⠀⠻⠂⠀⠀⢀⡄⠀⠀⣰⠀⠀⠀⣤⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠺⠀⠀⢀
⠀⠀⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⣾⠄⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠘⠃⠀⠀⣼⠀⠀⠀⠀⠀⠸⠇
⡆⠀⠀⠀⠀⣆⠀⠀⢰⡆⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢰⠄⠀⠰⠆⠀⠀⣾⡄⠀⠀⢾⠀⠀⣄⠀⠀⠷⠀⠀⡀⠀⠀⠉⠀⠀⢰⡆
⠁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⢰⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠿⠀⠀⠀⡀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⢸⠆⠀⠀⢠⣧⠀⠀⠀⠙⠃⠀⣠⡀⠀⢸⡆⠀⠀⠀⠿⠀⠀⢰⡆⠀⠀⠛⠀⠀⣦⠀⠀⠀⠀⠸⠇⠀⠀⠀⣴⠀⠀⠃⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⣆⠀⠀⠀⡄⠀⠉⠀⠀⠀⠀⣾⡀
⢰⡄⠀⠀⢰⠆⠀⠀⠀⠘⠛⠀⠀⣧⠀⠀⠀⣆⠀⠀⠿⠀⠀⠘⠃⠀⠀⠀⠁⠀⡀⠀⢠⡄⠀⠈⠋⠀⠀⠈⠉⠀⠀⠀⢰⡆⠀⠉⠀⠀⠘
⠀⠀⢀⠀⠀⠀⢰⡆⠀⠀⢠⡀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⡆⠀⠀⠀⢰⡆⠀⠀⣷⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⢰⡆⠀⠀⠀⠀⢀⣆
⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠘⠃⠀⠀⠀⠀⣰⠀⠀⢠⠀⠈⠛⠀⢰⠀⠈⠉⠀⠀⠀⠀⠀⠀⠼⠇⠀⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠈⠉
⠰⠄⠀⠀⢠⡆⠀⠀⠀⢠⠀⠀⠀⣸⡆⠀⠈⠀⠀⠸⠇⠀⠀⠀⡀⠀⠀⠀⣴⠀⠀⣦⠀⠀⠀⠀⠀⣤⠀⠀⢸⣇⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠉⠀⠀⠉⠀⠀⣶⠀⠀⠛⠀⠀⠀⠁⠀⢀⡄⠀⠀⠉⠀⠀⣦
⠀⠰⠇⠀⠀⠀⠿⠀⢀⠀⠀⢰⠄⠀⢀⡄⠀⠉⠁⠀⠀⣾⠄⠀⠀⠀⢀⣇⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠀⢴⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠉
⠀⠀⠀⢰⡆⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠸⠗⠀⠀⢀⣇⠀⠘⠁⠀⠀⢠⡧⠀⢠⡄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠋⠀⢀⠀⠀⠀⣄
⠀⠛⠀⠀⠀⢸⡆⠀⠀⢰⠀⠀⡀⠀⠀⢠⡆⠀⠀⢀⡀⠀⠉⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠁⠀⢠⡆⠀⠀⢼⠆⠀⠀⠿
⠀⠀⢀⡄⠀⠈⠀⠀⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠙⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠃⠀⢀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡄⠀⠀⠻⠃⠀⠀⢠⡇⠀⠀⠉⠁⠀⠠⠇⠀⠀⠈⠁⠀⠀⠀⠺⠀⠀⠀⠿⠀⠀⠸
⠀⣴⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⡀⠀⠀⠘⠗⠀⠀⢀⠀⠀⠀⢠⠁⠀⠀⠀⣶⠀⠀⠀⠀⣆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣤⣤⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠋⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⣠⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠆⠀⠀⠈⠛⠻⠿⠿⠿⠟⠋
⠀⠀⠈⠳⠤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣾⡟⠹⣷⠶⣄
⠀⠀⣄⣀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⣿⣿⣿⣷⣶⣾⣯⣽⣿⣿⣿⣟⣿⣿⣾⣯⣿⣯⣯⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⢿⣿⠿⠛⠉
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣾⣿⡶
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠟⠓
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁
⠀⠀⣀⣤⣄⣴⣦⣤⣀⣤⣶⡀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀
⠀⠀⠿⢿⣿⡿⠋⠿⡿⠟⠿⠃⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡏⠀⢀
⠀⠀⠀⠀⣿⣶⣶⣶⣶⠄⠀⠀⠀⠀⠉⠁⣿⡇⠉⠀⣀⠀⠀⠀⠀⠀⠈⢛⣡⡀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣶⣛⣿⣶⣶
⠀⠀⠀⣤⣿⣿⣿⣿⣿⣤⡄⠀⠀⢀⣤⣤⣿⣷⣶⣾⣿⡧⠀⠀⢀⣀⣿⣿⣿⣿⣿⣀⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠛⠿⠿⣿⣿⣿⠿⠿⠛⠀⠀⠀⠀⠈⠙⠻⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠶⢶⣄⣀⣠⡶⠞⠳⢶⣄⣀⣠⡶⠖⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠀⣀⣶⣤⠾⠋⠁⠘⢷⣄⣀⣀⣴⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡀⠀⢠⣶⡀⠀⠀⣴⣦⠀⠀⣼⠛⣧⠀⢠⡿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⠀⠀⢿⣨⡷⠀⠸⣇⣽⠆⠀⠙⢛⡋⠀⠈⠛⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣧⠀⠀⣭⣤⠀⠀⢨⣥⡄⠀⠀⣿⢻⡄⠀⢸⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠋⠀⠀⣏⣹⡇⠀⢸⣏⣿⠀⠀⠻⠞⠃⠀⠘⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⡀⠀⠈⣉⡀⠀⠀⢉⣁⠀⠀⢀⡾⣦⠀⠀⣰⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠇⠀⢸⡏⣷⠀⠀⣾⢹⡆⠀⠸⣧⡾⠃⠀⠻⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠙⠛⠁⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣆⠀⠀⠀⠀⠀⠀⢾⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠀⠀⠀⠀⠀⠀⠀⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⢰⣿⣶⡆
⠀⠀⠀⠀⠀⠀⣼⣿⡟⢁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣾⣿⠟
⠀⠀⠀⠀⠀⣼⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⣼⣏⣀⡀⠀⠀⠀⢰⣿⣯⣤⡄
⠀⠀⠀⠀⠰⢫⣿⣿⢏⣠⠄⠀⠀⠀⠀⢰⡿⢀⣠⡄⠀⠀⠀⢰⣿⣿⣶⠀⠀⠀⠐⠛⣻⡟⠀⠀⠀⠀⠞⢻⣿⡿
⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⢛⣿⣿⠃⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠚⢁⣿⣿⠃⠀⠀⠀⠀⠀⠟⠋⣽⡟⠀⠀⠀⠀⠀⣸⣿⣿⡶⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣸⣿⣃⡀
⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠟⣿⡿⠁⠀⠀⠀⠼⠿⣿⠁⠀⠀⠀⢀⣿⣿⡟⠁
⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠘⣹⡟
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⢰⣶⣶⡶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣶⣶⣶⡶
⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⣼⣿⣿⣿⣶⡦
⠀⠀⠀⠀⣰⣿⡟⠀⠀⣀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⢠⣿⣿⣀⠀⠀⠘⠛⢻⣿⣿⣿⠁
⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣤⡄⠀⠀⢀⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠛⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣷⣶⠂
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠾⢿⣿⡿⠁⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⣿⡶⠀⠀⠀⠀⠉⢹⣿⣿⠃
⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢉⣿⡿⠁⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠉⠉⠉⠙⠶⠖⠋⠉⠉⠙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⡀⣀⣀⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣐⡢⠀⠀⠀⠀⠀⠈⠏⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⠭⠶⠖⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠤⢀⣀⠀⢀⣀⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣔⣰⡠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠋⠉⠀⠀⠉⠳⣞⣡⣖⣠⠖⠳⢴⣠⢖⣰⣦⠾⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⠃⠈⠁⠀⢀⡤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠃⠀⠀⢀⡴⢋⠗⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠰⠿⠶⢞⡶⠂⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⡯⠴⠒⡾⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⠖⠉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⢞⡵⢋⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⣾⠗⠉⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀
⣟⣛⣻⣛⣟⣟⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣻⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠙⢆⠀⠀⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡼⠀⠀⡰⢶⡀⠀⠀⠀⠀⠳⢄⣠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⣸⠁⢳⡀⠀⠀⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠘⢦⠴⠃⠀⠀⡇⠀⠀⢣⠀⠀⠀⠑
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣸
⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠃
⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠹⡀⠀⠀⠀⠀⠀⠉⠒⠒⠁⠀⠀⠀⡸⠉⠳⣄⠀⠀⠀⠀⢸⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣼⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡏⣿⠟⢹⣿⣿⡿⡻⡝⣯⢻⣝⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⢶⣿⠉⣽⣿⠋⣙⡟⠛⣿⡛⠛⠛⠛⢛⡟⠻⡛⢛⠛⣿⡟⠛⣛⠙⢫⣭⠍⢹⣷⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠸⠁⠀⢹⠃⠀⢫⠁⠀⡭⠀⠀⡁⠀⠸⡏⠀⢱⡆⠀⢻⠇⠀⢻⠁⠀⢻⠀⠀⠻⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿
⡇
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠐
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠰⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠘⠅⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡁
⡇⠀⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⡇⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠐⡀⠀⠀⠀⠀⠀⠀⠀⠆
⡇⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⣧⣀⣀⣄⣀⣄⣀⣀⣤⣀⣠⣄⣤⣤⣄⣠⣤⣄⣤⣄⣀⣀⣀⣀⣀⣠⣄⣤⣀⣀⣄⣤⣀⣀⣀⣠⣄⣄⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠷⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠉⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠹⠟⠉⠉⠛⢿⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⢷⡄⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠿⢟⣿⣶⠀⠀⠀⠀⢀⣤⣤⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣐⣿⡅⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣦⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣸⡏⠀⠀⠸⣿⣿⣦⣄⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⣷⣿⠃⣀⣤⣄⠀⢀⣿⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠻⣿⡿⠿⠶⠶⠶⠾⠟⠋⠁⠀⠈⠿⠾⠛⢹⡿⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠿⠷⠿⠿⠆⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢀⣀⡀⢀⣿⠁⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⢠⣿⠉⠻⣾⠏⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣸⡏⠀⡀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣿⡿⣷⣄⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⢸⣿⠃⠀⠀⠙⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠉⠛⠋

⠀⠀⠲⢰⡂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤
⠀⠀⠀⢸⠇⡈⠀⠀⠀⠰⣆⠀⠄⢀
⠈⢷⠀⣸⠀⠠⠂⠂⠀⢇⡀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠤⢄
⢀⠀⢹⠟⣼⠀⠈⢠⣿⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⣦⣄
⠀⠳⣼⡶⠀⠀⠐⣠⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠘⡄⠀⠀⠘⢩
⠀⣄⠘⣦⣴⢤⢀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⡀⠀⠀⠌
⠀⣽⣶⣿⣹⡾⣏⠀⠀⠀⢀⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⠂
⠀⠈⢻⣿⠋⠀⠈⢳⠶⣤⣄⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠉⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⣸⣿⡀⠀⠀⠀⠀⠁⣸⣹⠿⠀⠀⢀⣠⣴⣶⡶⠓⠃⠉⠁⠀⡤⡄⢀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠸⠇⠿⠃⠀⠀⠀⠐
⠀⠀⣹⣿⡁⠀⠀⢰⠀⡄⣠⣿⡤⠔⠋⠉⠁⠀⠀⠠⣶⣴⣴⡆⠀⠃⠀⠘⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠈⠉⠃⡝⠊⠁⠀⠀⠀⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣤⡄⠀⠀⠀⠀⣶⣿⣿⣿⣿⣽⡟⡼⠽⠫⡱⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠿⢿⣿⣯⣦⣧⣀⡇⢠⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠐⠱⠇⠘⠘⠸


⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠤⠤⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⢤⡀⠀⠐⣶⣄⣠⠴⠚⢉⡉⠉⠉⠉⠉⠐⠒⠂⠤⢄⣀⡀⠀⣈⣉⠲⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⢀⣼⠃⠠⡀⠀⠀⠀⠉⠑⠂⠤⣀⠀⠀⢀⣠⡤⠽⠻⠅⠀⡠⠚⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣱⢾⡉⠀⠀⠀⠀⢀⠞⠀⢄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠏⠀⣇⠀⠀⠀⠀⠀⢀⡠⠔⠚⠫⠤⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣸⡿⠀⠀⡇⠙⢳⠄⣠⠖⠉⣠⠴⠒⠛⠒⢄⠱⡄⠀⣀⣠⡤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⡇⠀⠀⢡⠀⢀⣴⠁⠀⣸⠅⠐⠀⠄⠀⠦⢱⠱⠊⠉⠐⢄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣀⠈⠀⠀⠘⣀⡏⣼⠀⠠⡟⠀⠠⣦⠀⠁⠺⠏⢸⠀⠀⠀⠀⠑⠢⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⡠⠒⠛⠀⢿⠘⠀⠱⡆⠀⠀⠀⣒⡀⠐⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⢠⠎⠀⠀⠀⠀⠈⢧⡀⠀⠙⣤⠄⠈⠉⢴⡶⠖⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⡠⠛⣱⠋⠷⠒⠁⢰⣾⣝⢶⠤⣄⡀⠙⠦⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠋⠁⠀⣀⠤⠔⠲⠎⢀⡼⠁⠠⠤⢴⢶⡆⠸⣒⠇⠑⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡎⢀⡴⠋⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡎⡼⠷⠚⢩⠋⠀⠀⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢁⠊⠀⠀⠓⣄⠀⡴⠃⠀⠀⠀⠀⠰⢰⠃⠀⠀⢈⡶⢎⠋⠹⡙⠿⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⢀⡿⢅⠀⠀⢆⠀⠀⢸⢸⠰⡖⠈⠁⠀⠈⢧⠀⠈⢮⠢⣴⢄⢱⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠎⠀⠈⠑⢄⠈⠢⡄⠈⠄⣿⠀⠀⢄⠀⠀⠀⢣⠀⠀⠑⢎⠑⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠁⠀⠀⠈⢳⡀⡀⠀⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡜⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⢄⣰⣀⣀⡀⠀⠀⠀⠉⠁⣀⣀⣀⣀⣤⠤⠖⠚⠃⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠽⠉⠉⠉⢙⠫⢄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠀⠀⠀⡞⠁⢯⠁⠀⠀⣀⡴⠃⠀⠀⢣⠀⠀⠀⠸⣄⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠛⢦⠀⠑⢶⡏⠀⠀⠀⠀⠀⢈⣣⠀⡠⠂⢉⣸⡇⠀⠀⠀⠀⠀⠀⠈⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠸⣅⠀⠀⣠⡝⠒⠡⠤⠤⠔⠋⠉⠉⢉⠀⢸⣀⠔⠋⠈⠳⢤⡶⠒⣄⠘⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⠄⠀⠙⢧⠀⠈⢱⡀⠀⠀⣦⠀⠀⠀⠀⠘⠁⠀⠋⠱⣄⠀⢢⠎⢀⣠⠋⢀⡭⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⠓⠤⠞⠃⠀⠈⠃⠀⠀⠂⢀⠀⠀⠆⠀⠀⢹⡴⠛⣳⠏⠀⣀⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠷⠤⠤⠒⠒⠉⠉⠉⠉⠉⠙⠒⠒⠒⠊⠀⠀⠡⠤⠤⠤⠉⢉⡁⠼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠰⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣶⡄⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠸⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀⣠⣴⣿⣾⣿⣿⡇⠀⠀⠀⠤⢴⡏⠁⠀⠀⠀⠀⢸⠿⣿⣿
⠀⠀⣠⣤⣿⣿⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣤⣀⣠⣷⣄⣶⣾⣷⣶⣴⣿⣿⣿
⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⢉⣉⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⠓⢦⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠲⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⡷⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡠⠀⠚⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡞⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⢰⠀⠀⠀⡴⠀⠀⢠⠂⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠇⠀⠀⣠⠁⠀⠠⠃⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⡖⠀⠀⢰⠃⠀⢀⡆⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⡄⠀⠀⠀⠃⠀⠀⡌⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⡸⠁⠀⠀⠏⠀⠀⡼⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢰⠃

⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⢠⠠⠀⡆⢀⢆⠀⡀⠄⡄⠀⡄⠀⠀⡄⠀⠲⠀⡄⠄⡠⠀⡄⣄⠄⢀
⣀⣀⣀⣀⣀⣀⣀⣤⣀⣤⣔⣰⣀⣇⣜⣘⣄⣥⣇⣧⣄⣧⣄⣀⣬⣃⣸⣀⣏⣃⣣⣤⣂⣏⣢⣨⣄⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⢒⡲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⣠⠖⠁⠀⠀⠀⠑⡄⠑⠢⡀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢢⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⡱⠦⣀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢀⠎⠀⠀⠈⠲⠥⠤⣤⠤⣀⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⢴⠁⠀⢰⠁⠉⠑⠢⢴⠤⠔⠒⠒⠒⠾⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠾⢁⣸⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠠⠁
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⡸⣒⣈⡜⠁⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠸⡁⠀⠑⠓⠚⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠙⠦⣀⣀⣀⡠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⡠⡶⠈⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⠨⣖⣤⣤⢈⣉⣀⣈⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⢘⡟⠁⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡏⠁⠀⠀⠀⢫⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⡄⢀⣀⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢛⣛⣛⠶⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⠴⠊⢉⣀⣀⠀⠈⢻⣄⣤⠾⠛⠉⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⢸⡟⠁⡠⠖⠉⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡠⠔⠂⢉⡛⢷⣾⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⢀⠔⠋⠉⠀⣀⡈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡈⢿⣠⠃⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠟⠛⠉⠉⠉⠉⠉⠛⢷⣄
⠀⠀⣠⡶⠛⣫⠽⠛⠉⣉⡻⠿⢿⡄⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⢠⡾⢁⠔⠋⠀⣀⠴⠊⠁⠀⣀⠤⠶
⣿⡵⠃⠀⡠⠊⠁⠀⣀⠔⠋⠁⠀⢀⣠⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢿⡄⢀⠞⠀⠀⢀⠞⠁⠀⠀⣠⠖⠉⠀⢀⡠⠔⠒⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠈⠻⣎⡀⠀⡰⠁⠀⠀⣠⠎⠀⠀⢀⠔⠉⠀⢀⡤⠒⠉⠀⣀⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠉⠛⠶⣧⣄⣀⣰⠁⠀⠀⡴⠁⠀⠀⡰⠋⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡞⠀⠀⢠⠇⠀⠀⢸⠁⠀⠀⢰⠂⠀⠀⢸⠃⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠚⠀⠀⠀⠃⠀⠀⠀⠏⠀⠀⠀⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣸⠁⠀⢀⡏⠀⠀⢀⡇⠀⠀⢰⠃⠀⠀⡸⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⢠⠄⠀⠀⡀⠀⠀⢠⠄⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⡇⠀⠀⣸⠀⠀⠀⡜⠀⠀⢰⠃⠀⠀⡞⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠆⠀⠀⡤⠀⠀⢀⡆⠀⠀⡤⠀⠀⣰⠂⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠼⠀⠀⢰⠇⠀⠀⠼⠀⠀⢰⠃⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠠⠇⠀⠀⠴⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠿⠿⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⠿⢷⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⣤⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠉⠉⠛⠿⣶⣄⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠉⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⣶⣶⣶⣤⣄⠀⣿⡆
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠛⢿⣾⡇
⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢿⣦
⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻
⠀⠈⠙⠿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣽⡟⠉⠉⠉⠉⣩⣿⠋⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢀⣼⣿⣥⣤⣬⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣃⣀⣀⣀⣀⣈⠉⠉⠉⢉⣿⠏⠉⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⢶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⢠⣾⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣀⣀⣀⣀⣉⠉⠉⠉⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣿⡏⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⢦⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠛⠻⢦⣀
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡾⠛⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⢀⣤⠿⠶⠶⢾⠏⠀⠀⠀⠀⠀⠀⠹⡷⠶⠶⠶⣤⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠉⠉⠉⠙⢷⡄⠀⠀⠀⠀⠹⣆
⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⠞⠛⠛⠷⣦⣿⡄
⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠉⠛⢻⡛⠛⠛⠛⠛⠛⠛⠛⠻⣟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⣠⣴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠋
⢠⡾⠋⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣏⠉⠁
⠘⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⣴⠟⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⣠⡴⠟⢻⡄
⠀⠈⠉⠉⠁⠀⠀⠀⣤⠀⠸⣏⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣿⠀⠀⣾⠋⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢀⣤⡾⢻⡇⠀⠙⠛⠛⠋⠀⠀⠀⢀⣼⣧⠀⢸⡏⠀⠀⣸⡏⠀⠀⢻⣤⣤⣼⠏
⠀⠀⠀⠀⣰⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⣿⠀⠈⠻⠶⠾⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠹⣦⣀⣠⡿⠁⠀⠀⠀⠀⠀⠰⣟⠀⠀⢠⡿

⠀⠀⡖⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣰⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠂⠐⠀⠀⠈⠁⠐⣄⢻⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢘⠆⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⣈⣀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠆⣴⣆⣸
⠀⠀⠀⠀⠀⠀⢀⡴⢦⠀⠀⠀⠀⠀⠦⠀⠛⠤⠄⠀⠚⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⣿⣦⣞⣵⣿⣿
⠀⠀⢰⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣾⣿⡆⠀⠀⠀⠀⣀⣤⠞⠋⠀⢀⣸⣿⡿⣤⡀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢀⣠⢀⢀⣠⠄⡄⠤⠀⢴⣴⡿⠿⣿⠿⢁⣠⠴⠋⠙⠏⠀⣀⣴⣶⢿⡟⠁⠀⠹⢿⣾
⠀⠀⢸⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣖⡛⠛⠽⠟⠒⠀⣨⣴⠞⠛⠟⠁⠀⠀⠀⠀⠀⠈⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠋⡡⠛⠉⢀⣤⣶⣶⡿⠟⠛⠁⠀⠀⠀⠀⢠⣖⣦⣮⣿⡀⢸
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣂⣀⣠⠊⠀⢀⡶⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠟⠁⠀⣴⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣾
⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢉⡉⠉⣉⣻

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⣜⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣿⡧
⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄
⠀⠀⠀⠀⠀⢾⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡝⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢿⡷
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠻⣘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣻⠏

⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⣼⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣧
⠀⠀⠀⠀⠀⠙⠬⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠽⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡤⢖⣛⣉⣍⣙⣓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⣭⣭⣭⣭⣛⠲⣫⠖⠛⠉⠉⠉⠛⠻⢷⣮⡳⣄
⠀⠀⠀⠀⠀⠀⢠⢞⡴⠋⠉⠀⠀⠈⠉⠋⠀⠁⠀⢀⣀⣤⣤⣤⣄⡀⠙⣷⣬⣝⣓⠶⣄⡀
⠀⠀⠀⠀⠀⣠⡏⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠞⠋⠉⠀⠀⠈⠉⠛⢷⣌⠉⠙⠻⣷⣦⣙⣶⠶⢤⣀
⠀⠀⣠⢖⣯⢿⡴⠟⠋⠉⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠉⠛⠛⠿⢷⣮⡙⢦
⢀⡞⠑⠋⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⢳
⣾⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠈⠳⠦⣄⣀⣀⣀⣤⠴⠚⠓⠒⠒⠛⠲⣄⣀⠀⠀⠀⣀⣠⠴⠛⠶⢤⣄⣀⣤⡤⠶⠶⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⣰⣿⠀⢀⡴⣷⠀⠀⠀⠰⡇⢀⣼⡷⠀⣠⠾⡇⠀⠀⠀⢸⡁⣀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⠛⠛⠁⢠⠏⠀⣹⡄⠀⠀⣠⠙⠛⠛⠁⣴⠃⠀⣿⠀⠀⢀⣄⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣧⠀⠀⠀⠘⢤⣶⡿⠃⣠⠞⢹⡇⠀⠀⠀⠻⣴⣾⠟⠀⡴⠋⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣏⢀⣠⣿⠀⢀⡴⣷⠀⠀⠀⠰⡇⢀⣼⡷⠀⢠⠾⣇⠀⠀⠀⢸⡁⣀⣼⡇
⠀⠀⠀⠀⠀⠀⣠⡌⠛⠛⠁⢠⠏⠀⣸⡆⠀⠀⣠⠙⠛⠛⠁⣰⠋⠀⣿⠀⠀⢀⣤⠙⠛⠋
⠀⠀⠀⠀⢀⡜⠉⣷⠀⠀⠀⠘⢦⣶⡿⠃⣠⠞⢹⡇⠀⠀⠀⠹⣤⣾⠿⠀⣰⠋⢹⡄
⠀⠀⠀⠀⣿⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠰⡇⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢸⡁⣀⣼⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠙⠓⢦⡀⠀⠀⠀⣠⠴⠶⠶⢤⡀⣠⠴⠚⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠖⠚⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⣄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⣸⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡄
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠒⠚⠛⠉
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⠀⠀⢀⣡⠞⠛⠓⠶⣾⠟⠁⠈⠙⠓⠶⠦⣤⣤⣤⣴⣶⠟⠛⠶⢦⣤⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⡤⠶⠾⠛⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡠⠂⠀⠴⠗⢚⡽⠃⠀⠀⠀⠀⠀⠀⠀⠠⣠⡾⠃⠀⠀⣠⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⠜⠁⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠴⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣥⡤⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠚⣹⠏⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⠃⠀⠀⠀⣠⠾⠋⠀⠀⠀⢀⡔⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣰⠃⠀⠀⣠⠾⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠋⠉⠉⣩⠽⠛⠓⢶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠳⡄⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⣏⣀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠛⠢⣀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⠲⠧⠤⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣸⠉⠑⠲⠤⣄⠀⡟⣀⣀⡤⠤⠤⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣀⠴⠋⣿⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠘⠳⠦⠤⢧⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠜
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⣛⣒⢊⣡⠊⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡞⠀⠈⠻⢼⣀⠴⢯⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⠓⢤⣄⣀⡤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⢀⡴⡳⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⣄⣀⠀⠀⠛⠋⠀⠐⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠹⣿⣿⠟⠙⢳⣶⣶⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⣠⠽⠀⠀⠀⠀⣿⡿⠷⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⠇⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠁⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠛⠓⢯⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠃⠀⠀⠘⠛⠋⠀⣀⣀⣤⣴⣤⣀⠀⠀⢺⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⢁⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣜⣟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠂⠀⠲⣿⠹⢷⣴⣶⣶⣾⣶⣶⣾⣿⣶⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⣶⣦⣤⣶⣿⣿⢶⣤⣀⣤⣤⣄⠀⠀⠀⠀⠀⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠷
⠀⠀⣿⣿⣿⠋⣿⣿⣼⣿⣿⣿⣿⠿⠁⠀⠀⠀⠐⡇⠀⠀⠈⠉⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠁⠀⠀⠀⣿⣿⡏⠉
⠀⠀⣿⡿⣿⠀⣟⣻⣾⢿⡿⣻⡏⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⢧⣿⣿⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⣿⠏
⠀⠀⣿⡇⣿⠀⠀⠀⠀⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⠟⣿⣿⣿⡿⣧⣾⣿⣿⣿⣶⠀⠀⢰⡇
⠀⢰⣿⠀⣳⢤⡴⠦⠶⠶⠶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⡀
⠀⢸⣿⠀⣿⣶⢶⡄⣮⣠⠀⣿⠀⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⢼⣿⣿⣿⡇
⠀⠈⢿⣄⡏⣿⠄⡇⢸⣿⡇⣾⡇⠀⢰⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠀⢸⣿⣿⣿⣷⡀
⠀⢰⡇⣿⡇⠗⠘⠃⣾⢿⠃⣿⣧⢀⣿⣯⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠈⣻⣿⡿⠃
⠀⢸⡇⣿⡇⡎⣠⢄⢀⠀⠀⣿⣿⣿⣿⣤⣿⡀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⠀⠀⠀⣼⣿⣿⣿⣿⣷⣴⣾⣧⠉
⠀⠠⣶⣿⡇⠟⣿⡏⠰⠷⠆⣿⣿⣿⣿⡿⢿⣻⣿⣠⣄⣶⣄⠂⠀⠀⠀⠈⠁⠈⠃⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢻⣿⡇⠇⠈⠀⠁⠀⣀⣿⣿⡿⠿⠗⠾⢻⣿⣿⣿⠏⢏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣾⢿⣷⣄⣠⣴⣶⠛⠋⠀⢀⣴⡾⢓⣵⡿⠟⢹⠏⠂⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⢹⣿⣿⣿⣿⠁⢹⠇
⠀⠀⠘⣻⣿⣯⢿⣿⣿⡟⠛⢛⣷⡿⣶⠉⣽⠁⠀⡼⠘⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢹⣿⡏
⠀⠀⠀⣼⣿⣿⡿⣿⡟⢷⡄⢸⡏⠀⠙⣧⡏⢐⠀⣰⣂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⢸⣿⠃
⠀⠀⠀⠽⣟⣭⡞⠋⠀⠀⢳⣸⠇⠀⠀⠈⢿⣵⣾⣿⢷⣿⠿⡐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⣿⠁⠀⣾⡿
⠀⠠⠖⠚⠉⠀⠀⠀⢀⣠⠄⠋⠀⠀⠀⠀⠀⠙⣿⢃⡴⠿⣀⡸⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠘⠿⣿⡄⠀⣿⣇⠄
⠀⠀⢀⣀⣠⣴⠒⢚⠉⠀⡀⢈⡄⠀⠀⠀⠀⠀⠈⢿⣿⣶⠏⢀⠀⠀⠀⠑⠀⠀⠀⠠⠉⠀⠀⠀⠉⠛⢠⡿⠋
⠀⠀⠈⠛⠛⠻⠿⣿⣆⠀⢳⡈⢧⡀⠀⠀⠀⠀⠀⣈⡿⣿⣷⣏⡀⠀⠀⠀⠐⠂⠀⠂⠄⠀⢀⡄⢲⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠺⢿⣿⣦⠀⢻⣌⢷⡄⠀⢀⣤⠾⠛⠀⠠⣄⠋⠀⠀⠀⡴⠀⠀⣤⠦⡤⡄⠈⢀⣿⡿⠛⠂
⠀⠀⠀⠀⠀⠀⠴⠛⣿⣿⣷⣀⣹⣦⣿⠾⠓⠂⢀⡀⢠⣠⠆⠉⠝⡀⠖⠂⢠⠀⠄⠀⠠⣍⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣽⠛⠛⢻⡿⠟⠉⠀⠀⠲⠀⠀⢠⠊⠀⠁⠘⠀⠂⢐⠀⢄⠉⠐⢚⣿⣿⣿⣿⡿⠀⠐⢀
⠀⠀⠀⠀⠀⢠⢀⣤⣶⣾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⡦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠟⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉⠉⠉⠉⠙⠛⢿⣿⣿⣷⣄
⠀⠀⠀⢀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆
⠀⢀⣴⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣄⡀
⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣷⡄
⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠘⢿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⠀⠈⠻⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⠋
⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡄⠀⠀⠀⠀⠀⣴⣿⣿⣷⡀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⢀⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠋⠀⠀⠀⠀⠈⠻⢿⣿⠿⠃⠀⠀⠀⠀⠈⠻⣿⣿⠿⠃⠀⠀⠀⠀⠘⠿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⣸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠛⠓⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠛⠛⠓⠲⠶⢤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣀⣤⡤⠶⠆⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠋⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⢤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁



⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠯⢼⠟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢿⢨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠠⡏⠙⢦⢸⠈⢻⠉⢠⢳⠀⢸⣙⡆⣶⠀⢰⣏⡁⠀⠰⣋⠀⠙⡟⠁⣏⣹⢠⡞⠙⢦⢸⣠⠋⢸⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣀⡐⣇⣠⠞⢸⠀⣸⢀⡟⠉⣇⣸⣀⡇⣿⣀⣘⣇⣀⠀⢀⣈⡇⢀⡇⢀⡇⢹⡘⢧⣀⡞⢸⡉⢦⣸⣀⡀
⣿⣿⡿⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣠⡶⠟⠛⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⣀⣿⣦⣤⣤⣾⠋⠀⠀⠀⠀⠀⠈⢻⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⢠⡾⠋⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⢻⣦⡶⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠙⢷⡄
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢻⣦⣤⠶⣤⣤⡈⣿
⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠻⣿
⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠙⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⢀⣴⠾⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣙⡳⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠛⠁
⢠⡟⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣠⣴⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠈⢿⣤⣤⡾⠋⠀⠀⠀⠀⠀⣰⡟⠉⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⠀⠀⠀⣠⡶⠟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢻⣆⡀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠁⣿⠃⠀⢸⡏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⢀⣤⡾⠛⣿⠀⠀⠉⠛⠋⠁⠀⠀⠀⣀⣼⣷⠀⢸⣏⠀⠀⢠⡿⠀⠀⠘⢷⣤⣴⠿⠁
⠀⠀⠀⠀⢰⡟⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣴⠾⠋⠁⣿⠀⠀⠙⠷⠾⠛⠁
⠀⠀⠀⠀⠘⣧⣄⣠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⢠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠠⠄⠀⠀⠁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣤⣤⡄⠄⠀⠀⠈⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⠻⠇⣀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⡀⠄⠦⡀⢄⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠠⠀⡌⠑⠢⠤⠠⣄⣀⣀⠀⠀⠀⡠⠐⠉⢊⣵⢴⠈⠢⢅⠄⡀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⣲⣦⠀⢉⣙⠘⠍⠀⠀⢀⠐⠚⢂⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠛⠰⠿⢶⡇⢀⠀⡏⡭⢽⠀⡇⡛⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢠⡀⠄⠀⢲⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢀⠀⠀⠁⠀⠀⠀⠀⡀⠰⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠊⠠⠔⠂⠁⠀⠀⠀⠀⠀⠂⡀⠀⠀⠈⠀⠀⠀⠀⠀⢈⠈⠂⠉⣋⡐⣄
⠀⠀⠀⠀⠀⡐⢃⣤⡁⠀⠀⠀⠀⠁⠤⠤⠀⠀⠀⠀⠠⠀⠢⠀⠈⢀⣀⠀⠀⠒⠒⠢⡥⢜⠁⠉⠉⠁⠈⠋⠄⠁
⠀⠀⠀⠀⠀⠰⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠀⠠⠄⠀⠂⠐⠂⠀⠄⠀⠠⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⣌⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠁⡗⠰⠾⠃⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⡀⣠⠤⢴⠒⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠴⠒⠈⠀⠔⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢐⡪⡆⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠠⢪⣵⠗⡄⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠈⠿⡿⠀⠀⠀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠘⢴⠴⡺⠁⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣷⢿⣿⣷⠀⠀⠀⠀⠀⡰⡈⡎⢌⢎⠁⠀⠀⠀⣬⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢻⣟⣿⣿⠀⠀⠀⠀⢐⢘⢰⢩⢣⢂⣣⡄⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣟⣿⣿⣿⠀⠀⠀⠀⢘⠂⠡⢮⢎⠒⢘⡀⠀⠀⠀⠀⠉⠁⠀⠀⣴⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⡿⠏⠀⠀⠀⠀⠀⠨⢈⡔⡆⡌⠹⠂⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⢹⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡽⣤⡇⠀⠀⠀⠉⠋⠁⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣳⣶⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣷⠶⠞⣣⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⢀⣽⡛⠞⢉⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⣻⣿⣾⣯⣋⡆⠀⠀⠀⠀⢸⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢿⣿⣿⠀⠀⠀⣼⢿⣿⡇⠀⠀⢰⣿⣽⠿⣮⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢿⣝⣶⢏⣿⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠉⠙⠊

⣄⠀⠀⢤⠀⠀⡀⠀⢀⠀⠷⠀⠀⠀⡄⠀⡦⠀⢀⠀⢰⡄⠀⢀⡀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⡀
⠚⢰⡀⠈⠀⠀⠇⠀⠸⠆⠀⠀⡆⠀⠁⠀⠀⠀⠘⠀⠈⠀⣄⠘⠇⠀⠀⠀⠋⠀⣤⠈⠃⠀⠐⠖
⠀⠈⠁⠀⢸⠀⠀⢠⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣹⠀⠀⠀⠛⠀⠀⠀⢠⠀⠀⣆
⢲⠀⠀⡄⠀⠀⠀⠐⠃⠀⠀⣆⠀⢲⠀⠈⠀⠀⡄⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠴⠀⠗⠀⠸⠀⠀⢈
⠈⠀⠀⠋⠀⢰⡄⠀⢰⠀⠀⠁⠀⠀⡀⢀⡀⠠⣧⣀⡀⠀⠀⠛⠀⠀⠀⢲⠀⠀⠘⠀⠀⠀⡀⠀⡀⠘
⠀⢀⡆⠠⡆⠀⠀⣀⠤⢐⣠⠻⢛⠥⠢⠐⠀⠀⢈⡄⠂⠌⠉⠙⠒⠶⣤⡬⠀⣀⠀⠀⠀⠸⡥⠀⣥
⢀⠀⠋⠀⣠⣔⠚⠉⡴⡫⠡⢊⠩⡂⠈⠀⠀⠀⠀⠐⠈⠂⠉⠀⠀⠀⠈⠙⠲⡠⠈⠁⠢⢄⡀⠀⢠⡄
⠸⠀⡠⠊⠀⠁⠀⡜⢘⠨⡂⢑⢅⠂⠁⠀⠀⠀⠀⠀⠁⠁⡀⠀⠈⡀⠀⠀⠀⠘⢦⠀⠀⡀⠈⠢⡈⠁
⢀⢎⣢⠴⠀⠀⢰⢐⠕⠨⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⡀⢀⢀⠀⠀⠀⠈⣧⢐⠀⠀⡄⢝⡄
⠟⠉⠀⠈⠉⠀⣬⡵⠖⠓⠉⠈⠉⠉⠈⠙⠓⢦⣤⡀⢠⢠⣤⠴⠿⠓⠂⠡⠠⠤⠾⢜⡵⠚⠉⠈⠉⠙
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣗⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣉⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠁⠀⠂⠀⠀⠂⠔⠄⠠⠢⠠⠈⢄⠁⠌⠀⠨⠢⢀⠕⢔⢄⢀⢀⠀⡠⡂⡠⢀⢄⠔⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡐⡄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣧⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣿⠄⢀⠀⡀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠏⠂⢄⣱⣹⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣒⢾⣿⣽⣯⣿⣿⢻⣶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣿⣶⡟⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⡛⠻⠿⠿⠛⣋⣿⠿⠋⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣾⣿⠿⠿⠿⣟⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⡉⠀⢀⣀⡀⠀⠀⠀⠀⠰⢿⣇⠀⠀⠀⠈⢷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⢨⣤⣤⣾⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠙⠏⠙⠃
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣻⠁⢀⡤⠔⠦⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡀⠀⠀⠀⠸⣶⠎⠀⠀⢀⡾⠁⠀⢸⠀⠐⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠐⢧⣀⣀⣀⡄⢀⡴⠋⠉⠁⠀⠀⠀⡸⠀⠀⠄⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⢳⣴⣯⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⡰⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠁⠀⠀⠀⠀⠈⣭⣉⢿⣿⡟⢩⡄⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⢸⢿⡄⣶
⠀⠀⠀⠀⠀⠀⠈⠃⠁⠉⠀⢰⡾⠀⠀⠠⠀⠠⠤⣿⣿⢌⣿⡿⣿⡃⠀⠀⢠⠆⠀⠀⠀⠈⢡⡯⢰⣶⣾⡆⠀⠈⠉⠨⢟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢙⠀⠀⠈⠀⠀⠀⠿⣇⣼⡿⡟⠟⠃⠀⠀⠈⠀⠀⠀⠀⠀⢸⣧⣼⠿⢿⣿
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⢄⣰⠂⠀⠀⠀⢠⠆⠹⡋⢀⡧⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⢿⠃⠘⣄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⢀⠀⣄⣀⢠⣿⡶⣦⡧⣼⣣⣤⣷⣤⣄⣀⡀⠀⠀⢀⡀⡇⠀⠀⠈⢿⡷⣿⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠙⠛⠋⠛⠛⠛⠛⠛⠛⠓⠊⠈⠛⠛⠛⠋⠉⠁⠛⠛⠛⠛⠓⠚⠛⠂⠀⠀⠀⠒⠋⠁⠀⠈

⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⣠⣾⡿⠟⠋⠁⠀⠀⠀⠀⣀⣩⣽⣿⡇
⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠛⠋⠀⢀⣠⣤⣤⣤⣤⣄
⢠⣿⡿⠁⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⢀⣴⣿⠿⠛⠋⠙⠛⠿⣿⣦⡀
⣼⣿⠁⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣶⣤⡀
⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣠⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⢿⣿⡄
⣿⣿⠀⠀⠀⠀⠀⠀⠈⢀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀
⠸⣿⣇⠀⠀⠀⠀⢀⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣷⣄
⠀⠹⣿⣦⡀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠘⢿⣷⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠉⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⣼⣿⣆⠀⠀⠀⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠘⢿⣿⡿⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⣰⣷⡄⠀⠀⠀⣰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⠀⠀⠰⣿⣿⡿⠀⠀⠰⣿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⡆⠀⠀⢀⡞⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡞⠀⠀⠈⢷⡀⠀⡠⠢⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠹⣆⠑⠚⠁⠀⠐⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠀⠀⠀⠀⣰⣫⠖⠀⠀⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣏⢀⡆⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡴⠃⠠⡤⠀⠀⠀⠀⡔⡄⠀⠀⠀⠀⠀⡠⠀⠀⠈⢧⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠑⠁⠀⠈⠌⢧⠀⠈⠁
⠀⠀⠀⠀⠀⢸⠁⣱⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⠇⠀⠀⠀⠚⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠂⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠠⢤⣾⣿⡟⠑⡄⠀⠀⠀⠀⠀⣰⣿⣿⠉⢢⠖⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠉⠉⠁⠀⢠⠀⠀⢠⡄⠀⠉⠉⠉⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡟⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠓⠲⠶⠤⠤⠤⠤⢤⠤⠤⠴⠖⠒⠋⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣁⠤⠒⠒⢒⣒⠒⠂⠄⠀⠀⠀⠀⠀⢤⠐⠒⢀⡀⠁⠀⠐⠲⢤⣀⡀⢀
⠀⠀⠀⠀⢀⠔⠂⠉⠑⠂⠈⠄⣐⠉⠭⠄⠀⠬⢍⠀⠀⠀⠀⠀⠠⠦⠐⠉⠀⠀⠀⠀⠀⣀⠠⠌⠋⢈⠥⡀
⠀⠀⣠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠢⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⡆⠪⠑⢄
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠠⠊⠄⠀⠑⡄⢱⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠣⡀
⠀⠀⠀⠀⢄⡀⢀⡀⢀⠀⠀⡀⠠⠤⠊⠀⠀⠀⠀⠀⢠⠀⠀⠂⢠⠃⠀⠀⣃⣀⡀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢆⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠨⠑⢄⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠸⠀⠀⠀⠘⡀⠀⡃
⠀⠀⠀⠀⣴⢀⠀⠃⠃⠀⠈⠁⠀⠒⠂⠊⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⢀⠎⠀⠀⠑⠄⠀⠇⠀⠀⠀⠀⡇⢀⠁
⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠠⠄⠀⢠⠀⠀⠀⠀⢀⡠⠃⠠⠃⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠂⠌⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠁⠀⠀⠀⠈⠒⠒⠐⠊⠀⠀⡰⠁⠀⠀⠀⢀⠠⠤⢤⠠⠄⠀⠠⡀
⠀⠀⠀⠀⠀⡠⠄⠀⠤⡀⠋⡰⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⢀⢜⠀⠀⠀⠀⠀⠇⠖⠆⠘⠒⡒⠠⠌⡇
⠀⠀⠀⠀⠌⢀⠄⠀⢄⠈⡖⠀⠀⠂⠁⠀⡟⢠⢀⠤⠀⢄⠀⠀⠣⣓⠱⠁⠀⠀⠀⠀⢀⠇⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢂⠘⠄⠄⢸⠀⠇⠀⠀⢀⠃⢀⠋⠑⠁⠔⠀⠆⠱⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⡄⠊⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠈⠃⠵⢄⠐⠓⠊⢀⡀⠔⠁⠀⠀⠢⣀⠑⠌⣲⡶⠵⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠇⠦⠤⠀⠤⠄⠒⠁

⣿⡆⠀⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⢰⣿⡇⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⢀
⠿⠟⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣤⠀⠀⠸⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣴⣿⣆
⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠀⠀⠿⣿⠿⠀⠀⠀⢀⣾⣿⣿⣿⡀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠿⡿⠟
⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣄
⣆⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣿⡷⠀⠀⠀⣴⣿⣿⡆⠀⠀⠀⣠⡄⠀⢀
⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⢾⣿⠆⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠸⢿⠗⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⣠⣿⡆⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⠀⠀⠀⠀⢀⠀⠀⠀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⢠⣾⣧⠀⠀⠻⠿⠟
⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠉⠁
⣿⡀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡿⠃⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⣰⡄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣾⣿⣿⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠘⢿⣿⡿⠃⠀⢰⣿⡧
⠀⢠⣶⡄⠀⠀⠈⠉⠀⠀⠀⠘⠻⠿⠟⠃⠀⠀⠀⠀⣾⣷⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⢀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⣼⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣶⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠛⣀⣉⡘⠃⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⢠⡾⠋⠉⠛⣦⠀⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣶⣦⣤⣴⣶⣿⣶⣦⣄⠀⠀⠀⠀⣼⠇⠚⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⡃⠀⠀⢀⣀⠈⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣾⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠗⠐⠇⠐⠂⠸⠂⠺⠀⣉⠉⣉⢉⡉⢉⡉⢉⡉⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠗⠐⠇⠸⠆⠸⠂⠺⠀⣍⠀⣅⢀⡅⢨⡁⢨⡀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠖⠰⠆⠰⠆⠰⠀⠶⠀⣤⠀⣅⢀⡅⢠⡄⢨⡀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆⠰⠆⠰⠀⠶⠀⣤⠀⡤⢠⡄⢠⡄⢠⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠦⠰⠆⠰⠆⢰⠄⠶⠀⣤⠀⡤⠠⡄⢠⡄⢠⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠦⠠⠆⠰⠄⠰⠄⠴⠀⠦⠀⠦⠠⠆⠰⠄⠰⠄⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣬⡁⣠⣤⠈⢷⣣⡀
⡆⠠⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢈⣿⡳⣜⢿⣎⢻⣷⣔⠽⢿⣄⢠
⠈⠢⣀⡐⠒⣋⠀⠀⠀⠀⠀⠀⢈⠐⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⣯⠛⡛⢎⢢⡹⣷⣝⢿⣯⣂⠻⣧
⠀⠀⠀⠈⠉⠀⠀⣤⡤⢤⠖⠀⠈⠑⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⢴⣶⣷⣝⡿⠋⠙⠳⠘⠀⠑⠙⠊⠉⠀⠙⠁
⠀⠀⠀⠐⠒⠒⠚⠁⠀⠀⠉⠓⠀⠀⢀⣀⣤⣼⣿⣶⠲⣿⣿⣿⣦⡹⠿⠻⠃⠀⠀⠀⣀⡀
⠀⣀⢀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡰⣾⣷⡙⢿⣿⣿⣿⣷⡌⠣⠉⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⣿⣿⣍⢿⣿⣿⣿⣿⣧⡻⣿⣮⣿⣿⡦⠻⣿⣿⣇⡈⠒⠐⠠⠤⠔⠀⠀⠐⠒⠈⠀⢀⠀⠀⣤⣀⠰⣝⢷⣗⠄
⠀⠀⠈⢿⣿⣦⠻⠟⠹⣿⣿⣿⣮⣿⣿⣿⣆⢲⣾⣿⣿⣿⣿⣿⡻⣷⣿⣿⣶⣦⡺⣿⣿⣟⢦⡻⣿⣷⡳⠌⠢⡉⠳
⠀⠀⠈⢲⣝⢿⣷⣿⣧⡹⣿⣿⣿⣷⣝⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⡛⣈⣿⣿⣷⣕⢮⢿⣿⣦⡢⠈
⠀⠠⡙⣝⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣷⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣮⡻⣛⣿⣿⣯⣷⣝⠿⡿⡄
⠀⡝⢮⠺⣿⣿⣿⣿⣿⣏⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢭⣝⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣷⡝⠞
⠀⠈⣿⣿⣟⢿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣼⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⣦
⠀⠠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣻⣿⣿⣿⣿⣿⣿⣿⣄⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⠿⢯⡘⠌⠢
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡿⠟⡛⢮⢠⣧⠳⡀
⠀⠐⢠⡎⡙⡟⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡛⢯⡻⢷⢰⡆⣿⠀⣸⣿⣀⡈
⠀⠀⢐⢯⣿⢰⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⡏⣤⠁⡆⣼⣿⣿⢃⣼⣿⡇⠙
⠀⠀⠂⣼⣿⣵⣿⣏⠷⠈⠻⠿⠟⠍⠛⠟⠗⠙⠛⠉⠊⢛⠋⠛⣛⠛⠻⠿⠮⠙⠐⣿⢘⣷⣸⣿⣿⣿⣿⣿⣷⡄
⢠⣾⣷⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣶⣦⣶⣿⣷⣦⣔⢻⠿⣿⣿⣿⣷⣶⣶⣦⢸⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣶⣦
⠀⠉⠋⠁⠀⢀⣈⣀⣉⣉⣋⣉⣉⣉⡙⠛⠋⠉⠉⠤⣤⠤⠀⠀⢤⣁⠤⠭⢙⣐⣿⣿⣿⣝⣿⣿⣿⣭⣽⢿⣿⣶⣍
⠀⠐⠀⠂⠢⠀⠐⠀⠀⠈⠓⠐⠒⠶⠒⠀⠀⠀⠃⠙⠛⠉⠛⠋⠁⠀⣀⣠⣬⣴⠼⠗⠒⠛⠛⠛⠛⠋⠛⠻⠿⠛⠫
⠀⠮⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠓⠒⠒⠛⣀⡘⢛⣡⣛⠛⣻⡓⠁⠀⠀⠀⣀⣀⣠⣤⣤⡶⡶⠶⢶⠿⠛⢿⣶⠦⣜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣄⣒⣟⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⣉⣁⣀⣀⣀⣠⣀⣀⣀⣀⣈⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⢁⡔⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠠⢯⠀⠹⣶⡀
⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠐⠂⠙⠁⢀⡙⠀⢠⣚⣷⡄⣷⢀⠛⣧⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠈⠴⠇⢸⡃⠍⢺⣟⢠⠄⠈⢿⣦⡀
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠂⣤⠙⣷⣤⣾⣷⣬⡈⢈⠷⣾⡄⣈⣹⣓⡀
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠇⣾⣿⣿⣿⣿⣿⣧⣠⣾⣿⡷⣌⠁⠻⣍⠠⢀⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡗⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣎⣠⡁⠘⢸⣿⣿⠿⠿⠟⢹⣿⣿⣯⣽⣷⡜⠆⠀⠈⢏⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡈⠉⢸⣷⣾⣿⣿⣶⣾⣷⣷⣾⣿⣿⣿⢿⣿⣶⡄⠂⡀⠀⠡
⠀⠀⠀⠀⠀⣾⣿⣿⣿⠍⠁⠀⠀⠂⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⢠⠾⠿⣿⡿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⣬⣽⣷⣿⣿⠟⢉⣀⠆⡄⠀⠀⠄
⠀⠀⠀⠀⠀⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣢⣸⣶⣾⣿⣿⣿⣿⣏⣹⣭⠷⢶⣾⣀⣉⣉⡿⠋⢠⡔⢿⠿⢆⠑⠄
⠀⠀⠀⠀⠀⠛⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⣰⣿⣻⣿⡟⣋⣿⣿⣿⣿⣿⢓⡛⠲⠞⠉⠺⢋⠉⡿⠊⠁⣀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡾⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⣿⢻⣿⡟⣹⣿⣿⣿⣿⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠃⠀⡈
⠀⠀⠀⠀⢰⣿⣿⣿⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠇⣹⣿⡇⣿⣡⣿⣿⣿⡿⠻⣿⠿⠓⠁⢀⡀⠀⠀⠀⠈⣴⠁⠀⠐
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⢐⣼⣥⡇⠛⢳⣿⣿⠛⢶⣶⣿⡷⠦⠀⢸⡇⠀⠀⠠⠀⣿⠀⠀⠖⠒
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠘⠋⢹⣧⡾⠛⠟⠀⠀⣨⣵⣷⣦⣤⣍⣿⠤⠛⠁⠀⠀⡖⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠻⠀⠀⠀⠀⢀⣤⡀⠀⠈⠏⠁⡀⠀⠀⢀⣿⠿⢫⣽⣿⣿⣿⠆⣤⠤⠾⠀⠀⡀⠀⠄⢸⡅⠐⠀⠀⡀
⠀⠀⠀⠀⠀⢉⣹⣿⣿⡟⢳⣀⡄⣤⠴⣦⠘⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⢈⡹⠛⣿⣾⠋⣁⠘⡟⠘⠛⠁⠉⠛⣀⠀⢸⡇⠒⠀⠀⠁
⠀⠀⠀⠀⠀⣸⣟⣿⠏⠁⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠴⠶⠚⡄⠀⠈⠓⠈⠻⠀⠙⣿⠀⠁⠺⠛⠛⠁⠀⠀⠈⠋⠀⢸⡇⡀⢰⠀⣤⢀
⠀⠀⠀⠀⠀⠻⠿⠛⡇⠄⠠⠤⢦⡀⣤⣤⣆⣀⣀⣀⣀⣐⠋⡀⡀⣀⠀⠇⠀⠘⠀⢹⠃⢀⡒⠐⠂⠀⠀⠿⠁⣂⠀⣺⡇⠁⣀⣀⠃⣘⡂
⠀⠀⠀⠀⢀⣴⣖⢿⢳⣆⣿⣦⣾⡿⣮⣭⣿⣯⡟⠛⡻⣿⡷⠛⢛⣿⣿⡟⢰⣿⡿⠙⡇⠘⢋⣀⡻⠿⠶⢿⣟⣛⣋⡹⠟⠻⠟⠛⢒⡛⠃
⠀⠀⠀⠀⠀⠃⣳⣸⣘⣇⣻⣧⣿⢸⡟⠙⣻⡟⠛⠁⣀⡌⣠⠀⠀⠈⠉⠁⢩⠛⣛⠘⡯⢠⣄⠉⠀⣴⠶⢿⣿⣿⣿⣿⢹⣿⡀⢸⣿⠛⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠈⢉⣉⣩⡍⢹⣉⣠⠄⠈⢻⡇⢀⣺⣿⣷⣿⣦⣆⡀⠀⠀⠁⠎⠁⣴⣿⠀⠸⡆⠈⠿⡆⠀⣽⢿⡖⢿⠔⣛⠻⡈⠗⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣄⠙⠛⠀⢺⣿⠇⠀⢀⡉⠁⠸⠷⠈⠙⢿⣿⣿⣿⣷⣧⣿⣲⣍⣜⣿⡇⠀⠀⠀⠀⠐⠲⠧⠚⠛⢾⣶⠉⠁⢠⣄⣉⠙⠉⠁
⠀⠀⠀⠀⠀⢀⡾⢡⣼⠃⢰⡏⢀⣧⣤⠀⢀⠀⠀⠀⠀⣹⣄⠙⠛⣿⣿⣿⣿⣾⣿⡋⢿⠿⠇⢢⢀⡀⠀⠀⠀⠀⠀⢸⣏⠉⠁⠤⢤⣉⠑
⠀⠀⠀⠀⢀⡤⠄⠴⡾⠒⣾⡆⠈⠛⠳⠀⠀⠈⠀⣀⣠⣀⣿⡆⠀⠘⢿⣿⣿⣿⣿⣿⣿⣧⡀⢠⠙⠿⢿⣿⣿⣿⣶⣾⢩
⠀⠀⠀⠀⠈⠑⠀⢸⠇⠀⣽⠛⣦⣶⠀⠀⣠⣦⠀⠀⠀⠩⣈⡁⠀⠀⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣷⣄⣿⡿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠉⡆⠀⢩⣿⠛⠁⠀⠀⠈⠉⣽⠇⠀⠠⠴⠿⠿⣬⠰⠆⣿⣿⣿⡙⣿⣿⣿⣿⣿⣾⣯⢽⡉⠏⠙⢚⣿⣿⣿⣆⣦⡀
⠀⠀⠀⠀⠀⠠⢾⠃⢸⣿⡟⠘⠲⣿⡀⠀⠀⠀⣀⡄⢘⡀⣠⣤⡀⣀⣰⣻⣿⣼⣷⣬⣟⠀⠸⠿⣿⣷⣾⠟⠳⢿⣯⣿⣍⡁⠉⠁⠛
⠀⠀⠀⠀⠀⣀⡀⠀⠈⢩⠍⠀⠈⣯⡡⠀⢤⣴⣿⣿⣄⠀⠀⠬⠏⢹⣭⡏⣿⣿⣟⣿⣿⠀⠀⠐⠾⠟⠛⢿⣶⡆⣬⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠽⠁⠀⠀⢠⣤⣄⡁⠘⣷⡄⠈⠉⢠⣉⣽⠂⠠⡀⠀⠠⠌⠁⣨⣿⣿⣿⣿⠇⣠⡄⠃⠘⠻⢿⣯⣵⣟⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡗⠒⠀⣀⣤⣤⠴⣤⡿⠿⠟⠃⠀⣤⠄⠶⠘⣋⢹⣿⠟⢹⡟⠛⡉⠀⢃⡀⠀⣸⡇⠀⠉⠉⢯⡿⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠋⠉⠀⢅⣸⣟⠀⠂⠀⠆⠐⠂⣀⣠⣶⠋⠀⠈⡀⠀⠀⡤⣤⡎⠁⣤⣮⠁⠀⣹⡇⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠛⠃⠀⠈⠛⠛⠿⢿⡇⣴⣶⠀⠠⠀⣿⣾⠆⠀⠐⠇⣸⠉⠅⢾⣿⢖⣟⣿⣌⠣⣼⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⣰⠿⡌⣙⣫⡧⠀⠀⠀⢼⣿⣿⡷⠆⠰⠁⠶⠐⠠⠦⠀⣏⡏⢹⣿⣤⡇⣀⠀⠂
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⠁⠀⠀⣀⣘⣿⣧⣄⣉⠁⡀⠛⣉⣿⣾⠛⠉⠃⠀⡛⢀⣿⡀⢠⠀⣿⣇⣸⣷⣾⡿⢯⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠋⠅⠀⠀⠀⠏⠁⣴⣿⠿⠟⠈⡧⠴⠉⠹⢈⡻⣄⠟⣈⠁⠛⢉⡁⠂⣀⣿⠻⣿⡃⣻⡟⠻⣿⣷⣅⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠐⢚⣭⡅⠀⡶⠀⠀⠀⢨⡴⠛⠷⠉⢀⡐⠀⠾⠘⠀⣠⣸⣿⣶⣿⢷⡿⠃⣀⠀⣩⡌⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠿⠉⢉⡀⠀⠀⠀⠰⠀⡀⠀⢠⡄⠠⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣹⣾⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⢹⣿⠿⣷⣌⢻⡍⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠋⠘⣷⢿⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡈⠁⢄⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠁⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⢀⠀⠀⠀⢂
⠸⠀⠁⠀⠀⠐⠢⡀⠀⠀⠀⠀⠀⠌⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠂⠈⠁⠀⠀⠀⡀⠀⠈⠁⢒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠁⠀⠈⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠂⢁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠂⠀⠀⠀⠩⢤⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⡒⠋⠁⠀⢀⣀⣀⣤⡀⢴⠖⠂⠈⠉⠁⠀⠀⠑⠩⢒⡅⠀⢈⢉⣉⣠⡖⣶⠦⠖⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠰⠉⡄⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠡⠀⢾⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊
⢠⠆⠀⠀⠀⠀⠀⠀⢀⠁⠀⡁⠀⠀⡄⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞
⡆⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠋⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡛⢸⡄
⠑⠀⠂⠀⠀⠀⠀⠀⢻⣀⠈⠁⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣀⠀⡐⠧⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠸⠀⠻⠀⠠⠀⢀⠀⠀⢀⣀⡀⡈⠀⠠⠆⠈⢰⠊⡰⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠀⠀⠠⢦⣴⣀⣀⣤⡉⣀⠇⠀⢰⡄⠀⠀⠴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣆⠤⠀⡠⠀⠀⡀⠁⠉⠁⠛⠈⢹⠀⢀⡄⠈⠢⠀⠀⢃⠡⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣀⠌⠈⡳⢀⠀⠰⠒⣆⢀⡀⠐⣄⣀⠐⣄⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣩⣥⠰⠢⣭⠁⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠠⠦⡀⠀⠠⢀⡀⢠⠈⣄⡀⣀⣐⠆⣀⣈⡂⢀⡀⣀⠀⡀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡘⠘⠈⠉⠉⠁⠀⢈⣉⠀⠂⠈⠁⠈⠇⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠄⢀⡤⠄⠄⠀⠀⠈⠊⠀⠁⢤⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⡤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠒⠒⠒⠀⠓⠐⠀⠀⠀⠒⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣋
⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠃
⠀⠀⠀⠀⢸⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣿⣶⠟⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃



⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣁⠀⠀⠀⠀⠀⠀⣾⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢉⣿⡿⠁⠀⠀⠀⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶
⠀⠀⠀⠀⠀⠺⣿⡷⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃