Stylist Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠊⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⣀⣴⣾⣿⠿⠛⠛⠛⠻⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⣠⣾⣿⡿⢋⣤⡶⠛⣉⣤⣤⣤⣌⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⢀⣼⣿⣿⠏⣠⣿⠋⣠⣾⣿⡿⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⢠⣿⣿⣿⠃⣰⡿⠁⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⣰⣿⣿⡿⠁⣰⡿⠁⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣰⣿⣿⡿⠁⢰⣿⠁⠀⢸⣿⣿⠀⠀⠀⠀⢀⣤⣶⣶⣤⣤⣤⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⣰⣿⣿⡿⠁⢠⣿⠃⠀⠀⢸⣿⣿⡇⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠃⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⢀⣼⣿⣿⡿⠁⢀⣿⠇⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⠁⠀⣠⣿⣿⣿⡿⠁⢀⣾⠏⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠀⠀⣠⣾⣿⣿⣿⡟⠁⢀⣼⡏⠀⠀⡆⠀⠀⢀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠲⢤⣀⣀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⡿⠋⠀⢀⣾⠏⠀⠀⢠⡇⠀⠀⣿⠀⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢀⣴⠟⠁⠀⠀⢀⣾⠇⠀⢀⣿⠀⠘⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠠⠔⠚⠋⠁⠀⠀⢀⣴⣿⡟⠀⠀⣸⡟⠀⠀⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⡿⠋⢀⠀⢰⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⡀⢠⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⡿⠟⠉⢀⡠⠃⢠⣿⡟⠀⣠⠀⠈⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⠿⠟⠛⠛⠉⠁⠀⢀⣠⣴⠟⠁⣰⣿⠟⠀⣰⠇⠀⠀⣿⣿⣿⣿⣿⠃⣸⣧
⠀⠀⠀⣠⣾⣿⠿⢛⣩⡥⠖⠀⠀⠀⢀⣠⣤⣶⣾⡿⠟⠁⢀⣾⡿⠋⣠⣾⠏⠀⠀⢀⣿⣿⣿⣿⡟⢀⣿⡿
⠀⠀⣼⣿⠟⣡⣴⠟⠉⠀⢀⣤⣶⣿⡿⠿⠛⠋⠁⠀⢀⡴⠟⠉⣠⣶⣿⠋⠀⢀⠄⣸⣿⣿⣿⡟⠁⣼⣿⡇
⠀⢰⣿⠁⣴⡿⠃⠀⣠⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠟⠁⠀⣠⠏⣰⣿⣿⡿⠋⣠⣾⣿⡿
⠀⢸⡇⢸⡿⠁⢠⡾⠋⠁⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⡾⠃⡰⠟⠋⢁⣤⣾⣿⣿⠟
⠀⠀⠀⣿⠃⠀⠈⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁⣀⣠⣴⡿⠋⠀⢀⣠⣴⣾⣿⣿⣿⠟⠁⡀
⠀⠀⠀⡏⠀⠀⣠⣾⣿⣿⣿⡿⠟⠋⠉⢀⣀⣤⣴⣶⣶⣿⠿⠛⠁⣠⣴⣾⣿⣿⣿⣿⠟⠋⠁⢀⡼⠁
⠀⠀⠀⠃⠀⣰⣿⣿⣿⡿⠋⠀⢀⣴⣾⡿⠿⠛⠛⠉⠉⠀⣠⣶⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⣠⣴⣿⠟
⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠞⠁⠀⠀⣠⠖⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⣠⡞⠁⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣼⡟⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⢀⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⡿⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢹⡏⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⣧

⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⡀⠀⠀⢀⣦⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⢋⠉⠉⠀⠀⣾⠿⢛⠛⠀⠀⠀⠐⠠⣆
⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⡶⠀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠁⠀⠀⠉⠀⠀⠰⡦⠾⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠳⣄⠀⠀⠀⠀⠀⣠⠞⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠓⠣⠀⠀⠀⠀⠀⠀⠀⠀⣰⠲⢤⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠬⠁⠀⠀⠀⠈⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⢴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠘⢔⢾⠇⠀⠀⡀⠀⠀⠀⠂⢡⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣆⠀⠀⠀⠀⢀⠆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠄⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠄⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⡀⠀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠸⡇⢨⢿⢱⠀⢯⠈⠃⣿⠀⡇⢰⡍⣿⣇⡇⠀⠀⠀⠀⠘⢏⠐⡀⠀⢠⠀⣠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡗⣇⡷⢷⢸⡸⢎⠀⣀⠱⡄⠿⡇⡇⠸⡁⠇⠹⡇⠀⣠⠂⠀⠀⠀⠟⠁⠀⠠⣶⣿⠍
⠀⠀⢀⡤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠈⠊⠉⠘⠀⠙⠚⠉⠀⠁⠙⠃⠉⠀⠀⠁⠀⢋⠀⡀⠂⠁⣀⠤⣄⠈⠻⠁⠀⠀⠀⠀⣤
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠐⡀⠀⠀⠁⠀⠈⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠋⠈⠀⠁⠈⠀⠀⠀⠁⡠⠀⢨⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣠⣴⠾⠛⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢣⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⠞⢁⠻⠀⠀⠱⡄⢸⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠂⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⢄⡔⠁⠀⢈⠆⠀⠀⠀⠹⣾⡇⠀⠀⢠⠂⠉⠻⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠓⠒⠲⣖⠁⠀⠀⠀⠀⢀⡟⠉⠳⡦⢄⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠉⠉⠁⢲⡄
⠀⠀⠀⠀⠛⡀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⣏⣹⠀⠀⠠⠤⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⢐⠁⣠⠖⠉⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠑⠲⠖⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⢀⠀⠀⠀⠞⠋⠂⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣼⣶⣤⠀⠀⢰⠀⠀⢰⡇⠀⠀⢸⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠈⠉⠋⣉⠄⠀⢸⠀⠀⠘⠇⠀⠀⢸⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡄⠀⠲⠒⠃⠀⢸⣀⡄⣿⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⢀⡴⠋⠁⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠠⠶⠛⠀⠀⠀⢠⠎⠁⠀⠀⠙⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣠⣀⣀⠀⠀⠀⠀⣠⠏⠀⣠⠔⠀⠀⠀⠷⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⣾⣿⠟⠀⠀⠙⠛⠿⢋⣀⡾⢃⠤⠂⠀⠐⠆⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡏⠀⠀⣰⠇⠀⣰⢿⡇⠀⠠⢤⡤⠄⠀⢦⣤⣽⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⡈⣀⣤⣾⣟⣤⣾⠏⢸⠇⠀⠀⠀⠀⠀⠀⠀⠉⠳⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⡽⠟⢩⡿⣿⡟⠁⣀⠀⣀⣤⣀⠀⠀⢀⠞⠃⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢿⡇⢧⣄⠀⠇⠻⣇⣴⠇⠀⠛⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠻⡌⢻⣿⣦⣀⢹⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣧⡛⢀⣿⢿⣟⣼⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠟⣠⢎⣴⣿⠟⠁⢸⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠅⢠⣿⠏⢻⡇⠀⠀⣸⣷⢘⣧⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢺⣿⣦⡀⢙⣤⠞⠋⠁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⣴⣿⣿⠀⠉⢪⡛⢷⠀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⠀⣧⠞⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡰⠃⠀⣴⠇⠀⣼⡀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⢿⣄⠘⠹⠁⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠄⠀⠀⠀⠈⢑⡀⠀⠀⢀⠼⠁

⠀⠀⠀⠀⢀⠴⠂⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠐⢀
⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒
⠀⠀⠀⠀⠉⣉⣽⣿⠿⡏⠁⠀⢠⠊⠙⢲⣀⡞⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣽⣿⡿⠏⠁
⠀⠀⠀⠀⠀⡿⠋⣁⣤⡇⠀⠀⢸⡀⠀⡰⠉⢧⡀⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⢁⣠⡆
⠀⠀⠀⠀⠀⣶⣾⠿⠛⡇⠀⠀⠀⠠⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠏⣀⣤⣶⡇⠀⠀⠀⠀⠈⢄⢄⠀⠀⠂⠀⠀⠀⠠⡈⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⠇⠀⠆⠀⠐⠀⠠⠤⡴⡆⠀⠀⠀⡟⣁⣤⣶⡇
⠀⠀⠀⠀⠀⣿⠿⠛⢁⡇⠀⠀⠀⠀⠀⠈⡀⢱⠄⠀⠀⠀⠀⠀⠑⢀⣀⣀⡐⠁⠀⠀⠀⠀⠀⡜⠀⡈⠀⠀⠀⠀⢐⠒⠺⠅⠀⠀⠀⣿⡿⠛⠉⡀
⠀⠀⠀⠀⠀⣁⣤⣾⡿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠹⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠀⠀⠀⢒⣚⣩⡅⠀⠀⠀⣏⣤⣶⡿⠇
⠀⠀⠀⠀⠀⡿⠋⣁⣤⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢇⠀⠌⠀⠀⠀⠀⠀⠠⣬⣤⡇⠀⠀⠀⡿⠛⢉⣠⡦
⠀⠀⠀⠀⠀⣶⣾⠿⠛⡃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠌⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠨⠥⢖⡂⠀⠀⠀⣵⣾⡿⠟⠁
⠀⠀⠀⠀⡀⠋⢀⣤⣾⢇⡀⠀⠀⠀⠀⠀⠈⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠀⠀⠀⠀⠀⠀⣘⠓⠒⠇⠀⠀⡀⠛⢁⣤⣶⠗⡀
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠤⢀⣀⣀⣀⣀⠉⠉⡉⣙⣁⣀⣈⠥⠂⠀⠀⠀⠀⠀⠂⠈⠭⠅⠀⠀⠠⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠈⠢⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠠⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⢠⠀⠀⢠⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣤⡏⠀⠁⠀⠀⠀⠂⢸⣧⡆⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡟⡤⠀⠀⠀⠀⠀⠀⢠⠙⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠓⠶⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢀⡀⠀⠀⠀⠀⠀⠀⡰⠃⢠⣥⣤⡤⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠶⠂⠀⠀⠀⠈⠬⣿⡗⠢⠀⠀⠀⠀⠴⢪⣿⡯⠂⠀⠀⠀⠀⠀⠀⢈⡧⠄⢻⡇⠀⣹⠢⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣄⢀⠀⠀⡌⢠⡘⣉⠀⠀⠀⠀⠀⢀⣤⠎⠈⢻⣆⡌⠛⠛⠡⠀⣶⠋⠁⢦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⡿⠅⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠈⠓⠖⠒⠒⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠆⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠟⠋⢉⠉⠙⠳⢌⣡⣴⣾⡷⠗⣂⣤⣤⣾⢟⣡⣶⣿⣿⣿⣶⣦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠈⠉⣶⣿⡿⣱⡏⢠⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⢀⣴⣾⣿⣿⣿⡆⢻⣿⣧⢻⡀⢸⣿⣿⣿⣿⣿⣿⣟⣶⣿⣿⣿⣿⣯⣿⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⢀⣾⣿⣿⣿⢿⣿⣿⣆⡙⢿⣮⣧⡈⢿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⣾⣿⣿⣿⣿⣧⡛⢿⣿⣿⣦⣝⡻⣿⣶⣭⣛⣿⣿⣿⣿⣾⣿⣿⣽⣿⣿⡿⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⠀⢰⣿⣿⣿⣿⣎⢿⣿⣷⣝⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣟⣛⣋⣥⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢸⠀⢸⣿⣿⣿⡝⣿⣷⣝⠿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣿⡄⠀⣿⣿⣿⣿⣮⣻⣿⣿⣾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢿⣧⠀⠸⣿⣿⣞⠋⢉⠙⣿⠏⠀⠀⠀⠀⠲⠒⠒⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣇⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⣄⣳⣤⣤⣤⣀⣀⠀⠙⠛⠃⠀⠀⣀⣤⣄⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡘⣿⣿⡀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠐⡻⣿⣛⠿⠿⣿⣿⠀⠀⠀⣠⣀⡁⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣧⢻⣿⡇⠀⣇⢻⣿⣷⣆⠀⠀⠀⠀⠀⠨⠛⠟⡖⠃⠁⠀⠀⢰⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⣿⠿⣿⣿⣿⡇⢠⣿⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⢿⣿⣿⡇⣾⣿⣆⣿⢻⣿⡍⠻⣄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠁⠀⡾⣹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢦⡙⣿⣿⠛⠉⠙⢻⣿⣿⣿⢸⣿⡇⠀⠈⠻⣦⡀⠀⠀⢈⠛⠛⠋⢀⣤⡾⣵⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠏⣾⣿⣾⡇⣸⠃⣾⣿⣿⡄⣿⣿⡏⣾⣿⡇⠀⠀⠀⠘⢿⣦⡀⠀⢉⣡⣶⣿⣿⣾⣿⡿⢛⣉⣁
⠀⠀⠀⠀⠀⠀⣾⣿⣆⠻⣿⠟⢀⠇⣸⣿⣿⣿⠃⣿⡿⣱⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡶⢖⣫⣴⣿⣿⣿⠏⣴⣿⣵⣿⣿⠏⠘⣧⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⢟⣽⡿⣹⡏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣵⣿⣥⣾⣿⣿⡿⠟⠁⠀⠀⠈⠂⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣯⡻⢿⡿⠿⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠁

⠀⠀⠀⣿⣿⢾⣿⠟⣼⣷⢸⡟⣿⢿⣿⠟⣷⡟⠀⢰⣿⡆⣿⣾⢻⡟⣷⠀⢸⣿⡇⣼⣷⢸⡟⣿⣿⠀⠰⣿⣗⢸⣿⡘⣗⣀⣾⢻⣾⣷⣿
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠛⠋⠘⠛⠀⠚⠃⠀⠛⠛⠓⠛⠛⠘⠛⠛⠀⠚⠛⠓⠛⠛⠚⠓⠛⠛⠂⠘⠛⠛⠛⠙⠛⠛⠛⠛⠛⠙⠛⠛

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠤
⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣘⣉⣉⣉⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠗⠦⠀⠀⠀⠀⠈⢉⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡍⡍⠄⠀⠀⠀⠀⠐⠀⠀⠁⢸⠀⢸⠀⠀⠀⡀⢠⠀⡄⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠉⠄⠂⡀
⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠨⠀⠀⠀⢸⠀⢸⠀⠁⠀⠀⡎⠀⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡍⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠘⠀⡇
⠀⠀⠀⠀⠀⡒⡒⠒⠀⠀⠀⠀⠩⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠡⠤⠤⠀⠀⢀⣀⣐⠀⠀⠀⠀⢠⠁⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠘⣛⣉⣁⠀⠀⠤⠤⠀⠀⠀⠀⠈⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⢂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠪⡑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣑⣒⣲⣤⣴⣲⣤⣴⣦⣤⣶⣤⣶⣦⣤⣖⣚⣁⡀⠀⢆⠐⢄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⡄⠈⢦⡀⠈⢷⣄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠭⠛⠒⠻⠓⠻⠛⠛⠿⠗⠿⠽⠛⠻⠭⠥⠄⠃⠀⠀⢹⡀⠈⢷⡀⠀⠙⢧⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠄⠀⠀⠀⠈⣧⠀⠀⠻⡀⠀⠀⢧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠻⠄⠀⠈⢂⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠥⠶⠒⠦⠖⠾⠷⠳⠿⠞⠯⠽⠿⠮⠭⢉⣑⡆⠀⠀⠀⢎⠀⠀⡀⠻⠆⠀⠀⠀⢀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⡀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠒⠚⠉⠙⠚⠉⠑⠋⠙⠚⠉⠓⠋⠉⠓⠲⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉

⣿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣟⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣉⠉⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⢿⣵⣾⣯⡙⠲⠶⠾⠿⣟⣛⣀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠘⠉⠙⢿⣿⣆⠀⠀⠀⠀⠈⠹⣧⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣀⣤⣤⣾⣯⡙⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠈⣍⠉⠉⢁⠀⠀⠙⣿⡇⠀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠂⠀⢸⡏⣷⣀⠘⣧⡀⠀⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠻⣷⣾⣿⢷⣤⣶⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢴⣷⣷⠌⢧⡀⢹⡷⢻⠀⠉⠳⢻⡆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⢀⠀⠘⣷⡟⠁⣀⣴⣾⢃⡿⢁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⣿⠁⡞⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠻⣿⣮⡻⣄⠸⣏⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠊⣼⡇⠀⠈⢿⡟⢾⣧⠈⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⣿⣆⠛⠷⣄⣀⠞⠁⣸⣿⡄⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⣼⠟⡤⠚⢹⣿⣧⣀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⣧⣸⠀⠀⠀⠙⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣇⠀⢻⣄⠀⢺⡀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠙⠆⣨⡿⠀⠀⠈⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠚⠉⠀⠀⠀⢠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⣧⣴⣾⡿⣿⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠛⠁⠁⠛⠁⠀⠈⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⣀⡀⣀⠤⣤⣤⣀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠘⠳⢊⡱⣫⣿⣿⣿⣷⣄⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢀⣈⡼⢏⣬⣾⣿⣿⣿⡆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢂⡼⢋⢱⣾⣫⠟⣡⠼⣿⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠛⣠⢟⡽⠋⠉⠀⠃⣴⣿⣧⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⠋⣠⣤⣴⣤⣤⣄⠘⠋⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⢟⠋⠉⠉⠉⢉⣾⣿⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢀⡾⣿⡏⠉⠁⠀⠀⢁⡀⣿⣿⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣶⣮⡵⢿⡀⠈⠁⠀⠀⠈⢁⣹⣟⣶⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢀⡀⠀⠀⠈⠻⡀⠀⢠⣤⠀⢸⠁⠈⠉⣉⡴⢶⣟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠗⠈⣳⣦⡀⠀⣇⠀⢀⣥⣼⠇⠀⣠⠞⣡⡄⠈⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣬⣧⣤⣭⡀⣹⣦⣡⣄⠀⢀⣬⠀⣺⠇⢠⣬⣤⣤⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠦⢤⣬⣹⣿⠟⣡⢿⣀⣭⠉⣡⡾⠃⣀⠀⠂⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣴⡟⢁⣄⠀⠀⢴⡄⠀⠉⠰⣇⠈⠻⣯⣤⠸⠆⣰⣿⠀⠛⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⢿⣷⡄⠉⠀⠀⠀⠀⠀⠶⠀⢹⡆⠠⣤⣭⡴⠾⠟⢡⡄⠀⠀⠶⠀⠈⠓⠀⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣽⠃⣀⠀⠸⠃⢀⣀⠀⠀⡀⢻⣆⠁⠀⢠⡆⠀⠀⢀⣀⣤⣤⣠⡀⠲⠆⠀⠀⢻⡄
⠀⠀⠀⠀⢀⣴⠟⣁⠀⠉⠀⠀⡀⠈⠉⠀⠀⠀⠐⠻⠿⣶⠀⡤⠶⠞⠋⠉⠁⠀⢸⡇⣤⡀⠐⠷⠈⣷
⠀⠀⠀⠀⣸⣷⠀⠉⠀⢀⡀⠈⠁⠀⠃⢠⡰⠆⠀⠀⠀⠀⡆⢰⠀⠀⠀⢀⡀⠀⢸⡇⠉⣀⠀⢠⡴⠛⢧⡀
⠀⠀⠀⠸⣿⣅⠐⠆⠀⠈⠁⠐⠶⠐⠘⢳⣡⢆⡄⠀⠀⠀⡇⠘⠀⠀⠀⣠⣴⠈⠈⠛⢢⣝⠀⢿⡀⠀⠀⠙⢶⣄
⠀⠀⣀⠄⠀⠘⠳⠄⠀⢠⣤⠈⠀⢀⣀⣬⠿⠋⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠠⣤⣄⣀⡈⠓⠆⣽⣦⣤⣤⠀⠉⢳⣄⠀⠀⠀⠀⠋
⢀⡴⠃⠀⠀⠀⠀⠀⠉⠁⣠⡴⠶⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠇
⣼⠃⠀⠀⠀⢀⣠⣤⠒⠻⢿⣷⣶⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⣠⡴⠚⠛⠀⠀⣬⠙⠷⣦⣤⣀⠀⠀⣀⣿⠀⠀⠀⠦
⠻⣷⣶⣾⠿⢿⠁⠤⠉⠳⠀⢹⣇⠠⠄⠉⠁⠐⠒⠠⣤⣄⣀⣀⣁⡀⠐⠶⣭⣤⡀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠘⠷⠶⠛⣦⠀⢸⣿⡇⠀⠰⠆⠀⠐⢀⣤⣾⣿⣿⡿⠟⠷⣄⠀⠈⠛⢷⠐⢦⡆⠀⣠⣶⣷⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⡏⠀⣠⠀⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠘⣇⠸⡦⠀⠀⣼⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠿⢳⣿⠃⠰⣾⣿⣿⣿⡿⠛⢿⡀⠀⠀⠀⠀⢹⣆⠀⠀⠠⣿⣷⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣼⠋⣴⠀⣶⣿⣏⠀⣼⣿⣿⣿⣿⠀⠀⠀⠹⡄⠀⠀⠀⠀⢻⣇⠀⡀⠀⠈⠳⣌⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⡏⣴⣙⣷⣿⣿⠛⠀⣿⣿⣿⣿⡇⢠⡀⠀⠀⣷⠀⠀⠀⠀⠘⣿⡄⠿⠄⠀⠀⠈⠲⣧⡀
⠀⠀⠀⠀⠀⠀⣾⢿⢹⣿⢙⣿⣿⠀⠀⣿⣿⣿⣿⡇⠘⠃⠀⠀⣧⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢶⡄⠈⢷⣄⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⣿⠀⣼⠇⢸⣿⣿⣤⡄⢹⣿⣿⣿⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠹⣶⡟⠀⠻⣿⣿⡀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⢸⣿⡇⠀⡶⠀⠀⠀⣶⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣿⣿⣧⣄⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⢀⣿⡟⠀⢠⣄⠈⢿⣿⠁⠀⢸⣿⣿⡆⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⢸⣿⣿⠀⠀⠺⠆⠀⠀⠀⢶⠆⠀⠹⣿⡄
⠀⠀⠀⠀⢀⣾⣿⠀⠀⠈⠉⠀⢀⡀⠀⠀⣸⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠸⣿⣿⠀⣀⡀⠀⠀⣤⠀⠀⠀⠀⢴⣿⣇⠀⠀⠋
⠀⠀⠀⠀⢸⣿⠟⠀⢠⡄⠀⠀⠈⠛⠀⡰⢿⣿⣿⣇⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⡇⠉⠁⠀⠀⠋⠀⠀⣀⠀⠀⢹⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⡀⠀⣠⠞⠁⠈⠻⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠸⠙⢿⣶⠒⠒⢶⠀⢤⡀⠛⠃⠀⣿⡿⠀⡀
⠀⠀⠀⠀⠈⢻⣧⡘⠓⠀⠈⣡⠊⢹⠀⠀⠀⠀⠀⣻⠀⢀⠃⠙⢿⣿⣿⣿⡿⠛⣄⠀⠆⠀⣿⠀⠀⠺⠀⠀⠙⣦⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠿⣦⡄⠚⣷⡀⢀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠉⠉⠉⠀⠀⢿⡄⠀⢠⣿⠀⣰⠃⠀⠀⠀⢹⣷⠰⠟⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⣽⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠘⡟⢠⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡏⠀⠀⠀⠀⠀⣰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡾⠁⠀⠀⠀⠀⠀⢿⣷⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣠⣈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢠⠾⣦⣝⡻⣶⢬⡲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣴⣝⡻⣶⡽⣪⣝⠻⣮⣕⡻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⡾⣶⣝⡻⢗⡽⣪⣝⡻⢶⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢧⡀⠀⠀⠀⠀⢀⠞⠀⠀⢠⣟⡻⢶⣭⣺⢕⡻⢶⣭⡻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⢳⡄⠀⠀⢠⠎⠀⠀⣰⢷⣭⡻⢷⡯⣞⣝⡻⢶⣭⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠹⣄⢠⠏⠀⠀⣰⡻⢶⡭⣛⢕⡫⢶⣭⡛⠷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⢧⠀⠀⣰⣯⡛⢷⡮⣗⣽⡻⢷⣬⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡾⣾⢳⣰⢷⣮⣛⢿⣺⢷⣯⣛⠷⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡍⠁⠀⠹⣷⣮⢕⣯⣚⠷⣮⣙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⣆⣀⠀⠈⢾⣕⣮⣛⠷⣮⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠸⡄⢹⠳⢤⡑⢮⣝⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢠⠔⢳⡘⡗⠲⠽⣮⡻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⡰⠁⠀⠀⢃⢣⠀⠀⠀⠑⣌⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⡼⠁⠀⠀⠀⠘⡌⢆⠀⠀⠀⠈⢆⠀⣩⠭⢭⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⣧⠈⢦⠀⠀⠀⢸⢸⠁⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⡆⣠⠤⣽⣲⣄⣸⡼⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡜⣼⠁⠀⠀⠙⢯⣧⠞⢝⠦⣄⣠⡴⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢱⣹⡀⠀⠀⠀⢸⣿⡄⠀⠉⠓⠒⠋⠣⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢦⣀⣀⡼⡿⠀⠀⠀⠀⠀⠀⠀⠙⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠓⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⣸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣾⣿⣿⠟⠀⣰⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⠿⠋⢁⣤⠞⣿⣿⡿⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠿⠟⠛⣋⣡⣤⣶⠾⢛⣥⣾⣿⡟⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⡵⠶⠾⠟⠛⠛⠉⢁⣠⣶⣿⣿⣿⣫⣶⡿⠃⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⣴⠞⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⠞⣋⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣤⣤⣴⣯⡤
⠀⠀⠀⠀⠀⠀⢀⣾⣟⠵⣫⣿⣿⣿⣿⡿⠟⣩⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠸⣿⠋⣾⣿⣿⣿⣿⠟⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣸⣿⣿⣿⠃⣿⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⣿⡀⠘⣿⣿⣿⡇⡄⠀⠀⠘⠿⠿⠿⠃⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠘⢷⣄⠘⢿⣿⣿⡇⠀⠐⢄⡀⠀⠀⡠⠎⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡈⠻⣷⣄⠙⠿⣷⡀⠀⠀⠈⠉⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠉⠀⠀⠙⠷⣦⣈⠙⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡑⠦⣀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣬⣙⡲⠤⣄⡑⢦⣬⣛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠛⠿⣿⣿⣶⣿⣦⡙⢿⣷⣮⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣍⠻⣿⣿⣿⢸⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡿⠟⣡⣾⣿⠟⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣶⣿⣿⠿⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏

⠀⠀⠀⢀⣼⣶⣆⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⣬⣿⣿⣿⡄⢠⡀⠀⠀⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡏⣠⠎
⠀⠀⠀⢹⣿⣿⣿⣧⣸⡇⣶⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣼⣿⣿⣿⡏⠀⠀⠀⠀⡰⢻⠁⠀⠀⠀⠀⠀⠀⡠⢺⠃⠀⠀⠀⠀⠀⠀⣠⠔⢻
⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⢿⣿⣿⣿⣿⠃⠀⠠⠒⡏⣠⡆⠀⠀⠀⠀⢠⠒⠞⢀⡎⠀⠀⠀⠀⠀⠊⣛⠁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⣿⡿⠿⠀⢨⣿⣿⡿⠃⠀⠀⠐⠀⢛⠀⠅⠀⠀⠀⠀⠈⠒⢹⡁⡑⠀⠀⠀⠀⠀⠁⠀⠀⠀⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡯⠓⠀⠀⠀⠀⠀⠀⣰⣿⣷⣭⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣿⣕⣿⠟⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⣠⣿⠟⠿⠈⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟
⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠫⣺⠋
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠆⠀⢀⣴⣶⣶⣶⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⡟⠀⠀⢀⣴⡆⠀⠀⣾⣽⣿⣿⣿⠆
⠀⠀⠀⠀⠀⣴⣿⣯⠀⠈⠻⣄⠀⠈⠻⢿⣿⡿⠿⠛⠛⠋⠉⠉⠀⠀⠀⢰⣿⠁⠀⣠⣿⠋⠀⠀⡼⠋⠀⢰⡿⡷⡄
⠀⠀⠀⠀⢀⣽⣿⣿⣀⠀⠀⠀⠀⠀⠀⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣼⡟⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣅
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢠⣿⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠿⠿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠛⠋⠉⠛⠛⢎⠣⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⣀⣤⠴⠶⠦⠀⠀⠀⢸⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡀⠀⣠⡶⢛⡭⠄⣀⡄⠀⠀⠀⠀⠀⡇⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢀⡞⣡⡾⢋⣴⡏⣠⡟⡁⠀⠀⠀⠀⠀⠀⠇⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⣿⡟⢡⣾⡟⢰⣿⠏⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣿⡿⠀⣾⣿⠀⣿⡏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢻⡆⠘⡇⢸⣿⡏⢸⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠜⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⣀⢀⣾⠇⠀⠀⣾⣿⡇⢸⣿⣿⣷⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢞⣛⡫⠆⢀⢠⡟⣿⡇⣸⡿⣿⣿⣆⠀⠀⠛⠉⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣡⣤⠴⡫⠋⠀⢻⣇⣿⡇⢻⣿⣿⣦⠀⠀⠤⢶⣶⣶⣿⡗⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠀⠀⠀⠀⢀⡶⠘⣿⡿⠀⠈⣿⣿⣿⣧⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡴⠖⠀⢀⣀⣠⣤⣶⠟⠁⡴⣿⡇⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣠⣴⣾⣿⡿⠟⠉⠀⠀⢀⡆⢸⡇⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⣿⣿⣿⣥⣤⣴⣶⣾⡿⠃⣿⠀⠀⡄⠀⣽⣿⠇⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⣿⠿⠟⠛⠛⠛⠛⠉⠁⠀⠚⠁⠀⠜⠀⢠⣿⡿⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢀⠀⠀⣀⣤⣶⣶⠶⠶⠶⠶⠶⠒⣋⣴⢿⡏⠀⠀⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣰⠁⢀⣾⣿⠟⠁⠀⠀⠀⠀⠉⠉⠉⣩⣴⡿⠁⠰⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣼⣿⠣⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⡁⠀⠀⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢀⣔⣥⣾⣿⡿⠛⠋⠁⣠⡆⣿⡄⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⣿⣿⣿⣿⠟⠁⠀⢀⣠⣾⡿⢡⣿⣷⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢻⡿⠁⣠⣴⣾⣿⡿⠛⣡⣿⣿⡿⣠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣾⠿⠋⠉⡀⢠⣾⣿⣿⡿⣱⣿⡿⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⢀⡾⣰⣿⣿⣿⣯⣾⡿⠋⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣼⠇⣿⣿⣿⣿⠟⠁⠀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⣿⣿⢋⡆⢠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡙⣿⡇⣼⣧⡸⣅⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠸⣿⡝⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣠⣿⣿⡿⠛⠛⠻⠛⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⠿⠿⢿⣿⣿⡄
⠀⠀⢸⣿⣿⢿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⣼⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣏⣿⣿⣿⢻⡿⠃⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠈⣿⠟⠁⡼⠁⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠐⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠉⣹⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡛⠿⠄⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡄⠀⠀⠀⠀⠀⣰⣿⢿
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⢠⡟⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠟⢷⣦⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣾⣿⣿⡵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠠⡟⠋
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⣾⣿⣿⣿⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢀⣿⡿⠟⠛⠛⠿⠿⠿⠿⢿⣇
⠀⠀⠀⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⣼⣿⣿⣿⠻⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠊⣿⡇⠀⠀⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡦⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠁⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠿⠻⢷⡀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠠⢾⣿⣿⣿⡿⢸⣿⣿⣿⠹⣿⠈⢿⣿⣿⡆⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣧⠀⠀⠀⢀⣾⣿⣿⣿⢿⠀⠀⢹⣿⡇⠹⣿⣿⣿⣿⣷
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠻⣿⣿⠀⠟⠀⢸⣿⢿⠃⠀⠀⠀⢸⣿⣿⡟⣿⠈⢿⣿⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠉⢿⣿⣿⣿⠘⠀⠀⢸⠏⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠘⠃⠀⠀⢀⣾⣿⠘⠀⠀⠀⠀⠈⣿⢿⡇⠈⠀⠈⠗⠀⠀⠀⠀⢸⣿⡟⠃⠀⠀⠀⡼⢿⣿⣟⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠘⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠀⠀⠀⠀⠀⠀⠘⢿⣏⠂⠀⠀⠀⠀⠀⠀⠀⣽⡟⠉
⠀⠀⠀⠀⠀⠸⢻⣄⠀⠀⠀⠀⠀⠀⣸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⠀⠀⠀⠸⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠰⣷⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣷⡀⠀⣼⣿⣿⡀⣤⠀⠻⣧⠀⢹⡄⢠⣾⣿⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⡹⣿⣷⡀⢻⣿⣿⣧⣿⠀⠀⣿⣆⠘⠇⣀⠙⠿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠈⠙⠋⠀⠀⠈⣿⣿⣿⡟⠀⠀⠀⠙⡄⢀⡎⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⣰⣿⡷⠀⠫⢀⣈⡰⠀⠈⢿⣿⡧⠀⠐⠀⠀⠘⡄⠀⠀⠀⠀⢠⣼⣿⡿⠿⠟⠃⣠⡄
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣼⣿⠏⠀⣀⣤⠴⠒⠁⠀⢀⣤⢤⡄⠀⠑⣄⠀⠀⠀⠀⡇⠀⣸⣿⣿⡟⠀⠠⠶⣛⣉⣁⡀
⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⣿⡿⠁⠐⢻⠟⠁⢀⣤⡶⠧⠘⣿⡽⢿⣄⠀⠈⢷⣄⠀⢠⡇⢠⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢰⡇⠀⢠⡞⠉⠀⠀⢀⣠⣴⡾⠋⠁⠀⠀⠀⠘⢷⣜⢿⡆⠀⠈⠀⠀⢸⡇⣾⠟⠁⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠠⢻⠀⣴⠋⠀⠀⠀⠀⠈⠿⠋⠁⠀⠀⣠⣴⡀⠀⠈⠳⢿⡇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠴⠇⡸⠈⠁⢠⣦⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣿⣧⡀⠀⠀⠀⢻⡄⠀⠀⠀⣿⣧⠀⠀⢸⠀⣤⣤⣈⡛⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠩⡀⠀⢠⣿⠃⣴⣾⣿⣿⣿⣿⣿⣿⠟⢋⡉⠋⠀⢴⣶⣆⠀⢻⡄⠀⢠⣿⣿⣦⠀⢼⡇⠀⠀⣀⠀⣀⠀⠀⣰⣿⢃⣤⡄
⠀⠀⠀⠀⠀⠁⢠⣿⠃⠘⣿⣿⣿⣿⣿⠿⠋⠀⠀⡾⠋⠀⠀⠸⢯⡿⠀⠀⢉⠄⢀⠉⠙⠁⠀⠀⣠⡴⠚⠁⢸⣿⡆⣴⣿⣷⣿⣯⣴⠆
⠀⠀⠀⠀⡤⢺⣿⡇⠀⠀⠈⠛⠛⣿⣷⡆⠀⠀⡘⠁⠀⢀⣀⠀⠀⢷⠀⠀⠀⠀⠀⠁⡀⣤⡶⠛⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣭⡄
⠀⠀⠀⠀⠁⣹⡟⠀⠀⡠⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⢠⣾⡿⠁⠀⠘⡄⠀⢎⢀⡙⣁⡴⠋⠀⠠⡸⣷⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠠⣿⡟⠀⢀⡞⠁⠀⠀⠀⠀⠹⣿⣧⠀⠀⣠⣿⡟⠁⣠⣤⠀⠡⠀⠀⢰⠁⠹⠀⢠⣦⠀⠙⢿⡆⠙⢿⣿⣿⣿⠿⢋⣀⡀
⠀⠀⠀⠿⠿⠀⣰⡟⠀⢀⣴⡾⠂⠀⠀⠙⠿⠀⢀⡿⠟⠀⢠⣿⠏⠀⠀⠀⠀⣁⠀⢶⡀⠀⢿⣇⠀⠘⣧⠀⠀⠉⠻⠁⣠⣿⣟⠝⠂
⠀⠀⠀⠀⢀⣼⣿⠀⣴⣿⡿⠿⢦⣀⠀⢀⣤⢀⡾⠁⠀⢠⡿⠃⠰⠷⠠⠀⠀⠻⣷⡄⠙⠦⠘⣿⡄⠀⢻⠀⢠⠢⠀⢰⣿⢿⠊
⠀⠀⠀⠀⠘⠋⠋⠀⠀⣿⣳⡄⠀⠀⡴⠟⢁⠞⠀⠶⣤⣀⠀⠀⠈⠈⠀⠀⠀⠀⠘⢿⣦⡀⠀⠹⣷⡀⠘⠀⡆⠐⢠⣿⡟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣦⠀⠀⠈⢠⣄⠀⠀⠀⠉⠀⠀⠠⠈⠈⠀⠀⠀⠀⠹⣷⣄⠀⢻⣧⠀⠀⠈⢁⣾⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠘⢷⣦⣻⣷⡀⢰⣷⠀⠀⠀⢢⣴⣦⡀⠀⠀⠐⠈⠻⣧⠀⢻⡆⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠋⠀⠻⣷⣿⣿⣿⣿⣾⣿⡇⠀⠀⠈⢿⣿⣇⠀⠙⢦⣄⠀⠘⢷⣄⢿⡀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⡌⣿⣿⡄⠀⠀⠙⢷⣤⡀⠙⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⠟⠀⣾⠃⠸⣿⣿⡀⠀⠠⠈⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⢸⡾⠀⠀⠻⠿⠇

⡿⠿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⡿⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣧⠞⠹⣅⠀⠃⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣁⣀⣤⡴⣠⣤⣄⡀⠀⠀⢸⣉⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠵⣿⣶⣾⣏⣽⡟⠛⢻⣿⣄⠛⠛⠋⢙⢲⣤⣀⣀⣠⣿⠇⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣖⢦⣀⣼⡱⢟⠸⠟⣿⡿⢉⠄⠀⠘⣿⣘⣻⣿⣭⢱⣿⡟⣉⡙⣿⣯⡤⠤⠞⠁
⠀⠀⠀⢠⡶⣿⣿⢿⣕⣾⣿⣃⣻⠆⢠⢋⣹⣿⣾⣤⣤⡀⠘⢿⣿⣅⡈⠻⠉⠳⡿⣷⠸⣏⠰⣶⡄
⠀⠀⠀⢿⣻⡋⣹⣿⣿⣿⣵⢸⣿⣄⠰⣜⣻⢿⣿⡿⢋⣽⣦⠀⠙⢿⡝⢶⣄⠻⢷⡾⠷⣝⡒⣀⡀
⠀⠀⠀⠀⢹⣿⠟⣉⣭⣉⠛⣞⢩⣽⢗⢶⣶⣿⠟⣰⣿⣿⡬⠃⡀⠛⠁⢀⣿⣦⣴⣦⣴⣯⢟⣿⣧
⠀⠀⠀⠀⣿⣿⡀⠿⢿⣿⡆⢨⣤⣝⠻⠿⠟⠁⣴⣿⡿⠋⣠⡾⢻⣷⣶⡟⠛⠉⠉⠁⠀⢹⣿⡆⠈⣧⢀⡀⢀
⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⡇⢸⣿⡿⠇⠰⣠⣾⣿⣿⡾⠿⣛⣫⣭⣤⣤⣤⣠⣤⣤⣶⣶⣾⣃⠀⢠⣿⠁
⠀⠀⠀⢀⣿⣿⣿⡇⣎⠾⠇⢾⣛⣷⢞⣽⣵⡆⣻⠛⢿⣿⣛⠛⠻⠿⣿⣿⣏⢼⡹⣿⢏⢙⣿⣧⡾⠃⣀
⠀⠀⢘⣾⣿⣿⣿⣷⣌⣁⣀⣼⣷⣿⣿⡿⢫⣴⣿⡻⣦⣌⠻⢿⣿⣶⣦⢬⣈⢽⣷⣶⣿⣿⠋⣽⣶⡸⣿⣧
⠀⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⡋⣝⣿⢰⠋⣤⣙⣷⡸⣯⣷⣄⣙⠿⣿⣢⡽⣣⡙⣿⣿⢇⣼⣿⣿⣿⡝⡿⠇
⠠⣾⣿⣿⣿⣿⣿⣿⢱⣾⢿⣿⣷⣬⣭⣠⡀⢿⣿⣿⣿⡌⠻⢿⣟⠳⣮⣙⠳⣿⣯⣿⡷⠿⡟⠛⠛⠛⠁
⠘⣿⣿⣿⣿⣿⣿⣿⣦⣭⣾⣿⣿⣿⣻⠯⣿⡌⢿⣿⣯⠗⣀⡤⢿⣇⠘⢿⢗⣾⡿⠁⠀⠤⠟
⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡧⢸⡈⠻⣿⣁⣤⠞⣋⣷⣶⠿⠋⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣝⣛⣡⣿⣿⠆⣯⣩⣶⣠⢿⣫⠕⠂⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣶⣾⣿⣿⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⠁⣼⡄⢻⣏⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⣾⣿⠇⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠇⠀⣠⣴⠾⣛⠛⠻⣶⣄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢏⣴⣾⣿⣿⣿⣿⣿⣦⠈⢿⣇
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣿⠟⠛⠀⠀⠀⠀⠀⣠⣴⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⡄⢀⣀⡀⠀⠆⠀⣀⠉⠉⠛⣿⠿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⠀⢰⠛⣾⣖⠥⠄⠀⠀⠹⠗⡄⣀⣀⣄⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠿⠤⠖⠊⢉⣡⠶⣁⢿⣭⡟⣿⣭⣭⠁⠄⠀⡀⠈⠉⠁⢀⠂⠒⣄⠲⣔⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣾⡿⢿⣾⣾⣿⣿⡽⣡⡞⠀⢟⠀⢤⣁⢀⢠⠘⠀⠀⠙⢘⡴⢋⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⢠⣟⣷⣦⣤⠠⣌⣿⡾⢷⡯⡞⣿⡉⣿⠀⠈⢰⠣⣌⡙⢿⠦⠀⠓⣴⠮⠄⠔⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢏⣟⣻⣿⣰⣿⡾⡲⢾⠎⠿⡿⠗⢂⣼⣷⠘⢦⡄⠁⠀⠘⣀⠔⠁⠀⠐⠂⣰⡾⠛⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡻⣯⡿⣟⣿⣟⡇⢼⣻⢁⠊⢸⣷⣚⡁⠘⢌⠁⢀⠿⣉⡷⡽⣯⡀⠀⢀⠘⣷⣉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣾⢸⣿⣾⣷⣏⣼⠟⣉⠔⠛⠃⣠⣤⣀⣈⠳⣬⠃⢡⢐⠦⣿⣧⣗⠀⢧⣾⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⢽⣙⡾⣾⣿⣭⣿⣣⡞⣁⣴⠊⠉⠀⠀⠀⠈⠻⣯⡀⣰⢚⢷⡾⢋⡨⣑⣾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣫⠷⣧⢿⣼⢻⣿⣼⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⢻⡿⢟⠧⣀⡿⢛⣴⣼⠷⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣻⣿⣯⣹⣮⣝⣽⣞⢽⣿⠿⠋⠀⠄⠀⠀⠀⠀⠀⣸⠁⣆⢦⣉⣧⢭⣤⣏⡱⠊⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣿⣿⣿⡝⣿⣻⣭⠏⠃⠀⠀⠀⠀⠀⠀⠠⣴⡿⣧⡈⠳⡏⠙⣯⡠⠤⢰⣦⠔⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠛⠲⣾⡏⢾⣿⡆⠀⠀⠀⠀⠀⠀⢴⣾⠟⢀⡜⢡⣼⠸⢷⣾⠀⠆⠈⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢠⠈⠉⡍⣿⡇⠀⠀⠀⠀⠀⠢⡀⠀⢀⣠⣾⣧⡹⣿⣳⢾⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠾⣝⠲⣧⣿⣇⠀⠀⠀⠀⢀⠈⠁⠀⠀⠉⣛⢿⣿⣷⡱⠁⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⡜⡉⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢻⣿⠟⡩⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣣⣸⣤⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⢠⣧⡾⠤⠶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡝⡍⢳⣦⢤⣀⣀⡀⣠⣿⣦⣤⠎⢠⢳⠶⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣌⣮⣷⡤⡭⣿⣬⢟⢩⢭⣿⠒⠓⢺⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡏⢁⡴⠚⢻⠧⣤⣈⠈⢷⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡾⠀⣂⠷⡀⠀⠙⢆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠉⠈⠃⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠂⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣬⡓⢤⡀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡛⢿⣶⣌⡳⢤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⣠⠞⣡⣄⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣍⡻⢿⣦⣍⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⡿⢋⡴⠀⠀⠀⠀⠀⠀⠛⠛⢀⠀⠀⠀⠨⠀⠀⢀⠔⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⠻⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠳⠄⠀⠀⠀⠀⡎⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⡤⠀⠀⢀⠖⠋⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢩⠛⠉⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⢂⠘⢆⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⣀⠔⠓⠢⠀⠀⠀⡄⠀⠀⢠⠔⠈⠀⠉⠃⡀⠀⠁⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⢀⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢣⠀⠀⠀⠀⠈⡆⠰⡇⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠁⠀⠀⠀⢀⠀⠀⣀⡀⠀⠾⢥⡤⠚⠀⢴⡇⢤⠀⠀⠀⢀⠇⠀⠙⠂⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⢀⣀⡀⠀⠀⠈⠀⠀⢀⡇⠀⠁⢀⡴⠟⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠚⠉⠉⠁⠀⠀⠀⠀⠀⠄⠊⢣⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡂⣒⣾⠟⠀⠀⢤⣄⣀⠀⣀⣠⠴⠿⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢠⡐⢄⠂⠭⣛⡭⡭⣒⠵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣰⣷⣿⣿⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠐⢶⣦⣴⣶⣶⣦⣄⠀⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡄⠀⣰⠆⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠛⠀⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣬⣀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠘⢿⡿⣿⣿⣿⣿⣿⣿⣋⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⡿⣿⣟⣛⣙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠟⠛⠉⢻⣿⢿⡇⢸⣿⣿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠡⠜⠟⠻⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣟⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢠⡄⠀⠀⠀⠀⠈⢀⣿⣿⣿⣿⡟⠁⠀⢶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠃⠀⠸⣿⣶⣧⣀⣀⣴⣿⣿⣿⣿⣿⣴⣿⣦⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣄⠀⠘⠄⠀⠀⠀⠈⠻⠋⠻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⡀⠀⠀⣠⣴⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣷⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣽⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣿⣿⡿⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠈⣯⣩⣬⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⡶⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠄⢰⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣾⣿⣇⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⠟⣉⣿⣽⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⣯⣻⡙⠿⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣶⣯⡿⡟⠿⢿⣿⣿⣯⠙⡏⠻⡙⣏⠐⠀⠡⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣼⣿⣿⣿⣿⣿⣿⡔⣆⠀⡘⠛⣿⠀⠀⢀⡗⢨⠀⠀⡀⠀⠒⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠰⣿⣟⣿⢿⣿⣿⣿⣿⣿⣾⣷⣠⣿⣃⣤⣴⠇⣎⣄⣠⣁⡤⠀⠘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣿⣿⣿⡿⣫⡄⠳⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⡿⠟⢹⣧⡝⠀⠀⠀⢻⣿⡿⢿⣟⡛⠻⠿⠿⣿⣿⣿⣿⣯⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠘⠾⣻⡿⣟⢳⣤⣀⠀⠂⠈⢻⡟⢷⣤⣄⡀⠀⠀⠀⠀⠉⠛⢿⣷⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠈⠀⢴⣤⣬⣉⣉⠓⢉⠳⣄⠨⢀⣿⣦⣉⠉⠓⡀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠄⣴⣶⣦⡍⠙⢷⡀⠀⢘⣧⣼⣿⠻⣆⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠈⠻⣷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠦⠞⣷⠀⠀⠘⣿⣇⠈⣻⣿⣷⣿⣶⡐⢺⣿⡗⠀⠈⠳⣄⠀⠠⠀⠀⠀⠈⠛⠶⠄⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣛⠳⠀⠐⠈⣧⡀⠀⠈⠛⠷⠿⠿⠾⢻⠎⠀⢷⡇⠀⠀⡀⠀⡀⠀⠳⣦⡀⠀⠀⠀⠀⠀⠘⢦⡿
⠀⠀⠀⠀⠀⠀⢀⣾⣦⠀⢄⡀⠒⢠⡇⡛⠀⠀⣠⣤⣤⡀⠀⢠⣤⣾⣷⠀⠀⠙⣆⠀⠀⠀⢮⣿⣦⣀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣥⣙⢷⡌⠱⠆⢳⣠⡇⠀⠘⣿⣿⣿⣿⣖⣻⡍⠉⢻⡀⠄⠀⠈⠣⡄⠀⠈⢻⣿⣿⣷⣄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢠⣞⣿⠉⠀⠀⠀⠀⠈⠛⡄⠲⠆⠹⠻⠿⠛⠉⣻⣷⣄⡀⠻⣄⠀⠀⠀⠈⠀⠀⠈⣿⠹⣿⠎⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠘⢧⡏⠀⠀⠀⣬⣾⣷⣶⣤⠠⠔⠀⠀⠄⢴⣆⣦⡉⢛⣣⣤⣬⡢⡄⠀⠀⠀⠀⡄⣿⡇⠛⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⢲⣦⣴⣿⣿⣿⣿⣿⠇⡀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⡝⢧⡀⢄⢶⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡟⢮⣻⠟⢻⡟⠟⠿⡿⢿⣿⣿⣿⣿⡿⣿⣿⣭⣌⣿⣛⣿⢻⣎⢿⡎⡞⣿⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠛⣋⡀⠀⠈⣿⠀⡀⢀⠐⢂⠈⣽⣿⣷⡿⣿⣷⣿⣿⢱⡏⠀⠋⠘⠟⣿⡏⢠⠃⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣷⣷⢸⣿⣧⣕⠠⡍⣬⣹⡷⠋⠀⣀⠞⣹⢯⡟⢸⠇⠀⠀⠀⣠⡟⠀⠘⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⢿⣿⣿⣿⡞⡽⣣⢫⡟⡠⡀⠁⠀⠹⠏⢠⡿⢠⠀⠀⢰⣿⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⡄⠀⠀⠀⠀⢹⠋⠁⢸⡟⢿⠻⣾⡵⣣⢏⡼⡃⠂⠀⠀⣰⣶⡿⠁⠃⣄⡴⣿⠇⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠧⠀⠀⠀⣀⢿⡄⠀⢸⣷⡀⠀⢻⣷⣇⣾⢸⣿⣤⠀⢠⣿⡟⣡⢏⣾⠋⢠⡟⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢦⣰⣿⣿⡿⣧⠀⢸⣧⢡⠀⠀⠙⢙⣿⣛⣿⣿⡄⠷⢟⠰⣱⣿⣿⠀⣼⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠈⢠⣾⣇⢸⠀⠀⠀⣸⢿⣏⣿⣿⣷⠀⡌⠀⣽⣿⣿⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡞⡜⠀⠀⠀⢼⣷⣿⠻⣽⣿⡀⠁⢰⡏⢻⢿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠠⣀⡄⢠⠉⡴⣭⢱⣾⣿⣿⡀⠀⠀⠀⠈⣧⡇⠀⠀⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣠⣄⣠⡁⠀⠤⠀⢐⣊⣶⣻⣿⣿⣅⠀⠀⠀⠀⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⢖⡨⢃⡤⢀⠀⠀⢀⠀⠀⢀⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⠠⠤⢦⠆⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⡿⠰⣣⡞⠀⢀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡛⠠⣤⣿⠁⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⡿⠀⢠⣿⡟⢀⣴⡶⢲⡆⣾⡶⠛⣿⡇⣿⠏⣀⡿⠃⠀⣼⣷⠀⠀⣴⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡾⢱⣿⠇⢠⣿⣿⢃⣿⡟⢀⣾⢳⣿⣵⠞⠉⢠⣿⣿⠉⠀⠀⢸⣿⠃⣠⢾⣿⠇
⠀⠀⠀⢠⣤⠀⢀⡾⠁⣾⡿⢠⡏⣿⡏⠘⣿⡛⣋⡴⣻⡟⢿⡀⠀⢸⡿⣿⠀⠀⢸⡎⠛⠛⠃⣾⡟
⠀⠀⠀⠸⣯⡠⠟⠀⠀⢿⣷⠏⢸⣿⠃⠀⡈⠉⠉⠀⣿⡇⠘⣇⠀⠺⠇⠘⢦⣤⡼⢣⡤⠀⣼⡿⢡⣎⡗
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠘⠿⣤⠾⠁⠀⠀⠀⠉⠁⠀⠘⠳⠤⠾⠀⠀⠀⠀⢿⣀⣼⡿⠁⣞⡷⣞⠄
⠀⠀⠀⠀⢀⡴⢻⣿⠀⠀⣿⡇⠀⢀⣠⣴⠖⠛⣷⠰⣿⡇⢀⣴⠞⠓⣦⡀⠀⣶⡆⢀⣭⣭⣤⣤⣤⣤⣶⣶⡦
⠀⠀⠀⢰⠟⠀⢸⣿⠠⠾⠻⣤⣶⠋⣿⣿⠀⣠⡿⢡⣤⠀⣿⡏⠀⠀⠛⠃⠀⣿⣇⡤⣤⡀⠀⠀⣿⡇
⠀⠀⠀⣿⠀⠀⢸⣿⠀⣠⠞⠙⣿⡄⣿⡷⡞⠁⠀⢸⣿⠀⣿⡇⠠⠶⣶⡶⠂⣿⡏⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠈⠀⠀⢸⣿⣰⠏⠀⢀⣿⠇⣿⡇⢻⡄⠀⠸⠿⠀⠻⣧⣀⣰⣿⠇⠀⣿⡇⠀⣿⠃⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢻⣀⣀⣼⠟⠀⣿⡇⠀⠻⣤⣀⣠⠆⠀⠈⡇⠘⠿⠂⠀⣿⡇⠘⣿⣠⡷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠦⠠⠁⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠓⡄⠀⠀⠀⠀⠀⠀⢀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠖⠀⠀⠀⠀⠀⠀⠀⢘⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡤⠴⠶⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣀⣀⣠⣄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢦⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠝⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⢀⡠⠀⢀⠄⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣋⠉⠳⣄⠑⢤⠀⢶⣈⣉⢡⣻⣿⣿⣷⣀⣾⣏⣴⠊⢀⡔⢁⣴⣉⣉⣵⠖⣊⣭⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣥⢹⣶⣾⣿⣯⣼⣧⢸⣧⡼⠯⠉⠀⠈⠛⠁⠀⠉⢻⡿⣿⣇⣟⢠⣿⣭⣭⣽⡿⢟⠋⡉⠅⠠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⠀⠍⠿⣿⣿⣿⣿⣿⣿⡂⠀⠐⠀⠈⡏⠀⠀⠤⠀⣆⢻⣿⣿⣼⣿⣤⣿⣿⠘⡨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣁⣀⣐⢻⣿⣿⡟⣷⣿⠃⡀⣁⡶⢿⣿⡷⣤⡠⠎⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⢛⣡⡴⠟⣉⣤⣿⠆
⠀⠀⠀⠀⠀⢠⣏⣈⠹⠷⠓⢙⢙⢻⣻⣿⣿⡵⠟⠡⠜⠛⠁⣀⣀⣀⣀⡈⠙⠾⣡⠟⢿⣿⣿⣿⣿⣿⠯⠉⠆⠰⠀⠆⢠⠄⢠⠈⡁⠐⠃
⠀⠀⠀⠀⢠⡶⠈⢁⠰⠄⢃⠉⠄⠒⣃⣽⣿⣡⠝⣀⢴⡂⣀⣀⣩⣍⣁⣉⡓⣲⣬⣿⣷⣏⣿⣿⣿⣿⣄⣨⣅⠈⠀⠀⠀⠀⠈⠀⠁⠘⠂⡄
⠀⠀⠀⠀⠊⢀⠐⠈⠀⠈⢀⠐⢦⡼⢛⣻⣿⣷⣮⢕⣀⣿⠤⠤⠼⣶⠦⠭⣽⣟⠂⠙⣿⣿⣿⣿⣿⣿⠃⡍⢘⠛⠛⢋⣃⣀⣀⣀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢡⡶⢃⡐⠂⠼⣿⣷⣽⡯⠀⣸⣇⡒⢡⡘⣛⣒⡿⠄⣠⢾⣿⣼⣿⣿⣿⣌⠑⠀⠁⠚⣠⠄⠉⠋⢥⣭⣥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡞⠀⠖⠀⠈⣴⣿⣿⣿⠇⢉⢨⡯⣠⣾⡵⣩⣽⣛⣣⣿⣿⣿⣿⣿⡿⢉⠷⠶⣤⠈⠀⠀⠈⢁⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠃⣾⣿⠱⣿⣿⡾⢋⠀⠳⠾⢁⣰⡷⠚⢠⣿⢿⡟⣿⣿⣿⣿⡩⠄⠳⡶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡆⢩⣿⣻⣐⡧⠘⠃⠀⠀⠋⠑⠛⢦⣜⣯⡿⣎⣿⣿⣏⠣⠨⠄⠻⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣾⡟⣳⣎⡑⠀⠒⠀⠂⠴⠆⢴⣼⣿⣿⣿⣿⣿⣿⣿⣄⣥⣵⣞⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⣿⣿⣧⣶⢶⠰⠂⠆⢶⣾⣿⣿⣿⣿⣷⣿⣿⣿⡟⣿⠟⣉⣰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠚⠁⢙⢁⠎⣟⢻⢺⣿⣿⣿⣿⣿⣿⣿⣷⢛⣌⣷⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⢧⣶⡖⡾⣮⡶⣥⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣤⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⣿⠋⢸⡏⡇⢠⠉⣟⣛⣿⣿⣿⣿⣿⣿⣿⡏⠻⣿⣀⠐⣾⣿⣿⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣾⠃⠀⠀⠄⠀⠀⣀⣁⣈⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣏⡑⣿⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠃⠀⠀⠀⣙⡀⠀⣤⣭⣯⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣏⠛⣿⣿⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⢠⡀⠈⠁⠳⣿⣿⣿⢿⣿⣿⣿⡟⠛⣿⠀⢨⣿⡡⣽⣟⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠂⠩⣱⣿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠛⢠⣿⣿⣷⠚⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⡄⠀⠑⢤⡀⠀⠀⣄⡳⢦⣻⣿⣿⣿⡿⢿⣿⣿⣿⣄⣀⣤⣿⣟⠉⢿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠷⠀⢀⡀⢉⣲⣅⡠⣸⣿⣿⣿⠿⣹⠿⣾⣿⣿⣯⡏⠉⢸⣛⡉⣸⣾⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣴⣾⡏⣸⣿⣿⣿⣿⣿⠿⢿⣶⢿⣶⣞⣿⣿⣿⡇⠀⠐⣿⠞⣯⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠿⠿⠿⠛⠁⠀⣹⣛⣿⡷⣶⣿⣿⣿⣿⠀⢠⣷⠞⣿⣾⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⠿⠟⣺⣿⣿⣿⢿⣇⠘⡿⣿⣿⣯⡷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣒⡈⠿⣛⣿⣿⣿⣿⠀⣧⣜⣓⡚⣺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣬⣬⡴⠾⠛⢻⣿⠿⢿⣧⣀⠋⢙⣛⣿⣟⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⡛⠀⢲⡖⠛⣶⡝⠓⠚⣿⣛⣿⣉⣀⣾⣉⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⠓⠶⡜⣃⣤⣤⠤⢄⣀⣠⡞⣫⣥⣶⣦⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⢀⡈⠀⢰⣾⡟⡿⢁⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⣠⣾⣿⣿⣿⡘⢿⣧⢧⠸⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⣰⣿⣿⣿⣟⢿⣿⣦⣙⢿⣷⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⣿⣿⣿⣿⢿⣷⣝⣿⣿⣿⣾⣿⣿⣿⠿⠿⣿⣿⣿⣟⣋⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣆⠀⣿⣿⣿⣻⣷⣽⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠈⠉⠉⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⣿⡀⢹⣿⣿⣿⠿⢿⣿⠟⠉⠉⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⢿⣧⠀⢻⣿⡆⠀⠈⠁⠀⣀⣄⣀⣀⣀⠉⠻⠶⠀⠀⢀⣀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⢸⣿⡆⠈⢿⣿⡀⠀⠀⠀⠘⢿⣟⡻⠿⣿⠀⠀⢀⣀⣉⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣇⣿⣿⣧⣿⡇⢸⡎⣿⣿⣆⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠞⣻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣿⣿⡇⣼⣧⣿⣿⣿⢧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢀⡤⠤⡙⣿⡿⠛⠓⢿⣿⣿⢹⣿⠀⠙⢦⣄⠀⠀⠙⠷⠒⢀⣴⣯⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣴⡏⣾⣷⡇⡸⢰⣿⣿⡌⣿⡿⣾⣿⡀⠀⠀⠙⢷⣄⣀⣡⣶⣿⣿⣿⢟⣩⣭⣀
⠀⠀⠀⠀⢰⣿⣷⣙⣛⡡⢣⣿⣿⡿⢠⣿⣿⣿⡟⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣾⣿⣿⣟⣵⣿⣿⡿⠋⠀⠈⠆⠀⠀⠈⠻⢿⣿⣿⣿⡿⣿⣶⡾⣋⡾⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠁
⠀⠀⢀⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⠀⢀⡀⣀⣀⣀⣀⠀⣀⣀⢀⡀⣀⣀⣀⠀⣀⡀⢀⡀⣀⠀⣀⣀⣀⡀
⠀⠀⢸⡿⢼⣯⡼⢿⢿⡿⠹⡏⠹⡏⠀⡿⡧⡿⡿⢿⡿⠀⣿⡿⡾⠷⣿⢿⢿⠀⢽⡷⡿⣧⣿⡶⣿⠿⡿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠙⠛⠛⠻⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠛⢉⣩⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⢀⣤⣾⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⢀⣴⡿⠛⠉⠀⠀⠀⠀⣀⣠⣤⣤⠶⣶⣶⣶⣶⣿⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⣠⠟⠁⠀⠀⠀⣠⡴⠞⠋⠉⠁⢀⣠⠞⠋⢀⣤⣾⣿⣿⡿⢿⣿⣟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⣰⠋⠀⠀⣠⣴⠟⠉⠀⠀⢀⡠⠖⢋⣠⣴⣾⣿⢟⣩⣾⠟⠀⠘⣿⣿⣎⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢰⠃⠀⣠⣾⡟⠁⢀⣠⣔⣮⣵⣶⣿⣿⡿⢟⣫⣴⡿⠛⠁⠀⠀⠀⣿⣿⣹⣸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠃⢀⣼⣿⣯⣶⣾⣿⣿⣿⣿⣟⣻⣭⣷⣾⠿⠛⠉⠀⣴⠶⠖⠢⠀⣿⣿⡏⢸⡇
⠀⠀⠀⣀⣀⡀⠀⣿⡇⠀⠀⣾⣿⣿⣿⣿⡟⠙⠛⠛⣛⡛⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⣿⣿⡇⠘⠀⡀
⠀⡰⢋⣀⡀⠉⠀⠸⣇⠀⢰⣿⣿⣿⣿⣿⡏⠳⡶⠛⡿⣿⣷⡄⠀⠀⠀⠀⠀⢠⡾⣿⣿⠻⣶⣿⣿⠇⠀⢠⠇
⠀⠀⡊⠀⠁⠀⠀⠀⠹⡄⢸⣿⢿⣿⣿⣿⡇⠀⠙⠄⣳⣟⠋⠀⠀⠀⠀⠀⠀⠈⢒⣿⡛⠐⢹⣿⣿⠀⢀⡾⠀⠀⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⣿⡌⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢀⡾⠁⠀⢸⡀⣀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠙⠺⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⣼⣿⠏⡰⢫⠇⠀⠀⠘⠛⠃⠀⠀⢸
⠀⠀⢀⠴⠊⠁⢀⣀⡀⠀⠀⠢⡙⣆⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠈⣀⡈⠁⠀⠀⣠⣾⡿⠃⠀⢠⡏⠀⠀⠀⠀⠀⠀⣀⣴⠟
⠀⢰⣏⠀⠀⠀⠀⠀⠉⠓⢄⠀⠘⠜⠄⠀⢸⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⣀⣴⣾⡿⠋⠀⠀⣠⠏⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠈⠁⣠⠤⠒⠀⠀⠀⠀⠀⢳⠀⠐⠀⠀⣼⣿⡇⣿⣿⡿⠀⠈⠉⠛⣿⣿⣿⡿⠋⠀⠀⠀⠀⠁⠀⢀⡀⠀⠢⢄⣀⣀⡠
⠀⣠⠎⢁⡴⠚⠁⠀⡀⠀⠀⠀⠃⠀⠀⢠⣿⣿⡇⣿⣿⠃⠀⠀⠀⢸⡟⢸⣿⠁⠀⠀⠀⠀⣤⡀⡴⢻⣇⣀⠀⠀⠀⠁
⢰⠃⠀⣾⠁⠀⠀⠚⠃⠀⠀⠀⠀⠀⢠⣾⣿⡿⢰⡿⠁⠀⠀⠀⠀⢻⣇⠀⠙⢦⠀⠀⠀⠀⠣⢘⡀⢋⡉⠉⠳⣄
⡟⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠁⣾⠁⠀⠈⠂⠀⠀⠘⢿⡄⠀⠀⠀⠀⣠⢒⣡⢚⠛⢄⠲⢤⡤⠞⠃
⣇⠀⠀⠀⠙⠻⢶⣶⣶⣶⣾⣿⣿⠿⠛⠁⠀⢠⡇⠀⠀⠀⢰⠀⠀⠀⠀⠻⣦⠀⠀⠀⠉⣽⠁⠉⢸⡄⠀⠀⢷
⠘⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠳⣄⠀⠀⣿⠀⣠⠞⠙⢦⣀⠸
⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀⠸⠟⠁⠀⠀⠀⠈⠓⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⢧⡀
⣠⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣉⣢⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣀⠠⠂⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣒⡚⡒⢦⡹⡄⢀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢀⠀⠀⠀⡢⢄
⠀⠀⣀⣀⣧⠼⠃⣀⡀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⡴⣫⠖⠒⠂⠀⠃⢃⠜⠀⠀⠀⠀⠀⢀⡞⠁⢀⠔⠁⣀⡠⠂⠘⡌⢣
⠀⢰⡧⡄⠀⠀⢨⡁⠘⡀⠀⠀⡀⢠⡰⡄⠀⠀⢰⢃⠃⠀⢀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⣼⠀⣰⠋⠐⠋⠉⢠⠄⣀⢸⡈⣇
⠀⠈⣭⡠⠰⣍⣱⠇⠀⠒⠀⠐⠂⢀⡤⠋⠀⠀⠸⡄⠈⠀⠉⠀⠀⠀⠤⠹⠃⠀⠀⠀⠀⡇⢠⡇⠐⠄⠀⠀⠀⠀⡀⠈⡇⢹
⠀⠀⠀⠀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠀⠙⠄⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢳⠀⢧⡀⠀⠀⠀⠀⠀⠁⠀⡇⢸
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠍⠒⠀⠀⠀⠀⠀⡸⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠊

⠀⠀⠀⣠⠴⢶⡄⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⢒⣐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠠⠆⠴⠢
⠀⠀⢠⠣⠮⠝⣀⣀⣤⠽⠏⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠋⠁⣠⠞⡡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠰⠀⠒⠤
⠀⠀⠈⠧⡀⠲⢤⠶⠃⠀⢀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠀⠀⣠⡞⢁⡞⢀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠉⠀⠃⠀⠀⠀⠀⢀⡤⠖⠚⠋⠁⠀⡾⠁⠉⠀⠀⠃⠀⠳⡄⠀⠀⠀⠠⠀⠤⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠊⠀⠀⢀⣠⠤⠞⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠀⡍⢠⠀⢐⡂⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⡆⠙⡄⢂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢒⠀⠀⠀⠀⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠰⠀⡇⢰⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠃⠄⡆⢤⠀⠀⠀⠀⠀⠀⠰⡀⠀⡖⠊⠀⠀⠈⣂⠠⡀⠀⡀
⠀⠀⠀⠀⢀⠃⢸⠀⡾⠀⠉⠀⠈⢉⡟⠀⠀⠀⠀⠀⠀⠀⠸⠈⢀⡀⠀⢰⠈⠀⡄⠀⠀⠀⠀⠀⢀⠀⢻⠁⠀⠈⠁⠀⡱⠀⠀⠢
⠀⠀⠀⠀⡘⠀⢸⠀⡇⠀⠀⠰⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢯⡀⠒⠀⠀⢀⡕⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠸⠀⠰⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣿⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠹⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⢯⣅⣀⣤⣤⣤⠀⢰⢿⡿⣟⠻⣿⣿⡿⠿⣿⣿⣿⣿⡇
⣿⣿⣿⣦⣬⣾⣿⠏⣉⣿⣶⣿⣯⣭⣠⣾⣿⣿⣦⣤⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣿⣿⠋⣙⣿⣬⣿⣽⡏⣉⢹⣿⣿⣿⡿⢷⣥⡈⢹⠿⢿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠛⠛⢿⣿⡿⠛⠓
⣿⣿⣿⣾⠿⣾⡍⠉⢞⣿⣿⣧⣴⣿⣮⣵⣾⣿⢿⢿⣶⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿⠃⠀⠈
⣿⣿⣿⣦⢔⣾⣿⣦⣿⣿⡋⠉⠿⠛⣿⡿⠿⢷⣄⣤⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆
⣿⣿⣿⣿⣿⣏⡑⠀⣩⡿⠿⢿⡾⠿⣿⣠⣴⢸⡟⠉⣿⣛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⠶⢆⣤⣤⣤⡿⠀⠀⠀⠀⠀⠸⡧
⣿⣿⣍⠀⢎⣻⡿⣿⣿⣇⢈⣷⣶⡀⣸⡿⢿⡟⡛⢶⣽⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷⡀⢀⣤
⣿⣿⣿⣷⣿⣏⣈⣃⣼⡟⠹⡿⣿⣿⣿⣿⣴⣿⣿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀
⣿⣿⣁⠘⠛⢿⣿⠛⣿⣿⣶⠿⢿⣿⡿⠳⣠⣿⣇⡙⢠⣿⣿⣿⣯⠀⠀⠀⠀⣿⣿⠛⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣧⣿⠟⢻⣿⣯⣤⣿⣿⣬⣴⣾⣿⡟⠿⢿⡟⠻⣿⠙⣻⣿⣿⣿⠀⠀⠁⠹⣿⡿⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣟⠿⠿⢿⡗⠐⠒⠒
⣿⣿⣿⣷⣮⡿⠿⣿⣏⠉⡻⡿⠟⠉⠰⠶⣽⣷⣿⢷⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⢸⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠁⣁
⣿⣿⠏⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⢿⣿⣿⣿⡄⠀⠀⠈⠉⠱⠎⠉⠉⠆⢿⡏⠉⠉⠉⠁⠉⠈⠉⠁⠈⠀⠀⠈
⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿
⣿⣿⣿⣶⣦⣤⣤⣤⣤⣦⣤⣤⣤⣀⣀⣴⣶⣶⣶⣾⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⢤⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠇⠄⢨⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠐⡉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠖⠀⠀⠀⠤⠄⠆
⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠘⠄⠇⡸⠀⠀⠀⠀⠀⠀⢀⡀⢠⠄⠀⠀⠀⠀⠠⢘⠀⠀⠀⡛⠠⠀⠀⠀⠀⠀⠀⠄
⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠁⠈⡆⠀⡇⠀⠀⠀⠀⠀⡔⠙⠁⠞⠸⠳⣆⠀⠀⠐⠨⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⡠⠈⠀⡀⠀⠀⠀⠀⢂⡄⠀⢨⣧⣄⢀⢀⡀
⠀⠀⢀⠀⠀⠀⡀⣀⢀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⡰⠊⠉⠂⠈⠫⠤⡈⠃⡄⠘⠦⣅⡀⢦⠗
⠀⠀⠀⠀⠀⠜⠁⠀⠀⠑⡀⠀⢸⠀⢸⠀⠀⢀⠲⡀⠀⠀⠀⠀⠀⠀⠷⡄⢌⢲⠀⢈⢃⡟⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⠀⠀⢘⠀⠀⠀⠀⠀⠡⠀⢸⡀⢸⠀⠀⠀⠙⠀⣆⡀⠈⢀⣰⠂⠇⠀⠈⢢⡹⣏⠎⠀⠈⠀⠀⠀⠀⠀⠀⢀⠃⠀⡅
⠀⠀⠀⣤⣽⡀⠀⠀⠀⢀⠗⠀⠸⠇⢸⠀⠀⠀⠀⠑⠮⠁⠀⠀⡠⠈⠀⠀⠀⣠⢉⢈⡢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⢀⡀⡁⢀⣀⡠⠆⠀⠀⢀⠻⣿⠤⠀⠀⢀⣀⡐⠁⠀⠈⠢⣀⡀⠀⢸⣁⣽⠓⢶⠋⠀⠈⠉⠛⠒⠤⡴⢉⡁⠀⠠
⠀⠀⠀⠂⠀⠀⣸⢀⡀⠤⢀⣀⠈⣧⡠⣃⢾⣶⣁⠀⠁⠸⠈⠀⠀⠀⠀⢦⡴⠁⢐⠖⠚⠑⠂⠄⡤⢀⠀⠀⡀⢀⣀⡈
⠒⠒⠐⠒⠀⣋⣀⡬⠡⠤⠤⠬⠑⢆⠀⠙⠳⡌⠛⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⣰⡬⠃⠹⡦⠐
⠈⠉⠉⡽⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⠀⠉⢇⠀⠀⠀⠀⠀⠀⡗⣄⢠⡜⠀⠀⠀⠠⠄⠀⠀⠀⢰⠀⠁⠀⠀⢛⡶
⠤⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠒⠒⠒⢺⠀⠀⠀⠀⠀⢸⠘⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢢⢄⠀⠀⠐⠈
⠀⠐⣀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢗⢀⡀⠠⢼⡀⠀⠈⠀⠀⠸⠀⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⢰⠤⠀⢀⡠⠃⢀⡀
⠀⢀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⠀⠀⠀⠸⠀⠈⠁⠂⠀⢣⠀⠀⠀⠀⠈⠙⠒⠦⢀⡀⠀⠀⠀⠘⠉
⣀⠀⢦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠈⠉⠁⠑⠁⠀⣀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣁⣂⠆
⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠀⠀⢠⠀⠀⠀⣾⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠒⠲⡐⠀⠀⢉⡝⢻⠀⠀⠈⠀⢸⠀⠀⠀⡹⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠉⡀⢈⣀⣘⠀⢀⣀⠤⡴⠀⠀⠀⡇⠆⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣈⣴⠉⠃⠈⡀⢹⡉⠀⠁⢀⡇⠀⠀⠀⠇⢰⠀⠀⠀⡆
⠶⠒⠒⠚⠛⠉⠁⡠⠒⡄⠀⠀⠧⠎⠀⠈⡆⠀⡀⠀⠀⢰⠂⠘⡇⠀⠀⢱⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⢀⡠⠔⣀⠌⠁⠉⠉⢻⠀⢀⡴⠒⠒⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⠚⠛⠛⠑⠋⠀⠸⠧⠠⠄⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣶⣶⣶⣶⣶⡿⢷⣶⣷⣷⣷⣿⣾⣷⣾⣷⣿⣾⣷⣶⣶⣶⣿⣿⣶⣿⣾⣿⣷⣾⣶⣾⣷⣾⢷⡶⢾⠷⢷⣿⡾⢷⣾⠾⢶

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⣸⣷⠀⠀⠀⠀⠀⠀⠀⣼⡏⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢉⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣧⢀⣴⠟⠁⣸
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢨⣿⠇⠀⠀⠀⠀⠀⠀⠘⠿⣥⡤⠔⠁
⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢹⣿⠄⢉⡆⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠶⠿⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠦⠄


⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣿⣷⡄⠀⠀⠀⠀⢸⠁⠙⢿⣝⢮⡹⣧⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡟⠛⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⡄⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠈⢀⣀⢨⣿⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⡇⣿⠆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⣿⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⣾⣫⡾⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠘⠉⠉⠉⠁⠙⠖⠃⠀⠀⠀⠀⠀⠀⠿⠶⠶⠇⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠿⢿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠺⠋⣀⠀⠀⣀⠛⠗⠀⠀⠀⠀⠀⠀⠀⢪⢔⡵⡃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⣫⢞⡅
⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣕⣡⡆
⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠃

⠰⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣄⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣻⣟⣷⣦⣀⣄⣄⠀⣠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⡉⠙⣿⣿⣿⠋⠀⢻⣿⡿⠋⣽⣿⣿⠘⠀⠙⠻⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣷⣄⠈⠛⠁⠀⠀⠈⣿⠁⣼⣿⣿⣿⢸⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡋⠉⠉⠉⠳⣄⠐⢾⡴⣼⢣⣾⠋⢛⣿⡟⢸⣷⣦⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⢨⣄⣵⣿⣿⠰⣿⣿⡇⢸⣻⣿⣿⣷⣦⣄⡀⠀⠀⠉⠻⠿⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⢾⣷⣾⡟⣛⣿⠀⠋⠉⡇⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣤⣛⣿⣿⢡⣀⣧⣰⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⢾⣯⣿⣿⣿⣿⡿⣾⣿⣿⡇⢸⣿⣿⣿⣿⣿⠟⠙⠻⣿⣿⣿⣿⣶
⢤⢠⣔⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇⠀⣾⠀⠀⠀⣿⣦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡿⠟⢉⣾⣷⠀⣼⣿⣽⣿⣿⣿
⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢠⣿⡇⠀⠀⣿⣿⣿⣷⣼⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣡⣴⣿⡿⠥⠴⠿⠿⠿⠿⠿⠿
⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠒⠚⠛⠓⠒⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠒⠒⠒⠀⠉⣉⣁⣀⣀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⣶⣶⣶⣶⣶⣾⣿⣿⣛⣛⣻⣭⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠟⣹⣿⡛⣿⣿⣿⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠰⣄⣀⣥⡿⠿⣿⢿⣿⣿⣿⣿⠀⢀⣀⠀⠀⢀⣤⣄⣒⣻⣿⣿⣿⣿⣿⣿⣿⣦⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣭⠖⣚⡿⣿⣯⣿⣿⣿⣿⣿⠙⠏⠙⠂⣿⠁⠉⠉⠏⢹⣿⣿⣿⣿⣿⣿⣿⣼⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢩⣴⡞⠉⠳⣻⣿⣿⣿⡀⠀⠀⠀⠀⠋⡠⢀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠶⣶⣿⣿⣿⣿⣿⡀⠀⢈⣁⣩⣤⠄⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⢠⣟⣿⣿⣿⣿⣿⣿⣦⡀⠀⠂⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⢸⣿⡏⠻⠿⠿⢛⣻⣿⠹⣷⠶⠾⠛⣿⣿⣿⠿⢿⣿⣿⣿⡿⠃⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣯⠛⠛⢻⣿⣇⣠⣀⠀⠉⣽⡟⣧⣤⣁⠐⠾⣷⣛⣿⣿⡇⢨⠉⠉⠀⠀⣄⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⣿⣿⣿⡏⣿⣿⠉⠀⡹⢿⣾⣍⣛⠿⣣⣾⣿⣿⣿⠀⢀⣥⢄⠀⢠⣌⠳⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⡌⣫⡿⠏⢀⠀⣹⠟⣄⠀⠳⣾⠻⠿⣿⣿⡟⢻⣿⡾⡁⣠⡿⢁⣼⣿⡆⢿⡇⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⡶⠶⡿⠠⢏⣄⢘⣷⡀⠈⠛⠀⣸⡋⠁⢸⡏⠀⠀⣿⢁⣾⡿⢻⣷⡄⣰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⣨⣶⣿⡟⠛⣿⡿⠶⣀⠀⠉⠀⠀⢸⣷⠀⢰⡇⣨⣿⣿⡎⢟⠳⠟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⢿⣷⣶⣿⠀⢷⣏⣤⣽⣄⠀⢸⣿⡴⣯⣾⡿⠿⠻⠶⠿⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⢸⣟⣿⣿⣄⠀⠈⠉⠛⠋⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠈⠻⣿⣿⣯⣥⣸⣧⣾⣶⣾⣼⣿⣽⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⣭⣳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣿⣿⢿⣟⡻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣴⣿⣿⣟⡷⣮⣛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⣻⣿⣿⣯⣛⠶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⣿⣽⡻⢶⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣾⣿⣿⡿⣯⣝⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⠏⢠⣿⣿⣿⣯⣛⠷⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⣦⠀⠀⠀⠀⣠⠋⣠⣿⣿⣿⣟⢶⣍⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢷⡀⠀⣰⠃⣰⣿⣿⣿⢾⣝⡳⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣠⠤⡳⡴⠁⢰⣿⣿⣿⣟⠷⣮⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠽⠃⠙⣆⠀⠻⣿⡷⣭⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢷⡒⠒⠿⣶⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢹⡦⠤⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠋⢹⡀⢸⠙⠲⣌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡰⠃⠀⠀⢣⢸⡄⠀⠈⠳⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡜⠁⠀⠀⠀⠈⣇⢧⠀⠀⠀⠈⢦⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠞⠀⠀⠀⠀⠀⠀⢹⡈⣆⠀⠀⠀⠀⢳⡀⠈⣩⣭⣭⣲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠋⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⣆⠀⠀⠀⠀⡇⡾⠁⠀⠀⠙⢿⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣈⣓⢤⡀⠀⡇⢧⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣱⠋⠉⠉⠻⣮⣶⣛⣞⢧⡀⠀⠀⢀⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⠀⠀⠈⣿⣇⠈⠳⢭⣛⣚⣫⣞⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⣄⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢣⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣓⠦⠤⢾⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⠀⠤⠀⠀⠀⠀⠀⠀⠀⣴⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⢠⣶⣶⣴⣿⣿⣦⡀⠀⠒⠆⢀⡀⠀⠀⣠⠟⠀⠈⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⣽⡧⢿⣭⡷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⣁⡀⠀⠀⣼⣻⠏⠀⠀⠀⠈⠹⣏⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠃⠀⠀⣯⣽⠀⠀⠀⠀⠀⠀⣯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠉⠁⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⠀⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠘⢻⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⣟⣻⣒⣶⣲⣖⣶⣒⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢠⣾⣿⣿⣷⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠖⢰⣶⣶⠀⠀⠀⠀⠀⠀⠛⠛⠻⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠁⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⣀⢀⠀⠘⠿⠷⠤⣶⡶⠦


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣿⠿⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⢞⡽⢐⣯⣷⣮⣍⡻⣆
⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⣿⠼⣩⣶⢿⣛⣲⣉⠳⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⡄⠘⠷⣿⢸⣇⠾⢋⣤⣤⣌⠛⢾⡆
⠀⠀⠀⠀⠀⣼⠟⠉⠀⠉⠉⠀⠉⠀⠉⠉⢭⣿⢷⡀⠀⠀⠀⠀⠀⠀⢠⢞⣛⣛⡛⠳⠦⠙⠳⠙⠂⠀⠀⠉⢻⣧⢠⠁
⠀⠀⠀⠀⢘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⣴⠟⡛⣩⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣸⢠
⠀⠀⠀⠀⠈⣥⠤⠴⠦⠤⣤⠤⣤⠤⠶⠤⢦⡤⠉⠁⠀⠀⠀⠀⠀⢀⣴⢏⠾⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⡟⣸
⠀⠀⠀⠀⠀⣸⡀⠀⠀⢀⡏⠀⢻⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⣠⡿⢋⡴⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣿⣻⣄
⠀⠀⠀⠀⠀⣧⠉⠉⠉⠉⠀⠀⠈⠉⠉⠋⠁⡾⠀⠀⠀⠀⢀⡴⢛⣱⡿⢣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⠙⢷⣉⠁
⠀⠀⠀⠀⠀⠸⣇⡀⣠⣤⡶⠐⣶⣤⣄⢀⣀⠃⠀⠀⠀⠀⠀⠀⠀⢠⡖⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠹⣧⣐⢮⣥⣤⡤
⠀⠀⠀⠀⠀⢠⣧⣉⡉⠉⢀⡀⠀⠉⢉⡭⣼⡄⠀⠀⠀⠀⠀⠀⢀⣨⣾⠟⣴⢸⡆⠀⠀⠐⣿⣛⣿⡆⠀⠀⠀⢙⠿⠦⠭⠤
⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡘⣿⣇⣀⣾⣇⡿⠃⠀⠀⠀⠀⠀⠉⢉⣭⡴⠟⣡⢸⣷⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⡼⣿⣌⢷
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⣘⣿⣮⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⢹⣎⢻⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢻⡇⠀⠀⠀⠀⠀⠀⢀⡟⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠘⠅⠃
⠀⠀⠀⠀⠀⠀⠠⣦⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⢁⣴⠃⠀⡀⠀⣀⢄⢰⡄⢠⠀⣿⠃⣸⠇⣠⠀⣰⡿⠋⠉⠳⠀⠀⢠⡎⢹⡇
⠀⠀⠀⠀⠀⠀⢀⣿⢀⢹⡇⣾⡉⣸⣧⡞⢸⡇⣼⢀⣿⢀⣿⢠⡇⠀⢹⣷⠀⠀⣀⡤⡀⣿⠀⢜⣤⣀⢀⣤⣄⢀⣶⠴⣄
⠀⠀⠀⠀⠀⠀⠘⠻⣧⣾⠃⠈⠉⠈⠉⠓⠉⠋⠻⠚⠿⠊⠈⣽⠃⠀⢀⣿⣿⣸⣋⣼⠃⣿⡀⢸⡏⢸⢸⡏⢸⣇⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡿⠀⠀⣾⣀⣿⠋⠉⠻⠂⠙⠧⡼⠷⠚⠀⠻⠛⠘⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠔⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣾⣿⡀⢰⢁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡆⠀⣰⣾⣿⣳⣿⣿⣿⣿⣿⣿⣻⣿⣉⣻⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣚⡂⠠⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠘⠉⢹⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠁⠀⣈⡉⠁⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⢡⡄⠀⢀⣀⣠⣤⣶⣾⣿⡿⢱⠄⢀⠀⣾⠠⠄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡄⠀⠀⢀⡇⠀⠰⠀⣀⠀⠀⠒⣀⠲⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣿⡇⠀⢠⣿⡀⠚⡍⠛⠢
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⣴⣷⠔⠉⢛⡥⡤⣀⠀⣛⠒⠋⠉⡜⠛⣒⠿⠛⠋⠉⠌⡁⠩⠩⣠⠄⡈⠉⡓⠴⠸⢿⡇⠛⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⣿⠧⠘⠉⠁⢀⠔⡅⢀⠈⠁⠀⠁⠀⠸⠓⠒⠉⠀⢀⠄⠘⠆⢀⣿⠀⠀⡀⠉⠈⠑⡷⢤⠀⠀⠈⡖⠉
⠀⠀⠀⠀⠀⠄⠀⠙⠤⠊⠁⠀⡀⠂⠀⣼⢰⡄⠘⠃⠀⠀⠀⢠⡀⠂⢀⠀⠀⣿⢸⣿⡄⣀⣀⠀⢀⠀⠂⠀⡆⠀⠀⠇
⠀⠀⡆⠀⠂⠀⠀⠠⢀⣀⠀⢀⣤⣤⡤⣭⡁⠀⠰⠆⠀⣠⡄⣾⡇⠲⠵⠄⠜⠛⠛⠉⠉⠀⠄⠈⠀⠀⠈⠀⡇
⠀⠀⠁⠨⠁⠠⢈⠀⢀⠀⣀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠀⠒⠠⠅⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠻⠿⡷⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠃⢂⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢻⠿⠻⣿⣿⣷⣶⣶⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠻⠿⠿⠿⠿⠛⠋⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣟⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⢾⣛⣿⣭⠽⠿⡟⠚⢟⢷⣄⠄⠊⠁⠀⡀⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢽⡿⠛⣿⠉⣷⣿⣀⣁⢹⡤⠈⢧⢿⣧⠤⣤⡀⠀⣤⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣁⢠⢿⢈⣿⣿⣧⡁⢣⣿⣰⣸⣬⣿⣄⣾⣧⠴⣆⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⢸⣇⢸⣙⣿⣿⡿⣿⡟⣿⣻⣯⣵⣶⣷⣿⠿⠘⡘⢸⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⣾⣟⣿⣯⣽⣿⣶⣿⣿⢿⢿⣿⣿⡿⡟⣿⡀⡆⠃⢁⣗⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡟⣿⣧⣘⢻⡏⣿⣿⣿⣾⣿⣿⡟⠁⢧⢹⣧⣰⡰⠐⢸⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢳⠈⢻⠿⣿⢿⠛⢿⣿⡏⢀⣀⣷⣤⣼⣼⢿⣿⡷⠷⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⡆⠘⣆⣠⣼⣦⣾⣿⡿⢿⣿⣛⣿⣿⡷⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⢻⣿⣛⣿⣩⣿⣤⠿⠳⢻⡟⠛⠛⠁⠀⢸⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⠙⠛⠛⠉⠈⢶⣶⣾⣿⣥⣀⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣽⣦⠀⠀⠀⣴⣾⣿⣿⣿⣿⡿⠿⠂⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠛⠛⠿⣿⣷⠟⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣠⣄⣤⣤⣴⣿⣿⣿⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠤⠀⠀⠀⠀⠀⣔⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠉⠀⠀⠐⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⢀⣤⠀⣠⠞⠛⠑⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⠞⠁⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⣀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠻⣷⣄⣀⠘⠃⠀⠀⠀⠀⠂⠄⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣾⣿⡿⠧⣼⡀⠀⠀⠀⠀⠐⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡀⠘⠋⠉⠃⠤⢤⠄⠤⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⢤⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⣷⠀⠀⢠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠂⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢹⣿⣧⣀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠆⠀⠀⠀⢘
⠀⠀⠀⠀⡀⠀⠀⠀⠛⠀⠀⠈⠘⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠄⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠰⡤⠂⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠖⠋⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠊⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣠⠀⠀⠀⠀⠖⠛⠁
⡏⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⢨⣿⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠈⠁
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠉⠁⠀⠀⠀⠰⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠐⠂⠀⠀⠀⠀⠀⢀⢄⠀⠈
⢀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠊⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠐⠒⡀⠀⠠⠴⢣⡄⡀⠀⠀⠀⠀⠀⠀⣠⠶⠊⠈⠁⠈⠀⠀⠀⠀⣠⠴⠋
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠔⠂⠉⠀⠁⠀⢠⠊⠙⡎⠀⠀⠉⠚⢰⠋⢩⠄⠀⢠⣀⣀⣀⣀⣀⡀⠀⠄⠀⢄⣀⣀⣀⣀⢀
⣀⣀⣀⣀⣈⣒⣒⣒⣂⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣒⣂⣙⣋⣛⣁⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣈⣁⣀⣀⣀
⣿⣿⣿⠿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⡃⠀⠀⠀⠒⢛⣋⣉⠉⠁⠀⢻⣿⡄⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠐⠋⠹⠿⠻⠷⠒⢸⣿⡇⠀⠀⠈⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⢰⣿⢸⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⣠⡿⢡⠎⢸⣿⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⢠⡾⠋⠔⢁⣴⡿⠏⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⡀⠀⠀⠀⣸⡿⠃⢀⡴⢋⠔⢁⣴⠟⠋⠀⣀⣠⣴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠀⢀⣿⠇⠀⡾⡡⢋⣴⠟⠁⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡧⢣⡾⢁⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢸⡇⣿⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣯⣴⣭⣯⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣸⣿⣿⣿⣿⣿⢿⣿⡏⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠛⣿⣿⣿⣿⠃⠸⡿⣅⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⢸⣿⣿⣿⣿⠋⠰⠁⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⣀⣤⠄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣸⣿⠛⢿⣿⣿⣿⣿⣥⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠁⠀⠀⠀⠈⠃⠀⠀⠉⠉⠻⢿⣿⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠖
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣶⠄
⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣾⣿⣿⠷
⣷⣶⣶⣾⣿⣿⣦⣤⣤⣴⣯⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣭⣯⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣰⣏⡻⢷⣦⣝⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡾⣧⣍⡻⢕⡫⢷⣭⡲⢝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⣟⠿⣦⢝⡪⢕⡫⢷⣭⡙⠷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣴⣯⣛⠿⣺⢽⣪⣝⠻⢶⣭⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⣦⠀⠀⠀⠀⠀⡜⠁⠀⢀⡾⢷⣬⣛⠿⣺⢕⣮⣝⠻⢶⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠘⢷⡀⠀⢀⡞⠀⠀⢀⣞⡻⢶⡬⣓⢽⡺⢷⣮⣙⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢳⣄⠞⠀⠀⢀⣾⣝⡻⢷⡭⣳⢝⡻⢷⣮⣙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⣆⠀⢀⡾⣦⣝⡻⣗⠭⣶⢝⡻⢷⣮⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⣽⡟⢧⡼⢷⣦⣝⡫⣗⠯⣶⣍⡻⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⡁⠀⠈⠻⣷⣮⣕⡯⣓⠿⣦⣍⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢣⣀⡀⠀⠙⢮⣗⣯⣛⠻⣦⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢣⠈⡿⠦⣄⠳⣭⣛⠷⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣠⠞⣇⢸⠢⠬⣷⣌⠻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⡜⠁⠀⠸⡈⡇⠀⠀⠈⠳⡘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢀⠎⠀⠀⠀⠀⢣⢹⡀⠀⠀⠀⠙⡄⠈⠑⣒⣒⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠈⡆⠳⡀⠀⠀⠀⢸⢠⡟⠁⠈⠙⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠦⣀⠀⢸⠸⡄⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡜⣴⠋⠉⠛⢿⡷⡔⢳⡳⣄⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢹⣾⡁⠙⠮⣛⣒⣚⣽⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢱⡹⡄⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠳⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣳⠤⠴⣞⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⡿⢿⠿⠿⡿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⢀⣠⢤⡀
⠀⠀⣿⠀⠀⢠⡎⠁⠀⠀⠈⠙⡆⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣀⠀⠀⢸⠀⠀⢸⠀⠀⢹⣿⠀⠀⠀⢸⣿⠀⣼⠁⠀⢳
⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠘⠿⢿⣿⣿⠿⠿⠛⠛⠛⠛⠙⠉⠀⠀⠀⢸⠀⠀⢸⠀⠀⠸⣿⠀⠀⠀⢸⣿⠀⣏⠀⠀⢸
⠀⠀⣿⠀⠀⠀⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢾⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⢹⡀⢀⡟
⠀⠀⣿⠀⠀⠀⠀⠉⢲⡶⠋⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⠀⠀⠑⣿⠀⠀⠐⢾⣿⠀⠀⢹⡟
⠀⠀⣿⣦⡀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠀⠀⠀⣸⠀⠀⠀⢸⣿⠀⠀⢸⣇
⠀⢰⣿⡆⢹⡄⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠚⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣞⡿⠀⠀⢸⡿
⠀⠸⣿⡇⠀⠁⠀⠀⠘⠃⠀⠀⠀⢀⠀⠀⢆⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⣿⡄⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠑⢄⠸⣆⠀⠀⠐⠋⠁⠀⣠⣀⣤⡄⠀⠀⠀⠀⠀⠀⠰⣶⣶⣦⣶⣶⡶⠀⠀⣰⡾⠿⢿⣦
⠀⢠⣿⡇⠀⠀⡴⠁⠀⠀⠀⠀⠉⢦⠀⠈⠳⣿⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⣿⣅⠀⢠⣿⠂
⠀⠘⣿⡇⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠈⢷⣦⡀⠀⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠛⠿⠛⠁
⠀⠀⣽⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢰⠏⠑⢦⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡳⢦⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣤⡀
⠀⠀⠛⠀⠀⠀⠫⢗⠤⠤⠤⠴⡺⠏⠀⠀⠀⢀⠼⡀⠀⠀⣍⠈⣢⠀⠀⠀⢻⣻⣿⣿⣿⣿⣷⡄⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⣿⡇
⠀⠀⢀⡀⠀⠀⠀⠀⣬⣽⣮⣥⠀⠀⠀⠀⠀⢆⢀⡼⠀⠀⠀⠈⠉⠲⠀⠀⠀⠁⠙⠛⢿⡿⣿⣿⠆⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⣿⣿⣧⠀⢠⣤⣤⣤⡄⠀⠀⢰⣷⠀⠀⠀⠙⣿⣿⣿⡄⠀⠀⠀⠀⣹⣿⣿⣿⣶⢤⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠉
⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⣴⣾⣿⣶⡄⠀⠀⣿⣿⠃⠀⠀⡆⠀⣠⠟⠋⠉⣿⣿⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⡇
⠀⠀⣿⣿⣿⠀⠸⣿⣿⣿⠃⠀⣿⣿⣿⣿⡇⠀⠓⣿⡇⠀⠀⢀⡇⠈⠁⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇
⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⣼⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡷
⠀⠀⣿⣿⡿⠀⠀⢽⣛⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⡟⠀⠀⠀⣿⣿⡁⠀⠈⢿⣿⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡀
⠀⢸⣿⠇⠀⠀⢠⠞⠉⢙⢦⠀⡄⢀⠄⢀⡠⠤⣀⠀⠀⠀⠀⠀⣴⣿⣯⣌⢆⠀⠀⣰⠃
⠀⣸⣿⣀⠀⠀⠸⡀⠠⠋⡜⠀⠸⣼⠀⡎⠀⠀⡸⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⡐⣴⡇⠀⠀⢀⣠⠄
⠀⣿⣿⣿⣷⣤⣄⣈⢳⡎⢀⠔⢩⠟⠍⢳⠈⠉⢀⠶⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣵⣶⠾⠋⠁
⠀⠹⠿⠿⠋⠉⠛⠛⢹⣿⠀⠀⢊⠀⠈⢠⠑⠊⠁⠀⠀⢀⡴⠶⢤⣀⣠⠴⠿⣯⣿⣯⣷⣅⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡼⠋⠀⠀⠀⣿⠙⢿⣿⣿⣿⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡏⠀⠀⠙⢿⣿⠟⠁
⠀⠀⢀⡠⠤⠤⠤⣀⠀⠀⣴⡧⠂⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⣇
⠀⡰⠁⠀⠀⠀⠀⠈⠳⠎⠀⠀⠀⠉⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡞
⠀⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢠⢀
⠀⢘⣶⣿⣧⡄⠀⠀⠀⠀⠀⠀⣀⠀⢠⣾⠿⠿⠿⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⣀⠀⠀⡀
⠀⠈⠻⣿⣿⣿⣶⡀⠀⠀⠀⢰⣇⡰⠛⠁⠀⠀⠀⠀⠀⢘⣃⡝⡰⣡⢦⢰⠲⡆⢸⡏⠀⢧⡾⠜⡗⣼⢧⣤
⠀⠀⠀⠈⠻⣿⣿⣿⠆⠀⣠⡼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠹⠋⠓⠛⠛⠁⢋⡶⠙⣞⠛⠦⣈⣻⠇⠙⠂⠁
⠀⠀⠀⠀⠀⠈⠉⠈⢢⠞⣛⠅⡓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⣄⢀⠜⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠯⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠋⠈⠲⠾⠄

⠀⠀⠠⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡴⠦⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⢤⡄⠀⠀⠀⠠⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⡷⠈⠄
⠀⠀⠀⠁⠀⠀⠀⢮⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢀⣼⣯⣀
⠀⠀⢠⣄⠐⠀⠀⢶⢉⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢀⡄⠀⡀⢀⡀⠀⠒⢠⠂⠂⠀⠀⠀⠘⢁⣽⣅
⠀⠀⠀⠙⠢⣀⠀⠈⢏⢧⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠉⠁⠀⠀⢀⠈⠁⠀⠀⠀⡤⠀⠈⡁⠰⠆
⠀⠀⠀⠀⠀⠈⠓⠀⠈⠯⠢⠀⠀⠀⠈⠋⠀⠀⠂⠀⠀⠀⣧⡆⠀⠂⢶⠀⠀⠀⠀⢀⡀⠀⠀⠙⠃⠶⣄⠀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⡰⠂⢠⡄⠀⠀⠠⠰⣆⠀⠀⠀⡧⠀⠀⠈⣧⠀⠀⠀⠈⠡⠋⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠦⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⢆⣀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠙⢂⡀⠀⠀⠀⠀⠉
⠀⠀⢰⠃⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡂⠂⠀⢀⡤⠶⠟⢀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⣠⠀⠀⢀⡤⠖⠂
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡄⣸⢃⣤⡦⠀⠀⠂⠀⠀⠀⠔⠀⠠⠄⠀⠀⠂⠀⠐⠠⢶⠀⠀⠀⡾⠀⠀⠀⠂⡀⣠⠄⠀⠀⠘⡆⢨⡤⠖⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠙⠛⠙⡆⠐⠂⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠳⠀⠓⠀⠀⠀⠑⠋⠁⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠁
⠀⠀⠢⢂⡀⠀⠠⠀⠀⠀⠈⢀⠀⠀⡀⠀⠠⠀⡀⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠋⠉⣉⣉⡓⠦
⠀⠀⠀⡈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⣼⠁⢰⡇⢄⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠠⠀⠀⠀⠘⠇⠀⠈⠙⠻⢛⢫⡢⡀
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢠⠆⠐⠐⠈⠘⠃⠀⠾⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠑⠒⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠿⠗⠈⠢⢑⡇
⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⡟⠀⠀⠀⠀⠀⢰⠀⠀⢀⣀⠴⠒⢦⣀⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢢⡄⢀⣠⠴⠺⣁⠄⢈⢀⠄⠀⠀⣀⠀⠀⣠⠒⠁⠀⠀⠀⠀⠁⠈⠀⠀⠆⠀⠀⠀⠀⠈⠂⠀⠒⠒⠁⠀⠀⠸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠸⠁⠌⠁⠀⠀⠘⠀⠘⡄⠀⣦⣠⣟⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡇
⠀⣀⠤⠤⣄⠀⢀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⡼⠁⠀⠀⠈⣦⠋⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠛⣿⡇⠀⠀⠀⠀⢀⣀⣀
⡇⠀⠀⡴⠒⢿⠊⠑⡆⠀⢸⠀⠀⠀⠁⡀⠀⠀⢀⡤⢤⠤⠤⡀⠀⠀⢀⣀⣼⡇⢠⣿⡀⠀⠀⠀⡰⠋⠀⠘⣆⠖⠛
⢣⠀⠀⡇⠀⠀⠀⢀⠇⠀⡎⠀⢰⣊⣉⡥⢽⠀⠘⢧⡩⢉⣩⠇⠀⣴⣉⣰⣿⣿⡿⢿⡧⡀⠀⢠⠃⠀⢀⣀⣏⡀
⠘⡆⠀⠹⣄⠀⢀⡞⠀⢠⠃⠀⠘⠦⢤⡴⠊⠀⣀⣀⣩⣏⣀⣰⣋⡇⠀⠀⠀⠀⠀⢸⡴⠁⠀⢸⠀⢰⠃⠈⠁⡇
⠀⢣⠀⠀⠈⢦⡞⠀⠀⡌⠀⣀⡤⠴⢚⣏⡉⠉⠉⢀⠼⠧⡀⠀⢹⡇⠀⠀⠀⠀⠀⡟⠧⣄⠀⢸⠀⠘⡆⠀⡰⠁⢠
⠀⢸⡀⠀⠀⢸⠀⠀⠀⣧⡎⠁⠀⠀⠯⠥⠟⠀⠀⠈⠓⠚⠁⠀⠀⡇⠀⠀⠀⠀⢸⡁⠀⠀⠙⣾⠀⠀⢸⣰⠃⠀⡞
⠀⠀⡇⠀⠀⢸⡄⠀⢀⡇⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠴⠒⠒⠊⠉⠁⠀⣠⠔⢹⡄⠀⢀⡇⠀⢰⠁
⠀⠀⣇⣤⣤⣧⣷⣤⡜⠀⠀⠈⠙⠒⠦⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠔⠒⠉⠀⠀⢸⢳⠀⢸⠁⠀⡏
⠀⠀⡟⠻⠿⡿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣈⣇⣾⡀⢸⠁
⠀⠀⡇⠀⠀⡇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢠⡇⠀⠀⡇⠘⠒⠋⢱⠦⣀⠀⠀⠀⠀⣀⡤⠤⢤⣀⠀⠀⠀⠀⠀⢀⠠⠴⡷⠿⢿⣟⣛⡛⢻⣟⣛⡿⠋⡇
⠀⢸⠀⠀⠀⡇⠀⠀⠀⡘⠀⠈⠙⡖⠚⠉⠁⠀⠀⠀⠈⠙⣶⠤⠤⠒⠋⠀⠀⠂⠀⠀⡏⠉⠉⠉⠏⠁⠀⠀⡇
⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢀⡤⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⣇
⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣟⠀⠸⠀⠀⢠⣿⠀⠀⠀⠀⠀⢸⠀⠀⢠⡇⠀⠀⠀⠸⡄⠀⠀⢻
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣠⡴⠋⣿⠀⠀⠀⣠⠖⢺⣦⠀⠸⠁⠀⠀⠀⠀⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠓⣄⠈⠀⠀⣸⠋⢧⡀⠀⠻⠄⡾⢸⠆⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣀⡏⠀⠀⢠⠏⠀⠀⠙⠦⢤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠁⠀⢀⣴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠶⢶⣶⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣛⣯⣿⡿⢿⢽⣿⣶⣢⣩⠳⡄⣹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣩⣴⣪⣭⣭⣭⣉⣲⣮⣯⣻⣿⣿⡇⣽⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⡀⣱⢫⣾⡿⠟⣛⣳⣦⣍⡉⢽⣿⠿⠟⠛⢿⠿⢿⣿⡵⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀⣷⣿⠿⣳⣿⡿⠟⠛⢻⡗⢀⠔⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠝⡻⢋⣵⡾⣛⣭⡶⠿⣿⣿⡋⠁⣀⢤⣄⣀⣀⠀⠀⠀⣸⣟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠞⣫⡵⠋⠁⢀⣤⣿⣿⡿⠀⠀⣀⣠⣤⣌⠉⠀⢠⢫⣤⣿⠇
⠀⠀⠀⠀⠀⢠⠆⢀⠀⠀⢀⡾⢫⣿⣿⣿⣶⣞⣛⡿⠿⣷⣿⣁⠀⠀⠉⠻⠿⠈⠀⠀⢸⠻⡿⠋⢙⡆
⠀⠀⠀⠀⠀⡞⠀⠘⢤⡤⠌⠀⢘⣯⣥⣦⣴⣿⣿⣿⡀⢥⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⡣⢹
⠀⠀⠀⠀⠀⠃⢀⣠⡴⠶⢶⡤⢋⡾⣿⡿⠿⠷⠚⣽⣿⢠⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣀⡏
⠀⠀⠀⠀⡰⢪⣏⡵⠚⣩⡭⣡⡌⠘⣡⣴⣶⣷⣾⣯⣾⠸⣴⠏⢦⣀⠀⠀⠀⠀⠉⠩⢿⡞
⠀⠀⠀⠰⡇⢸⡏⣠⣾⢋⢸⡉⣇⡾⢟⣫⣭⣭⠷⣿⣿⡆⠀⠀⡀⠘⢿⣶⣤⣄⣀⣀⡼⠁
⠀⠀⠀⠀⠑⣿⣽⣵⢣⢸⡈⣷⠾⣴⣋⣡⣤⣤⣴⣿⢿⡇⠀⠀⢣⠀⠘⣿⠁
⠀⠀⢸⠀⠀⣿⣿⢸⡼⣧⣳⣽⣿⣿⣿⣿⣿⣿⣟⡽⠛⠀⠀⠀⠈⢧⡀⡏
⠀⠀⠈⢇⠀⠙⠺⠿⠿⠦⢬⢭⣉⣉⠉⠭⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⣀
⠀⠀⠀⠀⠑⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠒⠾⠷⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃

⢀⣤⡮⠜⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠠⢿⠏
⠀⠀⠀⠀⠀⠸⠿⢿⣿⡟⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣠⣤⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠚⠙⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⣇
⢀⣼⣿⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠀⠀⠀⠀⢿
⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠉⢰⠣⠀⠀⠀⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠈⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀
⣄⠀⠀⠀⠀⠀⠀⠀⡜⢄⢁⣄⠀⠀⠀⠀⠐⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻
⠈⠳⢦⡀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠉⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⢴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⣷⠄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠿⠇⠀⠀⠀⠀⠀⢓⠊⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⡿⠟⠉⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⣆
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠶⠒⠃⠐⠂⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠞⠀⡀⠀⠀⠀⠀⠀⢀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⠁⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⢀⣽⢿⠿⠟⠋⠀⠀⠀⠠⣾⣿⣿⣿⣿⡿⣫⣶⣄
⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣧⣙⠻⢦⣄⡀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣉⠛⠷⣤⣀
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣌⡙⠷⣤⡀
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣦⡈⢻⣄
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⢟⡄
⠀⠀⠸⣇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣵⣿⠇
⠀⠀⠀⢻⡄⠀⣠⡾⢡⡖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⠛⠛⠻⠿⢣⡾⠟⠋
⠀⠀⠀⠀⢻⣾⣋⡴⢋⡼⢋⡶⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠀⠀⢠⣾⣿⣿⡿⠉
⠀⠀⠀⢰⣿⣿⣿⣴⣋⡴⢋⡴⢋⡾⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡏⠀⢰⣿⣿⡿⠋
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣟⣴⢏⡴⢋⡴⢃⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⢀⣤⠞⠛⠋
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣿⣵⢟⣴⢋⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣬⡻⢦⣀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣼⠏⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣝⠳⣤⡀⢀⣴⠟⣱⠟⠛⠻⣆⢀⡼⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡇⠈⢹⣿⡁⠀⢿⣄⣀⣠⡟⢾⡁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⠈⣿⠀⠀⠉⠉⠁⠀⠈⠛⠶⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⣀⠤⠔⠛⠛⢻⣿⣿⣿⣿⣿⡻⣿⣿⣿⣷⣤⡀
⠀⠀⠀⣞⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⢬⡿⢿⣝⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠘⠶⣄⡀⠀⠀⠀⠙⠿⣿⣿⡄⠀⠀⠈⠓⠯⢟⡿⣿⣿⣿⣶⣦⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠃⠀⢄⡀⠀⠛⠀⠀⠀⠈⠉⠽⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⢀⣤⣆⡀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠁⢀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀⢧⠀⠀⣠⠾⠥⠤⠤⠐⠀⣰⠋⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⢣⠀⠈⠻⣿⣿⣧⠰⠇⠀⠀⠀⠀⣄⡰⢁⡞⢠⠆⡞⠀⣴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⡀⠈⠀⠀⠀⢈⣿⡿⠀⠀⡠⠀⠀⠜⠁⠁⠈⢀⠎⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⣼⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡙⠂⠙⠢⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣯⡑⡄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣷⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⡆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣄⢠⣴⣦⣴⣶⣶⡤⠤⠄⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠉⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢿⣿⣿⣿⣿⡟⣼⠋⠀⣿⣿⣿⣿⣿⣿⣿⣯⡚⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠏⠀⠀⢠⣽⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⢹⣧⡿⠇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⠇⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣾⡟⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⡿⠋⡀⠀⣿⣿⣿⣿⣿⣿⣟⡿⠛⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣭⣶⡿⠁⢠⢸⣿⡟⠻⣏⡁⠀⠀⢀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠟⠀⠀⠄⢸⣿⠁⠀⠈⢍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣠⠴⢾⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⠁⣸⣿⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⡘⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠋⠀⠀⠀⠀⠀⠁⢀⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣷⡶⠆⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠈⠁⠚⠛⠛⠓
⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠴⣆⠀⠀⠀⠁⣠⣶⡀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢀⣶⣄⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣾⣿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⢀⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢤⢧⣀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠐⢦⣷⣀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡼⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠘⢦⡼⠇⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⣄⠀⠀⠀⠀⢠⣿⣷⣶⣠⡀⠀⠀⠀⠀⠀⣰⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⢴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⢿⡿⠁⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⡀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠀⠀⠀⠀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⠐⠡⠆
⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠃⠀⠀⢀⡔⠱⠀⠀⠀⠀⠀⠀⣠⢘⠂⡀⠀⠨⠗
⠀⠀⠀⠒⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⠀⠀⢀⠎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣰⡄
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠃⠀⡠⠃⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡚⠀⡔⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠃
⣀⣀⣄⣀⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣛⢛⣉⡛⣻⡛⣻⠟⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠦⠀⢀⣾⣶⣦⠀⠀⠀⡀⣀
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢠⠀⡀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠘⠉⠒⠀⠀⠀⠀⠀⠙⠀⠀⢠⣠⡤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠃⠠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠩⠗⣄⠀⠀⠀⠀⣠⠞⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⠒⢦⠀⠀⠀⠙⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⡠⠊
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡖⣳⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠈⠃⠀⢀⠀⠀⠀⠑⠘⠃⠀⠀⠂⠀⠀⠃⢨⠀⠀⠀⠀⠀⠠⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠄⠀⢀⣤⠎
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⢸⡆⡇⡏⡆⢸⠉⠂⣧⢸⠀⡎⣻⣦⡇⠀⠀⠀⠐⢏⠠⠀⠀⠀⢀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡟⢣⡖⢧⡁⡷⡁⢀⢑⣴⠺⣸⡀⢇⠙⠹⡇⢀⡔⠀⠀⡀⠋⠀⠀⣴⣿⠏
⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢁⠈⣁⢁⠁⠈⢉⠀⠀⢀⠉⡈⠀⢀⠀⠈⠇⠠⠈⢀⠄⠒⡄⠘⠃⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠛⠁⠀⠀⠀⠐⠀⠂⢤⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠞⢡⠄⠀⢢⡀⣧⠀⠀⠀⠀⢀⣴⠏⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⢀⡰⠋⠀⢢⠀⠀⠀⢳⣿⠀⠀⢀⠐⠛⡿⠀⠀⠀⠀⠁
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢲⣎⠁⠀⠀⠀⢀⡏⠙⠶⢤⡈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⣐⢦
⠀⠀⠀⠘⡆⠀⠀⠠⠀⠙⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢇⠅⠀⠐⠂⠓⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⠀⠁⣴⠊⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⢋⠶⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠂⠀⠀⢉⡈⠀⢸⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠰⠿⡿⢧⠀⢸⡇⠀⢸⡇⠀⠈⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠀⠈⡁⠀⣄⣤⠀⠀⡇⠀⣷⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠁⠁⠛⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠋⣉⣷⣖⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠘⠟⠀⢬⣾⡋⠁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠔⣰⠇⣰⠒⠛⠀⠀⠽⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡖⠀⠀⠀⠈⠉⠠⡄⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⡻⠁⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⠻⣾⣳⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢰⣷⣖⠃⠀⠰⡿⣏⣊⠀⠀⠌⢻⡧⠨⢻⣷⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣴⠎⢻⣧⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢽⣿⢰⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠶⠓⡦⠀⠀⠀⠀⠀⠀⠀⠉⣺⡙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢢⢰⡇⠀⠀⠉⠀⠀⠀⠀⢠⡖⣦⢔⣿⡟⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⣼⣇⣤⠀⠀⠀⡀⠀⠀⠀⡠⠎⡸⠀⠀⠈⢑⡄⠀⠄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣽⣿⡆⠀⠰⠟⢛⠂⠉⢀⡔⠁⠀⠤⠚⠉⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⢛⣻⡟⠁⠀⠀⠠⠇⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠏⡻⠁⠀⠀⠀⠼⠀⠀⠀⠀⠀⢀⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣶⢏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡾⠟⠀⠀⠐⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣿⣿⡘⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⣀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⢸⠃⠀⠀⠠⡀⠰⡀⠀⠀⢓⣶⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣄⠀⠀⠀⠁⠀⠀⠀⠂⢈⣙⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣠⡜⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠟⢠⠀⠀⠀⠉⠙⢯⣀⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠄⡀⢁⣄⠲⣽⣷⠦⣿⢳⣔⠏
⠀⠀⠀⠀⠉⠉⠙⠛⠋⠙⠋⠉⠉⠋⠐⠀⠀⣀⣇⠀⠀⠀⠀⠀⡙⣦⠙⢷⠀⠹⡷⢻⠆⠐⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⠁⣈⣠⣬⣇⣀⠀⠀⣧⢦⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣷⡿⣟⣿⣿⣄⠰⣻⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠹⣯⠙⢿⣿⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⠀⢰⠂⢰⠀⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⠇⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄
⠀⠀⠀⠀⠁⠀⠀⠙⠋⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⡿⢋⣀⠇
⠀⠀⢀⣶⣿⣿⣦⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡇⠀⠀⠀⠀⣄⣀⠘⠿⠿⠟⠁⠀⠀⢀⣤⡔⠁⠀⢀⡾⠁
⠀⠀⠘⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣤⣴⡄⠀⠀⠹⣻⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⢀⡴⣋⣴⡆
⠀⠀⠀⠀⠉⡙⠀⠀⠀⠀⠀⢠⣤⣤⡈⠍⠀⠸⠤⡄⠀⠀⡀⠑⢀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠙⢿⣿⠿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡸⢇⠿⣼⢿⢻⣿⡟⡟⡿⣿⢯⣻⣿⢭⣿⣯⣻⡿⣝⣿⠯⣻⣭⣿⣸⣽⡿⣟⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣦⣿⣼⣿⣿⣧⣿⣼⣿⣽⣿⣿⣬⣿⣽⣿⣗⣛⢿⣼⣿⣯⣿⣼⣷⣧⣿⣧⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⡻⢿⡟⢟⠛⠷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⣋⡴⢫⡘⠻⣏⠲⣿⣿⠖⣹⠟⢋⡝⢤⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⢓⣒⡟⣿⠃⣾⣿⣷⠉⣧⣙⣋⣼⠉⣾⣿⣷⠘⣿⢻⣒⣚⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠉⢸⣿⣿⡇⢻⡒⠻⢿⡟⢰⡟⣹⣍⢻⡆⢻⡿⠟⣒⡟⢸⣿⣿⡇⠉⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢠⣿⣍⣉⣉⣱⢞⣛⠛⢶⡏⢻⣆⢹⡏⣰⡟⢹⡶⠛⣛⡳⣎⣉⣉⣩⣿⡄⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡔⣋⣩⣥⣽⡙⣷⠸⢿⣇⢸⡏⣯⡙⢿⡿⢋⣼⢹⡇⣸⣿⠇⣾⢋⣯⣬⣍⣙⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣦⡙⣿⣿⣿⣧⡸⠷⡶⠾⠿⢇⢿⣿⡞⢳⣿⡿⡸⠿⠷⠶⠾⢇⣼⣿⣿⡿⢋⣼⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡰⢫⡙⢧⣤⣴⠶⠷⣶⡙⠿⣿⣾⣏⠙⡇⢸⠋⣹⣷⣿⡿⢋⣶⠾⠶⣦⣤⡵⢋⡝⢆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢶⣿⣿⡶⢼⡧⢾⡷⠤⣿⡶⢜⣉⣉⣙⣿⣿⣉⣉⣉⡳⢶⣿⠤⢾⡷⢼⡧⢶⣿⣿⡶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⣝⣡⠶⠻⠿⠦⣴⡾⣋⣴⣿⣿⣏⣠⡇⢸⣄⣹⣿⣿⣦⣙⢷⣦⠴⠿⠟⠶⣌⣫⠌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⡿⢡⣾⣿⣿⡶⢳⡴⠷⢤⣤⡎⣽⣿⢇⡸⣿⣯⢱⣦⠤⠾⣶⡞⢲⣿⣿⣷⡌⢿⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠦⣉⡛⠛⠿⢡⣿⢰⣶⡞⢹⡇⡿⢋⣼⣧⡘⢿⢸⡏⢳⣶⡆⣿⡌⠿⠛⢛⣉⠴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠹⣿⣛⣛⣛⡻⢎⣉⣥⡾⢇⣼⡟⣸⣇⢻⣧⡸⢷⣬⣉⡱⢟⣛⣛⡛⣿⠏⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣉⢸⣿⣿⡇⣸⣋⣤⣶⣯⢸⣦⣹⣏⣼⡇⣽⣶⣤⣝⣧⢸⣿⣿⡇⣉⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⡉⢉⣧⣿⡄⣿⣿⣿⢀⡿⢩⡍⢿⡀⣿⣿⣿⢠⣿⣼⡉⢉⣵⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣬⣙⠳⡘⣋⣴⣏⢴⣿⣿⡦⣹⣦⣙⢃⠞⣋⣥⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⣤⣽⣯⣤⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢯⣿⣿⡟⣿⡟⣿⣿⢯⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⢺⣇⡏⣷⣾⣿⢸⣸⡇⣿⢺⡇⣿⣾⠸⡇⡇⣿⡇⡇⣿⢸⡏⣧⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠈⠉⠁⠐⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠐⠈⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠐



⠀⠀⠀⠀⢀
⠀⠀⠀⢴⣿⣷⣄⡀
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⠟⣠⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠀⠀⠀⠐⠪⣷⣄⠀⠑
⠀⠀⠀⢀⣼⡿⠛⠉⠉⠉⠀⣸⡿⠁⢠⠊⠀⠀⣤⣤⡀⠀⠀⢀⣤⠄⠀⠀⣶⡆⠀⠘⠉⠹⣷⣄⠀⠀⠀⠀⠀⠉⠳⡤⡄⠀⠀⠀⠢
⠀⠀⠠⠟⠉⠀⠀⠀⠀⠀⣰⣿⢁⡠⠁⠀⠀⣰⣿⣿⠁⠀⢸⣿⣿⣷⠀⠀⢹⣗⠀⠀⠀⠀⠹⣿⣦⡀⠀⡏⠉⠆⢀⡰⢃⡀⠑⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⢛⡿⠏⠀⠀⢸⣿⣿⣿⠀⠀⠈⣿⡄⠀⠀⠀⠀⠹⣿⣷⣄⡈⠁⡛⠁⢸⠁⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠈⠂⡸⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠃⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⡠⠄⠒⠲⡧⠤⣀⡀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢘⠀⠀⠀⣰⠃⠀⠀⠈⠉⢺⣿⣿⣿⣀⡀⠀⠀⠘⡄⠀⠀⠀⣀⡠⠜⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠒⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠉⠉⠉⠉⢹⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⣋⣩⣭⣬⣭⣉⡙⠛⠿⣷⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡾⠃⣠⣶⡿⠟⠋⠉⠉⠉⠉⠙⠓⠄⠈⠻⣷⣽⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⣴⡿⢁⣴⣶⣿⣿⣿⣷⣶⣄⠙⢦⣄⠀⠈⢿⣧⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣿⣿⣿⢰⡿⢀⣾⣿⡿⠿⠿⣿⣿⣿⣿⣷⡈⢿⣷⡰⡌⣿⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡻⣿⣿⣿⠈⣇⠸⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⣿⣷⣷⠈⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣉⠻⠿⣧⡈⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡿⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⣙⠛⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢀⣿⣿⡿⠁⣼⡿⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠏⢀⣠⣤⣀⣀⠀⠀⠀⠀⢠⣿⣿⡿⢡⣿⡿⠋⢠⡾⠋⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠉⠛⠿⣦⡄⢀⣿⣿⠟⢰⣿⢏⠀⢀⡡⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡇⠀⢿⡟⠛⠓⠆⠀⠈⠀⢸⣿⡟⠀⣿⠃⡆⣠⡾⠁⠀⠸⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠃⠀⢼⣿⣦⣤⣤⠄⠀⠀⠸⣿⡇⣆⢻⡀⢷⣿⣇⢠⣀⠑⠒⢛⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠻⣇⢻⣦⡑⠈⢻⣿⣦⡈⠙⠛⢛⠋⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣶⣄⡙⢿⡿⢷⣦⣬⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⢉⠻⢿⣷⣝⣦⡈⢉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣠⣄⡀⠀⠀⠀⢻⣷⣌⠻⣿⣷⠈⣿⣶⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⣿⣿⣿⣿⠏⢀⣀⣠⣾⢿⣿⡇⣹⡟⣠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣫⡵⠿⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠾⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠆⠀⠀⠀⡠⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠊⠀⣠⠰⠉⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⢈⣧⠊⣶⠔⣏⣲⣃⢶⡈⢄⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⡁⢼⠊⠁⢀⡆⣈⠁⣦⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢀⠔⠀⠀⠀⠀⠈⠁⠰⢬⣑⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠂⡠⠁⠀⠀⠀⠀⠀⢀⣀⣄⠀⠸⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⡰⠁⠀⠀⠀⡆⠀⠀⠘⠯⠽⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠐⡆⢄⠀⠀⢀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡂⠠⡜⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢆⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣧⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⣇⠀⠀⠑⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⡸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠈⠀⢠⠀⠘⡄⠀⠀⠈⠢⣄⠀⠀⠐⠄⠀⠀⠰⡂⡠⠔⠁⢡⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠄⠃⠈⠀⠘⡆⠀⠀⡎⠙⠝⠃⠤⠘⢢⠄⠀⢣⠈⠢⢀⠀⠑⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⡀⠀⠀⡇⠀⠌⠀⠀⡠⠀⠀⡄⠀⠣⠀⡀⠃⡀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠀⠀⠣⡀⠀⠆⠀⠘⢆⠐⠀⠀⠌⠑⡀⡌⠀⠈⠀⠀⠀⢢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠄⠀⠀⠠⠃⡠⠀⢀⡇⠀⡀⠀⠀⠈⠀⠓⠀⢂⠀⠀⢹⠐⠈⠀⢀⠀⢰⠀⠀⠠⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠱⢄⣠⡇⠀⠂⠀⠀⠠⠀⢴⣀⠨⡠⠀⠸⠀⠀⠀⢠⠀⢠⠁⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣸⠀⠀⠀⠒⠚⠤⠤⢾⠀⠈⠀⠀⠀⠘⠢⠜⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⢀⣤⣴⣶⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄
⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⢀⡿⢿⣆
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⣀⢀⣾⠇⠘⣿⡀
⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢹⣿⣿⣿⣿⣾⠃⠀⠈⢻⣿⠄
⠀⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣧⡞⠀⠀⣾⣿⡄
⠀⠀⠀⠈⠙⠻⠿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠏⢿⣶⣡⠾⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠮⡱⣿⠍⠉⠳⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠈⠊⣝⣚⠛⠛⠆⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⣀⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠻⣷⠆⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠻⢧⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠖⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣿⡟⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⢀⣾⡟⠀⠀⠀⢀⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⢀⣾⠏⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⣰⡿⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⣴⡿⠃⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠢⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠈⢿⣝⠛⠉⠉⠻⣾⣹⠆⠀⣿⣿⣿⣿⡀⠀⠀⣾⠁⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⣄⣤⣞⣽⠀⠀⢹⣿⣿⣿⣷⣄⠀⠙⠳⠄⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⡇⢹⢇⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⢀⣀⣄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠟⠀⠀⡼⠿⣿⢋⡠⠄⠀⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠙⢿⡏⠀⠀⠀⠀⠀⢰⣩⢆⠗⠚⠑⠒⢂⣀⠄⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣅⠤⣴⡎⡇⠀⠀⠀⠀⠀⠁⠀⣀⡀⠐⠒⠂⠣⠀⠀⠀⢀⠀⢸⣿⡇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⠱⡌⠳⡸⣷⡟⠀⣇⠀⠀⠀⠢⣜⠀⣀⣀⠠⠎⠀⠀⣀⠐⢸⣇⠠⡟⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⣷⣤⡐⢌⢰⢠⡇⠀⠀⡐⠈⠀⠈⠀⠉⠀⠘⠁⠀⠀⠄⠈⣿⠀⢡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠿⠿⠿⠷⠿⡈⢻⣿⣾⠀⠀⠀⠉⠢⠤⠀⢀⣀⣀⡠⠔⠂⠀⠸⡄⠹⣧⡾⠁⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⠹⣭⠀⠀⠀⠀⢀⠀⡜⠈⣿⣏⢄⠀⠀⠀⠠⣧⠀⡏⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⠃⠀⠀⠀⢹⡳⣦⣠⡄⣼⠀⡇⢰⡿⠋⠄⠀⢼⣆⠀⢿⣰⠟⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣣⠃⠀⠀⠀⠀⠘⣧⠀⠈⠑⠪⠒⠷⡾⠀⠀⡄⠀⠈⢿⡆⢘⣡⣤⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡀⠀⠀⠀⡀⢀⣿⣷⣄⡀⠀⠀⣸⠃⠀⢀⣿⡄⠀⠘⣿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡿⣄⠀⡀⠀⣸⣿⣿⣿⣿⣿⣶⣿⣶⣶⣿⣿⡗⠀⠀⠀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⢀⣀⣌⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡸⢣⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠛⠉⠈⠻⡿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣐⣡⡆⠀⠀⠀⠉⢄⡰⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣴⡴⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⡿⠛⠻⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⡤⢤⠊⠀⠀⠀⠲⠰⢾⣧⣎⣶⣃⢀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⡇⠐⣤⠠⢠⠴⠆⢪⣧⠀⠠⠉⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢉⣰⡏⢸⡄⠸⠇⠀⠀⠰⠘⠇⣠⠂⣀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣁⡏⣧⠀⢿⡆⠀⠀⠀⠀⢧⢰⡿⠀⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠉⡐⣧⣿⠆⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢹⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢛⡉⡇⢼⡇⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣥⢜⡅⣿⢈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠏⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⡀⠀⠀⡔⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠋⢀⡠⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⢀⣴⠟⠀⠳
⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠃⠟⠀⠀⠀⠀⠀⠀⠰⠃⡠⠞⠁⠀⣤⣄⡀
⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠘⠤⠘⢠⣶⠟⠙⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⣀⠀⡀⢘⣮⡙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠤⠖⠛⠁⠈⠉⠀⠉⠉⡟⠛⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⢀⡀⢀⣾⣄⠀⠚⠀⠀⠀⠀⠀⠀⠶⠂⢀⠇⠀⠙⢷
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠒⠸⠈⠁⠀⠤⠆⠀⠀⠀⠀⠀⢀⣠⣶⠄⢹⠄⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠹⣾⡖⣠⠇⠸⠀⠀⢳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠄⠐⠚⣇⡿⢓⣾⣆⠀⠀⢇⣤⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠋⠁⠀⠀⠠⠩⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠀⠶⠂⠄
⠀⠀⠀⠀⠀⣾⣋⡀⢹⣦⠰⡄⢹⡀⡑
⠀⠀⠀⠀⠀⢻⣿⣿⣴⣿⣐⣥⣼⣇⣿⣼⣃⡀⢀
⠀⠀⠀⠀⠀⠈⢿⣿⠿⠿⠛⠛⠉⠋⠉⠉⠁⠀⠀⢳⡀
⠀⠀⠀⢀⡄⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢸⣷⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢧
⠀⠀⠀⢸⣿⡆⢶⣿⣄⠀⠀⠀⢄⣀⢆⡸⢤⡙⠯⣀⣀⠾⡄
⠀⠀⠀⠈⣯⣧⡌⢟⣿⡄⠀⠀⠀⠉⠲⠁⠒⠈⠓⠈⠁⠀⠐⡀⢀⣀⣀⣤⡤⠤⠶⠶⣖⠒⠂
⠀⠀⠀⠀⢻⢿⠟⢸⣼⡷⠤⠤⠒⠒⠒⠛⣒⠻⠛⠓⠆⠄⠀⢻⣭⣥⣤⡶⠶⠚⠛⠋⠉⠉⠁
⠀⠀⠀⢰⣞⣩⣥⣄⠀⢀⣀⣠⣤⣴⣶⠶⠿⠓⢖⠘⡇⣠⠀⢸⣿⠛⠁
⠀⠀⠀⠸⣿⣭⣾⣿⢿⣿⣿⡟⠉⠁⠀⡆⠀⡆⣼⣸⣇⣿⣤⡾⠇⠠⠤⠤⠤⠤⠤⠄⣠⣄⣀⣀
⠀⠀⠀⠀⠉⢹⡟⣿⠁⣏⣿⣷⠀⠀⣰⣇⣼⣷⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢱
⠀⠀⠀⠀⠀⠀⣧⠀⠀⡟⣿⣾⣷⣿⣏⣿⣤⣤⣤⣤⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠸⡾⣷⣝⢝⠿⣿⣉⣏⣉⣀⣀⣤⠤⠴⠤⢤⡀⠙⣶⠀⠀⠠⠀⡄⠀⠀⣸⣼⣇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡜⢿⢇⡬⢽⣿⣻⣐⣒⣀⡬⢭⡍⠙⠳⣼⣦⣿⡅⠀⣀⠀⣇⣸⣧⣿⡿⠟⠋⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡛⣛⠦⢶⣿⢣⡤⠄⢠⣴⣷⢷⠞⢋⣿⣿⣇⣠⣿⣾⠿⠛⠋⢄⠀⢠⡄⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣙⣯⢗⢒⡶⣷⣶⣶⡾⠇⢿⣿⣿⣋⠁⠀⠀⠦⠀⠈⠑⠪⢀⠀⢸⠆⠀⠀⢀⡠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣉⣁⣀⡙⠲⠛⢛⣿⢿⣿⡗⠢⠠⣴⣿⣾⢧⠀⠰⠦⣄⠉⠛⡀⢀⣦⠾⣀⡤⠚⠉⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣭⡽⠿⢿⣟⡟⠈⣿⡷⣶⣶⣾⣿⣿⣾⣆⠀⠀⢈⣄⣤⠟⠿⣷⡎⠁⢀⡀⣤⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⠟⠙⠂⠀⠀⠀⠬⠅⢺⣿⣷⣾⣿⣿⣿⡏⠛⣿⣤⡴⠟⢉⠐⣸⡇⢻⡇⢀⣼⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠂⠤⢀⡀⠀⣴⣾⣿⣿⣿⣿⠿⣟⣿⣿⣾⠿⠿⠒⠒⠶⢓⣿⣿⣿⣧⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠤⢶⣿⣿⣋⣙⣷⣚⣉⣉⣤⣼⣿⣷⠿⠟⠋⠀⠈⣿⡆⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
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