Pizza slice Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠁⠀⠈⠉⠑⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣀⣀⣀⠀⠀⠀⠉⠓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠞⠉⠀⠉⠓⢄⠀⠀⠀⢀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠘⢿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠰⠃⠀⠀⠀⠀⠀⢨⡆⠀⣠⠋⠉⢢⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠈⠙⠛⠲⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣀⠀⠑⢤⣀⣀⣀⡤⠞⠀⠀⠉⠀⢐⣋⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢰⣋⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⠙⠋⠓⠲⢤⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠙⡄⠀⠉⠀⢀⣀⣠⡤⠶⢦⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠉⢦⡀⠀⠀⢀⣠⣴⠟⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⡇⠀⠀⠀⣏⠁⠀⠀⠀⢀⡷⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⣰⡿⠒⠛⠋⠉⣠⠾⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⡴⠋⠀⠀⠀⠀⠈⠑⠲⠴⠶⠛⠁⠀⠀⢀⣀⣀⠈⠉⠛⠛⠛⠛⠉⠀⠀⣀⣤⠶⠛⢻⣷⠖⠶⠚⠋⣁⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠿⠂⠀⢀⣀⣤⠶⠚⠋⠉⠀⠀⣠⡾⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢀⠖⢉⡼⠃⠀⢀⣠⠶⠚⠋⠉⠉⠓⠒⠦⣄⡀⣀⣠⡤⠶⠚⠉⠁⠀⢀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⣏⡔⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣠⡤⠴⠚⠋⠉⠀⢀⣀⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢸⡏⠀⠀⠀⣼⠁⢀⣀⣤⠴⠖⠋⠉⠀⠀⢀⣀⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣀⣠⠴⠟⠛⠉⠁⠀⢀⣀⣠⡤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣏⢀⣠⡴⠶⠛⠋⠉⠀⢀⣀⣤⠴⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢿⣏⣁⣀⣠⡤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⡵⡝⣆⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁⢀⣀⣙⠁⠘⣆⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⢷⠀⠐⢯⡁⠈⠙⣆⠸⡄⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠀⠀⠀⠀⡿⠀⢠⠞⣹⢦⣀⡿⠀⢻⡀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠻⣄⠀⠀⠀⢀⣠⠞⣡⣄⠈⠙⠁⠀⠉⢠⣶⡌⣇⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢴⣳⠀⠈⣩⣟⢛⡯⡄⠀⠛⢚⣠⠴⠶⠶⢤⣀⠉⠀⢹⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⡵⠖⡚⠒⠲⢤⡀⠘⠧⣬⠏⠀⢹⠀⣰⠋⠀⠀⠀⠀⠀⠈⢳⡀⢸⡇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡁⣴⠋⠀⠀⠈⠀⠀⠀⠹⡄⢰⣇⣀⣠⠟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣧⠖⠒⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢛⠛⡛⢻⠛⢞⠛⡞⠺⡛⢛⠛⡞⠻⡒⢻⠛⣗⠚⡞⠳⡛⢳⠛⢞⠛⡟⠻⡚⢻⠚⢣⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⠶⠷⠶⠷⠾⠶⠾⠶⠷⠾⠶⠾⠶⠷⠶⠷⠾⠶⠷⠶⠷⠶⠷⠾⠶⠾⠶⠷⠶⠷⠶⠷⠶⠷⠃




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠴⠒⠉⠉⠉⠉⠒⠲⠤⠄⠒⠒⠒⠢⢤⣀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⣀⠤⠤⢄⣀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠓⠒⠒⠒⠒
⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠤⠤⠀⠀⠀⠀⠠⠄⢀⡀⣀
⡞⠸⡀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⠀⠒⠈⣁⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⢀⡜
⠳⡀⠑⠦⡀⠀⠔⠈⠁⠀⠀⠀⠀⠀⠀⣼⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠐⠋⠉⠙⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋
⠀⠙⠦⣠⠊⢂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠹⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⠋
⠀⠀⠀⠀⠹⡄⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠙⣆⠈⠄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠈⠄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠄⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠄⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡄⠹⣿⣿⣿⣿⣿⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⡀⠙⢿⣿⡿⠿⠿⠟⠛⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠱⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠐⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠐⡀⠀⠄⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠱⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢄⠀⢠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠉⠉⠉⠑⠒⠢⠤⠤⠐⠒⠒⠒⠦⢤⣀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣠⠴⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⠓⠒⠲⠖⠒⠶⡄
⠀⠀⡠⠔⠊⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠚⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠒⠚⠒⠒⠒⠤⣀⠀⠀⠀⢠⠞
⣇⠀⢆⠀⠀⠀⠀⠀⡠⠔⠒⠉⠉⠉⠉⠀⠀⣠⣾⡿⠿⠷⠦⠄⠀⠀⠀⠀⠀⢀⡴⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠘⢆⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣸⠁
⠀⠈⠑⢦⡃⠈⠄⠀⠀⡀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡠⠄⠐⠂⠀⠀⠀⠀⣠⠔⠊⠉⠉⠁⠂⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⡰⠃
⠀⠀⠀⠈⢧⠀⠈⠀⠀⠡⡀⠀⠀⠀⠠⠁⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢲⠃⠀⠀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⢷⡀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠺⠀⠀⣰⣿⢿⣷⡄⠀⠀⠀⢀⣾⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢳⡄⠐⡀⠀⠀⠀⠈⢀⣉⠀⢻⠀⠀⠹⣷⣤⡿⠃⠀⢀⠀⠀⠻⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠐⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⡄⠀⠀⠘⡏⣯⠀⠈⣣⡀⠀⠀⠀⠀⠀⡠⠈⠳⣄⡀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠔⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠄⠀⠀⡇⠸⡄⠀⠈⠙⠓⠂⠀⠐⠈⠀⠀⠀⠀⠉⠁⠉⠉⠡⡂⠀⠀⠐⢄⠀⢀⡞⠀⠀⠀⠰⠋⠉⢢⢀⡔⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠄⠀⢿⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣠⠂⠈⠀⡾⠀⠀⠀⠀⢰⠀⠀⠖⠚⠀⠀⡠⠇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠐⡄⠘⣿⣦⣄⠈⠓⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠁⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠐⡀⠹⣿⣿⣿⣷⣶⣤⣤⣤⡯⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢠⠴⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠱⡀⠘⢿⣿⠟⠛⠙⠛⠁⢀⠠⠄⠀⠀⠀⠀⠆⠀⠀⠀⡄⢀⡾⣄⡀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡀⠱⡀⠀⠈⠓⠤⢄⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠏⠀⠈⠉⠉⠉⠉⠀⠀⡠⠀⠀⠀⠀⠀⠊⠑⠒⠒⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡔⠈⢳⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣰⠋⠓⠦⣤⣄⣠⣤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠊⡠
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡰⠋⠀⠀⠀⠻⡄⠈⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡃⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⣼⠁⢀⡜⠀⠀⠀⠀⠀⠀⠙⣆⠀⠢⡀⠀⠀⠀⠈⠄⠀⠀⠀⠐⠀⠁⡼⠁
⠀⠀⠀⣀⠤⠤⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁
⠀⢠⠊⠀⠀⠀⠀⠈⠁⠈⢂⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠊⢆⠐⠀⡀⠀⠀⠁⠀⣰⣿⣿⣄
⠀⢃⠔⠋⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⢳⡈⡀⠐⠀⠀⠁⠀⢰⠃⠘⣿⣿⡄
⠀⠌⠀⠀⠀⣴⢇⠈⢦⡀⠀⢈⠆⠀⠀⠀⠀⢸⣿⡟⠀⠀⢳⡈⢂⠀⠀⠀⢠⠏⠀⠀⢿⣿⡇
⠀⠸⣄⠀⡰⠏⠠⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠙⢦⣑⣄⣠⠏⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⡿⠛⣿⠿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣭⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠈⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠊⠉⣉⠤⠐⠒⠸⠄
⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣉⣀⠀⣔⠊⣉⣭⠭⠭⢶⢖⠬⠭⢖⢄
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢀⠊⡕⠂⢒⠕⡄⠉⠀⠸⡀⠀⢸⣜⣂⣄⣊⣼
⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⠔⠉⢷⡭⠭⢍⡺⢅⠀⠀⠀⠑⠤⣀⠉⠒⠒⣊⠜⢣
⡞⠒⠒⠠⢄⡀⠀⠀⠀⡠⢊⣀⣀⠀⡇⠀⠀⠀⠈⠉⠁⠀⠈⡆⣀⠔⠂⢣⠀⠈⠉⠁⠀⠀⠀⠱⡀
⢇⠀⠀⠀⠀⠈⠲⢄⠔⣱⢡⠒⠒⢍⢣⠀⠀⠀⠀⠀⠀⠀⣠⡟⢁⠖⠉⠀⠀⡀⠤⠄⢤⢔⣒⣒⢵⡄
⠀⠑⠢⠄⣀⠀⠀⠀⠑⠾⡒⠕⠒⢊⣼⠷⡢⠤⠄⠤⢤⢊⠍⠛⢍⢢⠀⡰⠋⠀⠀⠀⣧⡸⢄⣀⠱⣹⣄
⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠈⠛⢄⡉⠀⢣⠈⢂⠀⠀⠸⡬⣒⣒⡪⡼⠀⢇⠀⠀⠀⠀⠈⠪⠥⢲⡼⢣⠋⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠈⠒⢄⣉⡩⠐⠒⠂⢬⡄⠢⣉⠀⠀⠈⠢⢄⡀⠀⠀⢀⣠⡾⠔⢁⠜⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠈⠐⠤⡀⠀⠉⠒⠲⣤⡉⠆⠀⠀⢀⣈⣉⡉⠈⠑⠒⠈⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠈⠑⠢⣄⠀⢱⢱⠎⠀⡜⡕⠂⠑⡪⢢⠤⠤⡤⠖⢊⣉⣁⠦⠼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀⠀⠀⠉⠓⠤⣀⠀⠳⡨⠥⠭⣑⠏⠀⠈⠳⠚⡅⢰⡇⢎⠉⠒⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠉⠂⠬⡉⠉⠀⠀⠀⠀⠀⢠⠃⠀⠫⣒⡩⢩⠞⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⠀⠉⠒⠤⣔⠊⠲⣁⣀⣀⡀⠀⠱⣀⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣀⠉⠐⠲⠖⣂⠉⠀⠀⢀⣋⠥⠤⠤⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢄⡉⠑⠒⠬⣁⡀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠲⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠛⢉⣙⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⡁⠀⠀⠀⠀⠉⠙⠛⠶⣷⣠⡄⢀⡄⠈⠁⠠⠶⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⣠⡞⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢾⣁⡶⢀⡀⠐⠛⣛⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⡿⢃⣴⢋⡼⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⢠⡏⢈⣭⣴⢶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⠻⢶⣿⣡⣿⣥⠞⠁⠀⠀⠀⣠⡴⣶⡶⣶⢶⣄⡀⠀⠀⠈⠻⣇⣾⠁⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣾⣡⠞⢡⡾⣣⠞⣹⢷⡄⠀⣀⣠⣼⠟⢸⡇⣸⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣡⢞⣿⠟⣩⠟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣁⡴⣫⡾⣣⣞⣡⣼⡷⠛⣿⣁⣾⣤⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣿⢋⡴⢟⣥⢞⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣴⣯⣾⠟⣻⣁⣼⣷⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⢯⣴⣛⣵⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⣤⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⣠⣤⣤⣤⣄⡀⠀⠀⢠⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣼⣿⣹⣧⣾⣿⣿⣿⣦⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠈⣷⠀⠀⢠⡏⣿⢰⣿⡆⠀⠀⣿⣿⣿⣿⡿⠟⠛⠉⠙⠻⠟⠃
⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣷⣿⣿⣿⡇⠀⢠⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢿⣿⡿⠟⠻⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠸⣿⡄⠀⠀⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠛⣛⡛⠛⠛⠉⠉⠛⠗⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠸⣔⠀⢀⣀⣀⣀⣀⣤⣀⣀⣀⣀⠀⠀⢀⡿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠈⣷⠀⠘⣏⠉⠁⠀⠠⡄⠀⢠⠖⠀⠄⠉⢙⡏⠁⣼⠥⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢀⡠⠖⠛⣄⠀⢻⠀⣀⠤⢄⡀⠀⠈⠒⠘⡀⠀⣸⠁⢠⠟⢦⣀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣠⠞⡡⠀⢀⠔⡫⠀⢄⠀⠘⣆⠘⣷⠁⠀⠀⢰⠀⠖⠢⢀⡁⣠⠃⣰⠋⠀⠀⠈⠓⢄⠀⠓⠝⢦⣀
⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠁⠀⠣⠤⠝⠈⠀⡸⣆⠸⡗⠤⠔⠂⠀⡈⠀⠧⢠⠏⣰⠗⠒⠲⡄⠠⠇⠀⠑⢄⠀⠀⠈⠳⡄
⠀⠀⠀⣼⠁⠀⠀⣠⠋⠐⠲⠀⠀⠀⠀⠂⠀⡀⠘⡄⢻⡀⠀⢀⣀⠁⠀⢑⠎⣰⠻⡀⠀⠀⡸⠀⠀⢠⠒⠢⠳⡄⠀⠀⠽⡆
⠀⠀⠀⠻⣴⣀⣴⠁⠀⠀⢠⠂⠉⠀⡀⠁⡀⠈⠀⠹⡀⢷⠀⡅⠂⠆⢀⡞⢰⠏⠀⠈⠀⠈⠠⠒⠀⠘⠴⠔⠀⠘⣄⠀⣠⡟
⢀⡴⠖⠶⣄⠀⠈⠛⠦⣄⣳⡀⠀⢀⠆⠀⠀⡀⢀⠀⢳⠈⣧⠀⠀⢠⠞⢠⠏⡠⠀⡀⠊⠃⢀⡨⠄⡐⠈⣀⡤⠖⠋⠉⣉⣀⣀
⣼⠁⠀⠀⡟⠉⠑⠲⠤⣄⣉⠛⠿⢥⣀⡀⠀⢄⡡⠃⠈⡇⠈⠣⠴⠋⢀⡟⠀⠣⠈⠂⠀⠀⣂⣩⠴⠛⢋⣁⣤⡤⠴⢶⠉⠃⠈
⡟⠀⠀⢰⢁⠄⣄⠠⠄⠸⡉⡙⢲⢤⣈⠙⠓⠦⣤⣀⣀⡗⢀⠠⠤⣄⡘⢇⣀⡤⠤⠖⠚⣉⣡⠴⢖⠟⠛⠳⡄⠀⠀⠸⡄
⣿⠀⠀⢸⠰⠄⠴⠀⢠⠂⡈⠉⠁⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⣠⠴⠚⣋⣉⠀⠀⠸⡀⠀⠀⡘⢀⢠⠀⡇
⢻⢰⠀⢻⠀⠀⠀⠀⡀⢁⡀⠈⠃⢐⠁⠐⠀⠀⢙⡆⢠⠀⠀⠀⡈⠠⠀⢸⠺⣀⠀⠀⠀⢄⠇⠠⡄⠈⠀⠈⠀⠀⠁⠀⡇⠀⠇
⡿⠀⠀⢸⠀⠋⠀⡎⠀⠀⠘⡄⠀⠀⢁⣈⡤⠖⠋⠀⠈⢧⡀⠀⠁⠀⣠⣏⡀⠈⠓⠤⣀⠀⠀⢀⣀⠘⠤⠃⢀⠖⠒⡄⡇
⡇⠀⠀⢸⡄⠀⠀⠑⢤⣠⣴⠥⠖⠛⣉⡤⠴⠒⠚⠉⢳⡄⠈⠉⠀⠉⣾⠉⠉⠛⠲⢦⣌⣙⠲⢥⣈⠈⠆⠐⠌⠃⠀⢡⠇
⢻⡀⢀⢀⡧⠶⠖⠚⠋⣉⣤⠖⠊⠩⠀⠀⠠⡀⢢⠀⣼⠁⣠⠖⢢⡀⢸⡀⠰⢉⠙⠀⠀⠉⢙⠶⣤⣍⡓⠢⢤⣀⡀⡾⠀⠀⢠
⠀⠙⠚⢋⣀⣀⠤⠒⠉⡀⡈⠒⢊⠁⢠⡠⠈⠀⠊⣰⠃⡰⠁⠀⠀⢻⡀⢧⠀⠁⠈⠀⡀⢐⠁⠀⠀⢣⠉⠳⢦⣄⣈⡹⠦⡤⠞
⠀⠀⢰⠋⠉⠹⡄⠀⠤⠦⡄⠈⠤⠁⡀⢀⡀⠀⣰⠇⡼⠁⠰⠡⢈⠀⢷⠈⣆⠀⠀⠈⡀⠈⠢⠀⠴⠃⠀⠀⢠⠞⠉⠏⢧
⠀⠀⠸⣄⠀⠀⠘⢆⠢⠤⠂⠀⠀⡈⠀⠀⠈⣦⠏⣰⢅⠀⢀⠉⠁⠀⠈⢧⠘⡆⢉⠀⠠⠂⠀⠀⠀⠆⠂⡰⠃⠀⠀⢠⠏
⠀⠀⠀⠙⢦⡀⠀⠀⠳⣄⠀⢠⠂⠘⠦⠤⢴⡏⣰⠃⢲⠀⡈⠀⢠⠔⠒⢺⣆⠸⡏⠀⠂⢐⠉⢲⠀⣠⠞⠁⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠉⠲⣔⢤⠈⠑⢤⡀⠀⠀⢠⠏⢠⠏⢈⠁⠠⠴⠀⢃⠀⠀⢀⠿⡄⠙⡄⠀⠐⠂⣪⠞⠁⠀⢪⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠉⠳⣴⠋⠀⡞⠀⠈⡤⠠⡀⠀⠀⠑⠒⠉⠀⢷⠀⠘⢦⠔⠋⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢐⡾⠀⣸⣅⣀⠐⠄⠤⠃⠀⠈⠒⠀⢀⣀⣸⣆⠀⢻⣀⠀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢼⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠜⡇⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⣤⣀⣀⣤⣤⡬⠭⣤⣤⣀⣤⡤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠒⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠃⠰⠗⠲⢬⡟⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢊⠐⠆⠁⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠐⠬⠥⠒⠁⠀⠀⠀⠀⠀⠤⢄⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣄⠀⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠉⠁⠀⠀⠐⠋⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⡠⠁⠀⠀⠀⠉⠉⠛⢦⡀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠢⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠀⢀⠠⠃⠀⠀⠀⠀⠀⡅⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⡄⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡛⠆⠀⠀⠀⣠⢞⡶⠀⠀⠀⠀⠀⠤⠀⡀⠜⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠆⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⢰⣈⣋⡀⠀⠀⢶⣋⡥⠞⠁⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡀⠁⠀⠠⠤⢤⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⡀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢰⠀⠎⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⣠⠞⣡⠇⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⢦⣄⠀⠀⠈⠛⠚⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠙⠚⠁⢀⠉⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠉⠛⢦⣀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⡤⠞⠁⠋⠃⠀⡟⠀⠀⢀⣀⠠⠶
⠀⠀⠀⠀⠀⠀⠈⠉⡉⠁⠀⢴⡡⠀⠀⠀⠃⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⡎⣽⠝⠆⠀⠀⠀⠀⣀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠑⠒⠊⠠⠀⠀⠀⠊
⠀⠀⠀⢠⠀⢀⡀⡀⠤⠒⠉
⠀⠀⠀⠈⠒⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠓⠛⠛⠛⠒⠶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠹⣙⣇⡄⣠⡄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⠛⠿⠿⠷⠷⣿⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢠⡞⢉⠗⠀⠀⠀⠀⠀⠙⠿⢼⣼⣇⣆⡶⢀⢀⢀⡀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠤⠟⠀⠀⠉⠉⠙⠛⠺⢾⣴⢃⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⣠⠴⢶⣒⣒⣒⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⡤⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣴⢋⠕⠉⠁⠀⠀⠋⠉⡳⠆⠙⢦⠀⠀⠀⠀⠀⠀⠀⢸⣿⢇⡆⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢘⡇⠀⠀⠀⢀⡠⣄⠈⢿⡘⡄⡆⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢻⣤⡴⠏⡏⢻⡆⠀⠰⣏⣏⣍⣓⡾⠁⠀⠀⠀⣞⠤⠚⠀⠈⠳⣤⡃⣿⡄⢀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠤⣀⠀⠀⠀⠙⠛⠛⠉⡿⠁⠀⢀⢿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣹⠘⠸⢤⡄⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⣄⠈⢳⡀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣥⡀⡴⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠠⣆⣸⣦⠄⢧⠀⠀⠀⠀⠸⣦⣙⣒⣒⡥⠟⠀⠀⠀⠀⠀⣠⠤⠖⠒⠛⠛⠛⠛⡛⠲⢶⣤⣀⠀⠀⠀⢻⡇⣆⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⢞⠁⠀⢸⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡴⠋⢠⠊⠙⡀⠀⢀⠀⢊⠀⢀⠄⣨⠙⢷⣄⠀⠈⠳⣟⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⢐⠿⣹⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠓⠋⠁⠀⠀⠐⠁⠀⠁⠀⠁⠀⠀⢹⣆⠀⠀⣸⡄⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣠⢲⡄⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠀⠀⠀⢿⡀⣰⣯⠆⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡄⠀⢙⡆⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠬⠗⠀⠀⠀⠀⠀⠙⢦⡠⠖⠋⠀⠀⠀⢸⡇⣿⡁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠛⠚⠋⣁⣠⠖⠋⠀⣠⠤⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠄⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⢠⣿⡴⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⠒⠒⢚⡽⠟⣗⢦⡀⠸⡇⠈⠉⠉⠛⢻⢱⡄⠀⠀⠀⠀⠘⣷⣠⠔⠁⡠⠀⠀⠠⠤⠜⠀⠀⠀⠀⢞⢁⡀⠀⣰⡏⢸⣿⣿⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⠀⠀⢿⣾⣷⣤⠇⠀⠀⢀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠹⣧⡴⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠏⠀⣾⠸⣿⣇⡀⠀⢸
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢻⢸⠀⠀⠉⠉⠁⠀⠀⣰⣯⣤⣄⡀⠀⠀⠀⢰⣉⠀⠀⠙⢿⣮⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⣴⠞⠋⠁⠀⢀⣿⠞⠛⢛⠟⡿⣿
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠘⣏⠆⠀⠀⠀⠀⠀⠀⠙⠿⠶⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⢀⣀⣀⣠⣾⠃⠆⠌⡜⠸⡹⣹
⠀⠀⠀⠀⡼⠁⠀⠀⣀⣀⡀⠀⠀⠙⢮⡢⠀⠀⠀⠀⠀⣀⡤⠂⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⡶⣶⠾⢿⡟⢋⠟⢡⠃⠃⠀⠀⠀⠀⠁⠁⢁
⠀⠀⠀⣼⠁⠀⠀⣞⠁⣠⠟⠀⠀⠀⠀⠙⠳⠶⢤⣤⣤⣤⠶⠛⣁⣠⣤⣤⣶⣶⣾⣿⡿⣿⠟⡿⠛⣹⠋⠝⠁⠈⠀⠋⠀⣈⣀⣀⣠⣤⣤⣤⣤⡶⠶⠶⠶⠶⠞
⠀⠀⣼⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⣿⢿⡿⡿⠋⠟⠙⠁⠋⠈⢀⣁⣈⣡⣤⣤⡶⠶⠶⠾⠛⠛⠛⠋⠉⠉⠉
⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢴⡶⢾⠟⠫⠟⠡⠊⢐⣁⣈⣤⣤⣤⠶⠶⠶⠛⠛⠛⠉⠉⠁
⣰⠃⢀⣠⠤⠴⠖⠚⠛⠉⢋⣀⣁⣠⣤⣤⠶⠶⠾⠛⠛⠋⠉⠉
⠻⢮⣥⣤⣤⡴⠶⠶⠞⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⣈⣤⣤⣷⣤⡀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡁⠀⡂⠀⠀⠀⠉⠢⡀⠉⢪⠠⡀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣸⠏⠀⠃⠈⠀⠈⢱⡤⠀⠠⡠⠘⡀⠀⢱⠰⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⡠⠀⠁⢾⡟⢀⠠⣀⡀⠀⠐⠿⠇⠀⣴⣿⠴⠀⠀⠨⢠⠂⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠼⠀⠀⠀⢻⣧⠀⠙⠿⠟⠀⢀⣠⠴⡞⠅⡀⢀⣀⣴⡵⠃⠐⠀⠀⠀⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣀⠁⠐⠀⠀⠒⠂⢄⠀⢀⠀⢼⠿⡟⣧⣣⣤⡴⠶⠟⠉⠁⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⢀⡐⠁⠀⠈⣻⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠱⠈⠑⠀⠐⣡⠾⣟⠛⠋⢀⡂⠤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⢸
⠀⠀⡠⠐⠈⠁⢻⣶⣶⣿⣿⣿⣿⡷⢀⡿⠛⠀⠀⠀⠀⠀⠇⠀⣠⠎⠀⠙⠋⢀⠀⠀⠁⠀⢀⣱⡄⠀⠀⠚⠋⠒⠤⢄⣠⣼⣳⡀⠀⠀⠀⡐
⠀⠐⠁⠀⠀⠄⠀⠉⠛⠿⠿⠟⠁⠐⠁⣀⠔⠿⠗⠀⠀⠐⠀⠀⣟⠀⠀⠀⠀⠷⠃⠀⠀⣠⠟⢁⡀⢀⠀⢠⣶⣶⣶⣬⣿⣿⣿⠃⠀⠀⠀⠅
⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠑⠒⠒⠁⠀⠀⠀⠻⣦⡲⠖⠀⠀⠆⠐⣿⡏⡰⠋⠀⠈⠉⢙⡛⠿⣿⣿⣿⠟⠛⠀⠀⠀⢀
⠀⠀⢆⡤⠞⠛⠋⠹⢦⣀⣠⠶⠒⠒⠖⠚⠳⣆⠀⢀⣀⣀⣀⣀⣀⠈⠛⠷⠶⠶⠶⠾⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣉⣀⣀⠀⠀⠀⠀⢸
⠀⠀⠈⠢⠤⠤⠐⠐⠒⠚⠒⠒⠂⠀⠤⠀⢀⡹⠴⠋⠀⠀⠀⠈⠛⠒⠚⢛⣷⠀⢀⡴⠶⠬⠭⡤⢬⣀⠀⢀⡴⠛⠏⠉⠈⠙⢷⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠀⠀⠀⠀⡛⠤⠞⠁⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⢈⡇⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣀⣀⡉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⡴⠋⠁⣤⠈⠉⢦⠀⠙⢮⡳⣄⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡞⠀⠀⠀⠀⠀⣀⢸⠇⠀⠀⠙⢮⡳⣄⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⢶⠀⣧⠘⠃⠀⠚⠀⣠⠞⠀⠀⢀⣠⢤⣝⣞⢦⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠞⠁⢸⡆⠈⠳⠦⠤⠖⠋⢁⡤⠴⠖⢧⡀⠀⠀⣉⡿⢳⡀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⣀⣠⠜⠀⠀⠀⠀⠀⠀⣰⠃⣤⠀⠀⠰⠎⢻⡉⠹⣄⠀⠱⡄⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⠴⠒⠢⢌⠉⠀⢠⡴⠶⠦⣄⠀⠀⠻⡀⠀⠰⠆⢀⠀⣰⠃⠀⠈⠳⡄⠱⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡼⠁⠀⠙⠀⠀⡇⠀⠀⠳⣀⣀⣀⣑⡦⠀⠈⠓⠒⠶⠖⠚⠁⠀⠀⠀⣀⡟⠀⢳⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⡇⠚⠀⠲⢈⡱⠃⠀⠀⣀⣈⣭⠥⠤⠶⠒⠒⠚⠛⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⡙⠒⢋⡟
⠀⠀⠀⠀⠀⡴⣹⠁⠀⠀⠈⠒⠒⣒⣭⠴⠖⠚⣉⣩⡤⠤⠶⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⡼⢱⣃⣀⣤⣴⡶⠟⠋⣉⡤⠖⠚⠉⠁
⠀⠀⠀⠀⢧⣀⡤⠖⠋⣡⠴⠚⠉
⠀⠀⠀⠀⠀⠈⠲⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠲⢍⠢⠄⢀⡀⠈⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⡡⠤⠤⠤⢄⣀⠑⢄⡀⠙⡄⠀⠘⠓⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠉⠠⠈⠲⠤⠤⠤⠤⠞⠀⠀⠉⠒⠮⣖⠂⠤⡀⠈⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢪⠕⠒⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠈⠳⢄⡙⢄⠀⠀⠀⠔⠛⣆
⠀⠀⠀⠀⠀⣀⠠⠔⠊⠁⠀⠀⢘⣒⠒⠒⠊⠁⠀⣎⠀⠀⠀⠀⢙⠆⠀⡋⠈⠉⠉⠉⠑⠆⠈⠢⣑⠂⢴⡈⡀⢸
⠀⠀⢀⠔⠋⠀⠀⣴⠂⠉⠉⢳⠄⠀⠀⠀⠀⠤⠄⠀⠈⠉⠉⠉⠁⠀⠀⠈⠒⠒⠂⠀⠒⠁⠀⢀⡨⠷⣂⣈⠴⠋
⠀⠀⡌⠀⠀⣁⣀⣀⠉⣉⣉⣁⣤⣤⡤⣄⣠⡄⠀⣀⣀⣀⣠⣒⣒⣉⠱⣄⠀⣀⠤⠆⠙⠙⠛⠋⠉⠈⠁
⠀⠀⠀⠉⠉⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠈⠀⠙⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉







⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠁⠀⠀⠀⠀⢤⣀⡀⠤⠀⠀⣠⠀⢠⡄⠂⣄⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠋⢀⡆⠙⠳⣤⠔⠊⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⣀⠀⣠⠬⠤⠋⠀⠀⣀⡠⠤⠽⡏⠉⢀⡤⢟⠁⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠐⠒⠀⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣠
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢖⡦⣶⣾⠿⠗⠋
⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⣀⡈⠙⠂⠀⠀⠀⠀⠀⢀⣀⣀⡠⣀⣤⠤⠤⠐⠒⠒⠛⠛⠙⠃⠉⠀⠈⠙⠋⠆⠐⠈
⠀⠀⠀⣄⠈⠫⠹⠆⠀⠀⠈⠁⣀⡤⠤⠖⠚⠛⠋⠉⠉⠁
⠀⠀⢈⣀⡀⠀⠤⠐⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠉⠲⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣮⡻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣉⣀⣀⣤⠾⠀⠀⠀⠀⠀⡀⠈⡆⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⢋⣼⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠚⣠⠤⡉⠉⠁⡀⠀⣀⠘⠶⠶⠞⠃⠀⣹⠀⠀⢀⡟⠀⠀⠀⣀⣴⡿⣿⢧⣶⣶⣿⣿⣿⣿⣏⣛⣋⣡⣾⣿⡇⣿⣿⣿⡇
⠀⠀⠀⠀⣀⠔⠉⠀⠀⢷⣄⣼⡀⠒⠁⠈⠁⠀⠠⠒⣒⣈⣉⡥⠤⠖⠋⠀⠀⣠⣾⣿⣿⠸⢿⡗⣿⣟⣽⣿⣷⣾⣿⣿⣟⣿⣭⣭⡵⠿⠟⠋
⠀⠀⣠⢚⣁⠀⠄⠤⢐⣊⣉⠩⢄⣀⣠⠶⣄⠀⡏⠉⠉⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣟⣷⣤⣤⢿⣿⣿⠿⠿⣿⡟⠉⠉⠉
⠀⠀⠘⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠈⠀⠀⢸⣀⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠛⠛⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠠⠎⠀⢰⣿⡆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣀⠀⠀⠀⠀⠈⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡰⠁⠀⣠⣄⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡜⠁⠀⠀⠻⠋⠀⠀⠀⢸⣷⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⣶⠄⠀⠀⠀⠈⠉⠀⠀⢠⣤⡀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠈⢣
⠀⠀⠀⠀⠀⢀⠞⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⡠⢧⡀
⠀⠀⠀⠀⢠⣾⣷⣄⡀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⣀⣴⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣦⣄⣀⠈⠉⠐⠒⠒⠒⠠⠤⠤⠤⠄⠒⠒⠒⠊⠉⠀⣀⣠⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⠉⠉⠁⠒⠲⠦⠤⠤⠄⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⡠⠄⠬⠭⠭⢅⠒⠒⠦⠤⣀⣀⣀⣀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⡀⠀⠑⠤⠤⠄⣀⠀⠕⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⣄⢳⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠔⠈⠉⢀⡸⠃⠀⠀⠀⠀⠀⣀⡤⠤⢖⠒⠒⣦⠐⠧⠄⠀⠤⠔⣋⠇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠈⠒⠒⠋⠁⠀⠀⠀⠀⠀⣴⠋⢈⣀⣀⠤⠴⠚⠁⠀⣀⡤⠔⠒⠉⠀⠀⣀⠠⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⣀⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⡀⠤⠤⠖⠒⠉⣀⡠⠤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⢀⡴⠋⢠⠊⠁⠀⣀⣀⣤⠇⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠉⠀⣀⡠⠤⠖⠒⠉
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠉⠉⣉⠩⣁⡠⠒⠒⠂⠉⠉⠀⣀⡠⠤⠴⠒⠒⠉⠁
⠀⠀⠀⠀⠹⣑⠒⠐⠒⢂⣉⣀⣀⡤⠤⠤⠖⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⠀⠀⢖⠊⣁⠄⠀⠁⣐⠠⠄⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⣁⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠉⠢⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢠⠤⠀⢚⠉⠉⠙⠊⠉⠛⠒⠒⢛⡒⠀⠤⢤⠀⠀⠢⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠾⡏⢀⡔⠈⣠⣶⣾⣷⣦⣍⠂⠠⢀⠖⠦⠖⡀⠀⢁⡦⠡⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣾⡿⠛⢻⣿⠟⠻⣯⠈⠸⠠⢂⣬⣶⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⢸⣿⣇⣀⣼⣿⣷⣾⣿⡇⢀⣰⡿⢿⡟⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⢿⣿⡿⢻⣿⣀⣿⣟⠁⢐⣿⣷⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠻⢿⣿⣿⣿⠿⠃⠀⢸⣿⣅⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⠀⠀⠐⠁⠀⡄⠀⠹⢿⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣥⣤⣬⣁⠘⠂⠉⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠉⣿⣧⠀⣂⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢿⣟⣿⠀⢀⠄⣀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⡿⠁⠀⠁⣰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡀⠑⢃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡤⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠻⣅⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠈⢆⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⢋⠁⠀⢀⠧⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⡟⠁⠱⡍⢳⡀⠀⠀⠉⠉⠒⠂⠤⣄⣀⡀⠀⠀⠀⠀⢸⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠐⠀⠀⠀⣇⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣛⠉⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣿⠁
⠀⠀⠀⠀⠀⣰⡿⡍⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣼⣿
⠀⠀⠀⠀⠀⣿⠀⠹⣆⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠇⢠⣿⡏
⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧⡀⠈⠲⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⣠⠇⢀⣾⡿⠁
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⢦⡀⠈⠲⣄⣀⠼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⠚⠁⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠈⠙⠒⠢⣀⠀⠀⠀⣸⠛⣆⠀⣀⣀⣀⣠⠴⠋⠀⣠⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⡀⠉⠉⠉⠁⠀⠈⠁⠉⠉⣁⣠⠤⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠒⠚⠋⢉⣡⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣆⠀⠡⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡋⠔⠀⠘⡆⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠊⠀⢀⡄⠀⢸⡀⠈⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕⠁⡠⠐⠈⠀⠀⠀⠀⠇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⡡⠐⠁⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠕⠀⠀⠀⣀⠠⠄⠀⠐⠂⠉⣀⣀⡇⠀⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⣀⣀⣀⡬⠥⠤⠤⠒⠒⠒⠉⠉⠉⠉⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⢀⣀⣎⠰⡀⠀⠈⠂⠄⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡟⠉⠀⡌⠢⡈⠢⡀⠀⠄⡀⠀⠒⠠⠀⠀⠀⠀⠀⠀⢀⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⡤⠀⠀⠀⡇⠀⠀⠈⢂⠈⢢⡈⠢⠀⠈⠐⠠⡀⠀⠀⠈⠁⠀⠀⡘⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⠔⠁⠀⠀⢀⢀⠇⠀⠰⠀⠀⠑⡄⠙⢦⡀⠑⢄⠀⠀⠁⠀⢀⠀⠀⢠⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠐⠁⡀⠀⠀⠀⡄⢸⠀⠸⠀⠀⠀⢦⠈⠢⡀⠑⢄⠀⠑⠀⡀⠀⠀⠀⢠⠃⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠔⠀⠀⠐⠀⠠⠃⠀⠀⡘⠀⠀⠀⠀⠀⠘⠁⠀⠑⢄⠀⠱⣄⠀⠀⠀⠀⡰⠃⢀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠔⠁⠀⢀⠌⠀⠠⠁⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠑⠀⠈⠳⡄⣠⠞⠀⡐⣡⠋
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠔⠁⠀⠀⠀⠂⠀⢠⠁⠀⢀⠃⢠⡇⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⣠⠞⠁⡠⢊⠜⠁
⠀⠀⠀⣠⠞⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⣨⠖⠁
⠀⠀⠈⠣⢄⡂⢄⠈⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠈⠀⢀⣀⡤⠖⠋⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠈⠑⠢⢅⡂⠠⠀⡈⠉⠉⠒⠒⠢⠤⠤⠤⠧⠤⠤⠔⠒⠒⠉⠉⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠍⢉⣭⢛⡋⠙⠒⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤⡀⠀⣘⠂⠀⢹⠆⠀⠀⠀⠉⣽⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⣦⣀⡼⠀⠀⠉⠉⠑⠀⠀⢀⠤⠐⠿⣶⡄⠈⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠉⠓⢄⠸⣆⣀⣠⡴⠃⣀⠀⠈⢳⣄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣦⣤⡄⠀⣤⡀⠓⠦⠤⠶⠋⠀⠈⠉⠉⢀⣀⣀⠀⠀⠀⠉⠳⣤⠾⣫⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⠋⡩⠅⢠⠀⡼⠀⢀⣂⣶⣶⠁⠀⢠⡎⠁⠂⢨⠹⡆⣀⠴⠂⠁⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢦⠽⢶⠞⠊⠀⠀⠈⠉⠉⠛⠀⠀⠀⠻⠦⠶⢾⣿⢛⣁⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠴⠁⣈⠇⣠⡔⠲⠓⢲⡄⠀⠀⠀⠀⠀⠀⢀⠜⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⠋⠡⠀⠙⣇⣘⣀⣸⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠁⡆⠀⠀⠐⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⢷⠀⣀⣠⠴⠃⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠰⠟⠛⠤⠿⢿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠒⠒⠂⠀⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⡠⠤⠀⢤⣤⠖⡓⢂⠛⢠⠔⠦⢤⡐⡶⣤⡠⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠈⡆⠀⣶⣷⠶⠀⠀⠐⠢⠗⠀⠈⠛⠒⠰⣄⠀⠀⠑
⠀⠀⠀⠀⢀⠊⠀⣠⠞⠁⠚⡀⠀⠀⠀⡀⢀⠟⠀⠀⠀⠀⢲⡟⠂⢠⣤⠀⠀⠀⠀⠀⠈⠓⠀⠀⠈⠂
⠀⠀⠀⡐⠁⢠⠞⣉⣨⣤⠢⡜⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠘⠷⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠡
⠀⠀⡐⠀⠀⠃⠼⡀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡂⠀⠀⢁
⠀⢀⠁⠀⢠⠛⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠒⢄⡀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⡀⠀⠄⡅⠀⠀⠀⡄
⠀⠄⠀⠀⡘⠀⠰⠒⠀⠀⠀⠀⣀⠀⠉⣿⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠊⠀⢾⡿⠋⠘⠀⢿⡄⠀⠀⠠
⠀⠀⠀⠀⣇⡤⠀⠀⠀⠀⠀⠀⢿⣦⣴⠚⠃⠀⠀⠀⠠⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠶⠿⢋⡄⠈⣧
⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠛⠊⠁⠀⠀⢻
⠀⠀⠀⠀⢸⡟⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⡼⠀⠀⠀⠀⣄⠀⠀⢀⢹
⠀⡄⠀⠀⠀⢷⠘⠿⡿⠋⠁⠀⠀⠐⢄⠀⠠⠀⠐⠀⢀⡀⠀⠀⢀⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡀⠀⠰
⠀⠠⠀⠀⠀⠈⣀⠤⡁⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠈⠁⠀⠀⠻⠿⠟⠀⠀⠀⢀⣶⠄⢀⣀⡐⣸⡸⠀⠀⠂
⠀⠀⠄⠀⠀⠀⢈⠂⠑⢄⣀⡠⠂⢉⣁⡀⠀⠀⠐⠄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢀⣰⡿⡴⠉⠁⠀⡐
⠀⠀⠈⡄⠀⠀⠀⠢⠀⠀⠁⠀⠀⠿⠟⠁⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠈⣱⠞⠀⠀⠀⠠⠁
⠀⠀⠀⠈⢄⠀⠀⠀⠀⠑⢄⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠐⠊⠁⢀⢀⠾⡁⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢤⣀⠀⠠⠀⠈⢀⢠⠄⣄⡀⡀⠀⠀⠀⠀⢄⡢⠞⠁⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠉⠓⠶⣄⣀⣀⠀⠐⢆⣁⣙⡠⠤⠔⠊⠁⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠤⠀⠀⠀⠀⠀⠒⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠋⠉⠛⠛⣛⣛⠛⠛⠛⠛⠛⠻⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢿⡾⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣸⠇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠈⠙⡆⠀⢹⡏⠉⠉⠁⡤⡀⠀⢀⡔⠒⢌⠉⠛⣻⠉⢠⣯⠍⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠞⢣⡀⠀⣷⠀⢀⣀⣈⠁⠀⠈⠣⠴⢊⠀⢠⠇⠀⣼⢧⣄⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⢀⣠⢞⠄⠀⣠⢖⡩⠤⡀⠀⢳⡀⢸⣴⠃⠀⠀⢱⠀⡔⢤⠀⠓⠀⡞⢀⡼⠁⠀⠈⠓⢦⡀⠐⢎⠳⣄
⠀⠀⠀⠀⢀⡴⠋⠁⠉⢀⠔⠁⠸⣄⣐⠇⢖⠄⢳⡀⢻⡦⣀⡠⠎⢀⠑⠀⣜⠁⡽⢁⣾⠤⠤⣄⠀⣶⠀⠙⢦⡀⠀⠈⠳⣦
⠀⠀⠀⢠⠏⠀⠀⠀⡴⠃⡤⡄⠀⠀⠀⡠⢄⢸⢁⢳⡈⢧⠀⠀⠀⠘⠃⠀⠣⡼⢁⡾⡇⠀⠀⠈⡆⠀⠀⣠⠤⣝⢦⠀⠀⠈⣷⡄
⠀⠀⠀⢻⣠⡄⢀⠞⠁⠀⠀⡠⠤⠤⡄⠡⠊⠈⠣⠄⢧⠘⣇⢀⠊⠍⡆⠀⣰⠃⡾⠁⠑⠤⠤⠊⡀⣄⠀⢇⣀⡸⠈⢧⡀⠀⢘⡇
⠀⢀⣤⣤⡉⠛⠛⠶⣄⡀⢸⡁⠀⠀⢘⠀⠘⠅⠀⠀⠈⣇⠹⡆⠑⠊⠀⡰⠃⡼⠁⣀⠀⢠⣦⠀⠂⢘⠀⢔⠆⠀⣀⡤⠟⠶⠛⠁
⣰⡯⠀⠀⣻⠒⠦⣤⣀⠉⠓⠷⣦⣔⠋⠀⠀⢐⠁⢕⠀⢸⡄⠹⣄⣀⡼⠁⣼⠃⢎⠠⣸⠀⠀⢠⠚⢋⣹⡤⠖⠋⠁⣀⣀⣤⠾⠏⠳
⣿⠀⠀⢀⡏⢀⡀⢀⢈⠉⡗⠶⢤⣉⠙⠳⠦⣌⣑⠉⠀⠀⡇⠀⠈⠁⠀⠰⡇⠀⠀⢉⣀⣠⠤⠞⢛⣉⣤⣴⢶⣛⠉⠉⠁⢸
⣿⠀⠀⢸⢰⠁⠘⡆⠈⣀⡑⠶⠤⠋⠙⠲⢤⣀⠉⠙⠓⠒⡡⠒⠉⠉⠙⠲⣝⠛⠋⢉⣡⡤⠶⠚⠋⠁⡎⠀⠀⠈⡆⠀⠀⠸⡇
⢿⢠⠀⢸⠀⠉⠉⠀⠐⠇⠜⢀⣤⠀⡠⠠⠄⠈⠓⢦⠀⢀⠀⠀⠀⠀⠀⠀⢹⣤⡞⠉⠁⡔⠐⢢⠀⠀⠙⠤⠀⠴⠁⠘⠞⠀⡇⠀⡄
⣼⠸⠀⢸⠀⡠⡄⢀⠔⠒⠲⡄⠀⠀⠣⣁⠜⠀⣀⡼⠃⢸⡀⠀⠒⠆⠈⠁⣸⠉⠳⢄⡀⠑⠃⠊⠀⠛⠀⡔⢠⠀⠀⣀⣀⠀⡇⠀⠃
⡟⠀⠀⢸⡄⠀⠀⢸⡀⠀⠀⡸⢀⣀⣤⠶⠞⠋⣁⣀⣤⣄⠙⠦⢀⢀⠠⢴⠧⠤⣤⣀⡉⠓⠤⣀⡠⠒⡦⢌⠈⠀⢨⡀⢈⢢⡇
⣧⠀⠀⠀⡇⠀⢀⣀⣩⡶⠾⠛⣋⣡⡤⠖⠋⠉⠁⠀⠀⢸⠆⠀⢀⡀⠀⢸⠀⠀⡠⠬⡙⠓⠶⣤⣉⠓⠦⣼⣀⠑⠀⠉⠁⣸⠁
⠹⣆⣰⣦⠟⠋⠉⢁⣠⠤⠲⣏⠁⣤⠃⠀⠀⡎⠂⣱⢀⡟⢀⡜⠉⠙⣦⠈⣇⠀⢅⣂⠅⠀⠀⡠⠚⠛⢷⡦⣍⡙⠒⠦⠤⣇⠀⠀⣺
⠀⠀⠉⣠⡤⣤⠚⠉⠀⠠⠕⠈⡡⠤⡀⠪⠂⠈⠉⢀⡞⢀⡞⠀⠠⢄⠘⣇⠸⡄⠀⠀⢐⡆⠀⡇⠀⠀⢀⡇⠀⠙⠳⣦⢤⣽⡓⠚⠉
⠀⠀⢸⡃⠀⠈⢣⡀⡔⠛⢳⠀⠘⠊⡠⠒⠲⢄⠀⡾⢁⡞⠀⠘⣐⡠⠃⠹⡄⢱⡒⢢⡀⠠⠀⡈⠒⠒⠋⡀⠀⢀⡼⠁⠈⠃⣷
⠀⠀⠘⢿⡀⠀⠀⠳⣕⠒⠊⠀⠀⠀⡇⠀⠀⢈⡾⢁⡞⢢⠀⢠⡄⠀⠀⠀⢻⡄⢳⣈⠅⠈⠊⢁⡀⠀⠘⠛⣠⠞⠀⠀⠀⡴⠃
⠀⠀⠀⠈⠳⣤⡀⠀⠈⠳⣄⠀⠯⠀⠙⠒⠒⣿⠃⣼⢀⡿⢀⢄⡀⡰⠊⠉⠙⣷⡈⢧⠐⠱⢰⠅⠈⡆⢀⠔⠁⣠⢄⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠙⢦⡑⡄⠈⠳⢤⡀⠀⢀⡼⠁⣸⠁⢤⠀⠐⠔⠀⢣⡀⠀⢀⠟⣧⠈⢳⡀⠀⠑⣪⠕⠁⠀⠀⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠉⠳⡞⠁⢠⠇⠀⢩⠖⠲⡄⠀⠀⣉⠉⠁⠀⢹⡄⠀⢳⡴⠋⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⣳⠇⢀⣼⣤⣀⡘⠤⠴⠃⠀⠈⠓⢀⣀⣀⣨⣧⡀⠘⣧⣀⣀⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣟⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⢿⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣤⣀⣠⣤⣤⠭⠭⣤⣤⣤⣤⣤⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⡨⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡠⠊⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⠄⠀⠀⡀⢊⡴⢾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠁⠀⡀⢈⠄⠀⠀⠋⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢀⠔⠁⡠⠃⠈⣠⠔⠀⠀⠀⢉⠿⢀⠾⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⡠⣪⠆⢀⠞⠁⠀⢤⣤⠞⠁⠀⠁⠀⠀⡸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠊⡠⠊⠀⣠⠖⠁⠠⡀⠀⠀⠀⠀⠂⠁⠀⠀⠄⠀⢁⠽⣄
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠄⠊⡠⠎⠁⢠⠞⠁⢀⢊⠜⡡⣀⣀⠄⢥⡖⡄⢀⣒⠄⢀⣀⣤⡘⣆
⠀⠀⠀⠀⡴⠛⡉⠳⡔⠄⠈⠀⢀⡴⠁⠀⠀⢄⡛⠊⠀⠁⣝⢒⠒⠒⠅⠀⡠⠐⡩⠖⠲⣽⡜⢆
⠀⠀⠀⢸⠁⣠⠤⠤⠂⠀⢀⡴⠋⢀⡠⠤⡄⠈⠉⠀⠀⠠⠤⣤⠀⠀⠀⠞⡡⠊⢀⠀⠠⣬⠷⣎⢆
⠀⠀⠀⠈⢧⣘⢤⡈⠤⠞⠋⢀⡎⣁⣤⠾⠋⠁⠀⠀⠀⣀⣴⠏⠀⠘⠗⠊⠀⢀⡤⠂⠓⠦⢀⢤⠘⣆
⠀⠀⠀⠀⠀⠈⠙⠿⣷⣆⠤⢀⣉⡈⠁⠀⠀⠈⠘⠛⠻⠛⠉⠐⢂⠀⠀⠀⢰⣏⣀⣴⠾⠁⠈⠊⠖⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠷⣿⣵⣒⠤⣄⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠉⠀⠐⠀⠀⠀⠀⠨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢯⣙⠲⣦⣄⡑⠀⠀⢠⣤⢤⣀⠀⠐⠅⢠⠠⠄⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢍⡛⠳⢤⡛⠉⢙⣾⠀⠀⠀⠀⠠⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣉⠳⣼⠤⠥⣆⠀⢀⠀⠑⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣮⣳⡄⢘⡀⠀⢀⠀⠾⠷⡄⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣎⠁⠀⠸⡄⠀⠀⠈⡄⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢂⠀⢣⠈⢦⠼⠟⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⡆⠄⢧⠀⡗⠀⠀⠀⠀⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡈⠞⠁⠛⠀⠀⠀⠀⠸⡙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠀⡾⢀⣀⠀⠀⠀⠁⠈⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⠵⠁⠈⠑⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡴⣞⡯⠭⠭⠭⣍⣳⡆⡼⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡰⠟⣛⣛⣛⡻⠿⠆⣠⡻⣷⣄
⠀⠀⠀⠀⠀⡴⢫⠞⠙⣆⠀⠀⠿⢣⢏⡞⣵⣮⢱⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢫⣶⡜⣿⣿⣅⣸⠃⣴⡟⠍⣦⢹⣧
⠀⠀⠀⠀⣼⢱⠋⠿⠗⠈⢧⠿⣣⢋⡞⣶⠆⠀⠀⢱⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⢴⣇⣂⣿⣜⢇⡼⢁⣼⡋⣹⣿⣿⡧⣻⡇
⠀⠀⠀⠀⣧⣾⠤⠤⠤⡤⠬⣷⡧⠬⠭⠭⠭⢭⢭⡍⠉⠀⠀⠀⠀⠀⠀⠀⢘⡃⣛⣛⣛⣛⣛⡊⢁⣈⣉⣉⣉⣉⢉⡁⠉⠁
⠀⠀⠀⠀⢷⢹⠀⢀⡘⠟⡼⣡⣷⡀⠀⣶⠄⡼⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⢿⣿⢿⣤⠟⡼⠇⢻⣿⡋⢻⠟⣼⠇
⠀⠀⠀⠀⠈⢯⡳⡝⢋⡜⡡⡍⠁⠹⡔⢀⡼⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⠳⣤⢏⡞⡳⣶⣧⡹⡿⢟⣼⠟
⠀⠀⠀⠀⠀⠀⠙⢯⣟⠦⠽⢧⣤⠴⣻⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢢⣜⣓⣒⠿⣛⣧⡰⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠛⠛⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠦⢤⣴⣼⠋⠉⠙⠒⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠙⠻⠦⣄⡀⢈⡉⠓⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⣚⣿⣿⡿⣿⣿⡦⠀⠀⡆⠀⠀⠀⣀⡆⠀⠈⠙⢿⡄⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠾⠛⠛⠛⠻⠂⠛⠋⠁⠀⠀⠙⠂⢐⢉⣉⣀⣀⠀⣴⣄⠙⠶⣶⣯⠀⠈⢢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠂⠀⢰⠀⠀⠀⡾⢸⠀⡟⣿⠿⣿⣦⡀⠀⠀⠀⠛⢦⣶⣿⢿
⠀⠀⠀⠀⠀⠀⣠⣯⢿⡿⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⠄⠀⢀⡤⡈⠐⠀⠿⠿⠶⠒⠛⠁⠀⣠⠤⣖⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠼⠛⠛⠉⠀⠐⠯⠗⠠⠠⠄⠉⣉⠉⢉⠉⢀⡀⠀⣀⠉⢁⣠⣤⡤⠴⠂⠉⠭⠯⠟⠓⠛⠉⠉
⠀⠀⠀⡠⠀⠀⠀⠀⣈⡥⠦⠖⠚⠛⠣⠀⠈⠉⠉⠉⠉⠉⠁⠘⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠐⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠂



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⡠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⠀⠉⠉⠙⠊⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠲⡄⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠀⠀⠀⠀⢠⠰⠌⡡⠃⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠅⠾⠃⠀⠀⠤⠒⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡙⠂⠀⠀⠴⠶⠶⣤⡀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢹⠀⠀⠐⠀⠀⠀⠀⠀⠠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⠞⠀⠀⠀⠈⢰⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠈⠁⠀⠀⠀⠀⠀⠸⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⡀⠀⠀⠀⠐⢒⠲⡄⠀⠀⢀⡤⣶⠄⠀⠀⠀⠀⠠⠀⠀⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠆⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⢰⣘⣊⠀⠀⠀⣖⣩⠴⠋⠀⠀⠄⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⡀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠘⠂⠀⠀⢉⡁⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢤⡐⠎⡀⠀⠀⢀⠀⠀⠀⠀⠀⣠⢏⡴⠃⠀⠀⢀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠲⢤⠀⠀⠈⠙⠉⠀⠀⢀⣀⣀⣀⣀⠀⠀⠈⠋⠀⣀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣧⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠓⠤⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡾⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣥⡀⠀⡾⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⡴⠤⠴⠞⠉⠀⠀⠁⠀⡇⠀⢀⡴⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠤⡲⡄⠀⠘⠊⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠘⢜⡣⠂⡀⠀⠀⡀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤
⠀⠀⠀⠁⠴⠾⠃⠁

⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⡶⠶⠞⠛⠛⠛⠉⠀⠀⢀⣀⣀⣀⡈⠉⠉⠉⠯⠿⢿⣗⡲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠛⠉⠁⠁⠀⠀⠠⠖⠒⠲⠭⠁⠀⠀⢄⡀⠀⠈⣉⣉⣐⠂⠤⠤⠀⡀⠀⠉⡓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠸⣀⣀⠴⠋⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠾⣯⠹⠿⣟⢶⡀⠈⠀⠀⠈⠙⣨⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠏⠇⠀⠀⠀⢀⣀⣀⣀⣀⡀⠁⠄⠀⠀⠒⢊⣼⠉⢀⡐⣿⠆⠘⠈⠱⣏⡄⠀⠀⠀⢦⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢀⠐⡝⠦⠷⠒⠬⠓⠨⡀⠇⡘⠂⠂⣀⠺⡗⠂⢫⡄⠁⠠⣖⡄⠀⠘⣿⢀⡀⠀⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠆⠀⠁⠀⠄⠠⠘⡈⢓⡖⡥⠤⠄⠀⠁⣼⠄⠠⠈⠀⠀⠉⢀⢀⠀⡟⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⢄⠀⠁⠀⠀⠉⠀⠊⠄⠁⠀⠀⠀⠈⢄⠀⠀⠀⠐⠀⠀⠘⠚⠰⠇⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡔⠩⠄⢀⠑⠦⣄⣐⣀⣀⣰⠃⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣔⢠⡖⠉⢉⡐⣷⣤⡀⠨⡠⣀⡠⠠⠀⠀⣀⡈⠉⠉⠅⢀⢴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⢟⡂⢀⡛⠀⠁⢙⡀⠈⠀⠀⠀⠀⠠⠀⢤⣤⢢⣀⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡱⣆⠁⣀⡰⣻⡶⠄⠀⠀⣀⠨⣄⣀⣘⡠⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⢲⠿⠚⡈⡀⢈⠁⠀⣠⡏⠉⠋⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡁⣼⢳⣬⠉⠉⠤⠀⠀⣿⠖⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡹⠟⠋⠀⠀⠀⡀⠀⢻⡍⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢈⠉⠻⢢⠈⢑⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⡀⠊⠒⠀⠈⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠶⠶⠶⠶⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡛⠛⠛⠿⠓⠦⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡾⢿⠾⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⣶⣶⣿⣷⣶⣶⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠿⠿⡃⠀⠀⠀⢀⣠⣤⣀⣉⣶⣶⣶⡶⠾⠛⠋⠉⠉⠉⠉⢻⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠁⠀⠀⠀⢀⣠⣶⣤⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠻⣷⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢁⠀⠀⠀⠠⣄⠀⣀⣸⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠈⠳⠘⢻⣦
⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠁⠀⠀⠀⢠⣶⣾⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⢀⣤⠞⠛⠉⠀⠀⠀⠀⢢⣤⣉⠙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⣠⣾⣿⣿⣶⣶⣀⠀⠀⠈⠉⠉⠛⢻⣟⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠘⢿⣧
⣼⣿⡍⠉⠁⠀⠀⠈⠉⠛⠻⠿⣶⠶⠿⣿⣿⣦⣄⡀⠀⠀⠠⢄⡀⠀⠀⠀⡀⠈⠑⢦⡀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⡄
⠉⠻⢿⣶⣤⡀⠀⣶⣤⣦⣤⣄⡈⠑⠂⠀⠉⠙⠻⣿⣷⣄⠑⢦⡙⠲⣄⣀⠈⠂⢄⡀⠈⠲⣄⠀⠀⠈⠙⢷⣤⡈⠢⣄⠰⣄⠀⠀⠐⠘⣿⡆
⠀⠀⠀⠉⢿⣷⡀⠸⣿⣿⣿⠿⣿⣿⣾⣶⣤⣄⠀⠀⠙⠻⢿⣦⣍⣳⣤⡙⠳⣤⣤⠉⠳⣤⡈⠓⢷⣄⠀⠀⠙⢿⡦⠈⠓⠌⠑⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠈⢿⣧⠀⢻⣿⣿⣤⣿⣿⣿⣿⣙⣿⣿⣿⣷⣶⣤⣈⡉⢉⠉⠛⢷⣬⣿⣿⣿⣦⣿⣶⣤⡈⠻⣦⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠘⣿⡄⠀⢻⣿⣿⣿⣧⣄⣼⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣅⡀⠀⠈⠙⠛⠿⠿⠿⢿⣿⣿⣿⣆⠹⣄⠀⠀⠁⠀⠳⣄⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⣿⣿⣽⣿⣿⣿⢿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠈⠙⠻⠿⣿⣷⡘⣷⣤⠰⡘⢷⡑⢄⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠸⣿⣿⠿⢿⣷⣴⣿⠻⣧⣼⣿⣶⣿⣤⡿⠋⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⡀⠀⠈⠙⠻⠿⣷⣾⣦⣿⣌⠳⡄⠱⣄⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢻⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⠉⣻⣿⣿⣶⣿⣷⣾⡿⠛⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠉⠙⠻⢿⣧⡙⣆⣘⣆⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣿⣿⣿⡃⣰⣿⣿⣀⣸⣿⣿⡟⠉⣻⣿⣿⣿⣿⣷⣦⣿⣿⣦⣠⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣄⣀⠀⠁⠘⠿⢿⣷⣌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣌⠉⠙⠛⠿⢿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⠋⢙⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣤⣴⣿⣇⣠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣷⣦⣄⣀⠈⠉⠛⠻⠿⠿⠿⢿⣿⣿⣷⣾⣿⣿⡟⠛⢻⣿⣿⣷⣴⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣶⣤⣤⣄⣀⣀⠀⠉⠉⠛⠛⠿⣿⣶⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⡁⢰⣿⣿⡉⣹⣿⣿⣀⣼⣏⣈⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣶⣦⣤⣀⡀⠀⠈⠙⠿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣦⣤⣀⠈⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣏⣁⣽⣿⣿⣿⠋⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢷⣶⣤⣀⡀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣧⣠⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣄⣀⠀⠀⠉⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⣤⣤⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠋⠉⠃⠀⠂⠀⠠⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣀⡀⠀⠀⣀⡀⠠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡀⠒⢄⡀⠀⡜⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⡀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⢿⡀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⠀⠄⢈⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠉⠙⠓⠀⠠⠤⠀⠐⠀⠀⠀⠉⢁⣀⣤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠐⠀⢤⡤⠀⠤⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣤⡴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡰⠟⠉⠀⠀⠀⠀⠀⢀⣀⣠⠶⠄⠀⠀⣉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢠⠜⠉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠐⠒⠉⢁⣠⣤⠶⠞⠉
⠀⠀⠀⠀⣰⠏⠀⠀⠀⢞⣀⣤⠤⠖⠋⠁⣀⣤⠴⠶⠋⠉⠁
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠉⢉⣀⠴⠖⠋⠉⠁
⠀⠀⠰⢆⠁⡀⠀⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠉⠉⠐⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣃⡀⠰⠶⠠⠞⠀⠈⠙⠶⠛⠂⢀⠄⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠙⠛⠓⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢣⣌⠀⣈⡄⠀⠀⠠⠄⢀⠀⠀⠴⠈⠈⠠⠤⠘⣛⠛⠓⠶⠤⠤⢀⣀⣀⣀⠀⠀⠀⢠⠄⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠾⠃⠀⠈⠋⠡⠄⠐⡄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠒⠓⠀⠉⠉⢩⠑⠠⠄⣦⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⣈⠓⣴⠊⠀⠀⠠⣄⢀⡠⢤⠠⣄⠀⠈⠀⠈⠑⢂⡴⠦⠤⠄⠀⡹⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠠⠀⠒⢦⣄⡀⠀⣀⠉⠀⠈⠁⠀⠀⠀⠈⠀⡐⣶⠓⠂⠀⢀⡰⠤⠚⠀⠀⠀⠀⢀⣠⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠅⠀⣀⡄⠀⠌⠀⠀⢘⡩⠿⠿⠆⠀⠀⠀⠐⠂⠤⠄⠂⠁⠈⠁⢚⣦⠄⠁⠂⢀⣤⡴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⢠⡬⠃⠀⠀⢠⡴⠊⠀⠀⠘⠀⠰⠶⠀⡈⠀⠀⠀⠀⢀⣀⡄⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠉⠠⠀⠂⠀⠀⡠⠂⠀⢈⠀⠀⢀⡀⠀⠀⠘⠃⠀⠐⠓⠀⡀⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠙⠒⠀⢁⣤⡴⠂⠈
⠀⠀⠀⠀⠀⡴⠃⠀⢀⡀⢀⠽⠂⠀⠀⠀⠀⠀⠈⣀⣤⠴⠖⠋⠉
⠀⠀⠀⢀⠞⢡⡄⠒⢉⡉⠲⠀⠈⣁⣤⠴⠖⠊⠉
⠀⠀⢴⠁⠀⠀⠈⢀⣀⠀⠔⠛⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠄⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⣀⣀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠒⠀⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢈⡉⠁⠘⠂⠠⠄⠀⠠⠤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡘⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠁⠒⠈⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⢿⡀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠑⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠔⠚⠉⠀⠈⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠉⠁⠀⠀⢀⣀⣤⠔⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣇⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠒⠈⠁⠀⠐⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⢤⡤⠖⠀⢀⣤⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡤⠀⠀⢀⠀⠂⠀⢉⡀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢀⡀⠀⠲⠄⠀⠀⠀⠉⣀⣤⠶⠊⠉
⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠲⣤⡄⠗⠀⠉⣀⣠⠴⠖⠋⠋
⠀⠀⠀⠜⠁⠀⠀⠀⠀⠈⢁⣀⠴⠶⠛⠋⠁
⠀⠀⠰⢄⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠡⣄⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠚⠠⠶⣿⠿⠿⣷⠦⡀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡋⢠⡀⠨⣀⠀⠀⠠⠈⠑⡄⠀⠱⡌⢂⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⢠⣼⠏⠀⠀⠀⠀⠀⢀⣵⠆⠀⠪⡖⠘⡀⠀⢘⡀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⢈⠔⠁⠐⣿⡿⢀⡐⣆⣀⠀⠀⠙⠿⠃⢠⣾⡿⠞⠀⠀⠸⢀⠇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠈⠀⠀⠀⠄⠏⠀⠀⠀⢻⣿⡐⠌⠿⠟⠁⠀⣀⡤⠶⡛⠄⠀⣀⣠⣴⡷⠃⠘⠀⠀⠀⠀⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣀⡡⠐⠀⠀⠒⠒⠤⡁⠀⡄⠀⣾⠿⡟⣧⣡⣤⣤⠶⠾⠋⠉⠀⠀⠈⠛⠛⠟⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠽⣿⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠈⢆⠈⠂⠤⠐⣡⡼⣿⠛⠛⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠠⠀⠈⠹⣧⣤⣶⣿⣿⣿⣿⣷⠄⣿⠿⠆⠀⠀⠀⢀⠸⠀⠀⣠⠎⠀⠛⠛⠀⠀⠀⠙⠁⠀⢙⣆⣀⠠⠤⠴⠋⠳⠤⣀⢂⣍⣟⡆⠀⠀⠀⠀⡇
⠀⠠⠃⠀⠀⠀⠀⠈⠻⠿⣿⣿⡿⠋⠴⠊⠀⡠⢶⣶⠄⠀⠀⠄⠀⢠⡏⠀⠀⠀⠀⣎⠶⠀⠀⠀⣰⠟⠉⠀⠀⠀⢀⣴⣶⣦⣌⣿⣿⣿⡿⠀⠀⠀⢀⠃
⠀⠈⢦⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠴⠋⠀⠀⠄⡤⠴⠂⠀⠀⠀⢷⡀⢤⡤⠀⠀⣀⠠⣴⣿⢃⡤⠋⠁⠙⠒⠺⢿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠀⠸
⠀⠀⡄⢀⣠⡴⠶⠶⣦⡀⠀⢀⣠⣤⣤⣠⣤⣤⣄⠒⠒⠂⠀⠤⠄⠀⠈⠙⢷⣤⣄⣀⣀⣀⣾⣿⣼⣆⠀⠀⠠⠀⠐⠂⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⡖
⠀⠀⠙⢏⠁⠀⠀⣀⣀⡙⣖⣉⣁⣀⣀⠀⠀⠀⢻⣄⣰⠟⠛⠛⠛⠻⣷⣀⣤⣤⣤⠉⠉⢉⣁⣘⠿⠟⠁⠄⠀⠀⠀⢀⣤⡶⠶⠒⠶⣦⡄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠉⠡⠤⠤⠄⢀⡀⠀⠀⠀⠐⢿⡀⢠⡿⠉⠉⠉⠙⠉⠙⠶⣤⡴⠋⠀⠁⠀⠀⠀⠈⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⣀⠤⠤⠤⠄⣤⡤⠤⠤⠒⠒⠀⠉⠉⠑⠒⢤⠀⠤⠤⠒⠚⠉⠉⠉⠓⠒⠤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠳⣄⣀⣀⡀⠀⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡐⠠⣄⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⢏⠏
⠀⠀⠀⠀⠀⠀⠀⡧⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠈⠑⢦⠀⠀⠀⠀⡤⠒⠒⠒⢤⡎⡞
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠄⠐⠘⡄⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠁⢈⡇⠀⠀⢸⠀⠀⢀⠁⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⣠⠞⠀⠀⠀⠘⢄⠀⠀⡸⡽
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠉⠀⢀⠔⠂⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣆⠀⠀⠀⠀⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⠦⣀⠀⢀⡠⠃⠀⠀⠀⢀⠤⠒⠒⠦⡀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⢹⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠂⣀⠞⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡠⠚⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⡌⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡄⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠙⠤⣀⡠⠞⠀⠀⡠⠴⠶⢤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡞⠀⠁⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠱⣄⠀⢰⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠉⠹⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡞⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⠔⠚⣉⠱⠒⢂⠀⠀⠀⠒⠒⠖⣉⠉⠀⢀⠇⠀⠀⠀⠀⠀⠈
⡶⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠊⠉⠁⠀⠀⠀⠀⠄⠠⠊⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠃⠀⢸⠁
⠳⣌⠑⢄⠉⠉⠉⠀⠀⠘⠉⠀⠀⠀⠀⣀⠄⠒⠈⠅⠀⡀⢌⡣⠐⠠⡀⠀⠀⠁⠈⠠⠤⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸
⠀⠈⠳⡄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⠡⠔⠂⠀⠀⠰⠠⠕⠈⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⠢⣄⠉⠢⢄⡀⠀⠀⠂⠀⠘⢦⠄⠀⠀⠀⠀⠀⠐⡀⢀⠠⠃⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠉⠢⣄⠉⠉⠑⠢⢤⡀⠀⠀⠀⠈⠁⠐⠀⠈⠀⢀⡠⠔⠊⠉⢁⡀⡀⠠⠀⠄⠈⠉⠑⠲⣄⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠈⠑⠢⣄⠀⠀⢠⠀⠀⢠⠎⢀⠀⠀⠀⠈⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠑⠦⡀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⡿⠀⠀⣠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠈⠑⠤⡀⠙⠭⣒⠤⢄⣈⣀⣀⣀⣁⣀⡤⠄⣒⠭⠊⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠈⠑⠒⠤⢉⡑⠒⠒⠒⠂⠐⠒⠉⠁⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⡀⠀⠀⠉⠑⠤⣀⠀⠐⠈⢀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠉⠑⠰⠓⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⡼⠀⣀⠔⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣤⣤⣞⣂⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠁⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡀⠈⠀⠀⠀⠀⡠⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣀⠠⠞⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⢀⡀⢀⠀⠀⣀⣀⠠⠤⠀⠀⠀⠀⠉⠈⠃⠀⢀⠀⠀⠓⠉⠀⠀⡆⠀⠀⠀⠀⢠
⠨⡙⢄⡂⠀⠤⠤⠀⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠰⠀⠀⠀⠀⠀⢸
⠀⠈⠢⡀⠠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠤⠤⠀⠄⠂⠀⠁⠀⡠⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠢⢌⠀⠄⠀⠀⠀⠈⠃⠀⣀⡀⠀⢀⠠⠀⠊⠀⣀⡀⠠⠤⠤⠀⠀⡀⠀⠀⠀⠀⠐⠀⢀⠊⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠁⠂⠀⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⡀⠈⠑⠄⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠄⡈⠂⠄⡙⠠⢀⡄⠀⠄⠀⠄⠠⣀⠂⠙⣁⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⢀⠀⠀⠐⠄⢉⠀⠁⠈⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢰⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⠀⠀⠀⠈⠒⠄⡀⠀⠁⠒⠀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢠⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⢀⡌⠄⠊⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠰⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠠⠀⠀⠠⠈⠀⠉⠢⠀⠀⠀⠄⠀⢀⠐⠂⡐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣴⠆⡠⠀⠀⠁⠀⡀⠀⠀⠀⠀⠗⠀⢄⡀⠈⢀⠀⠰⠱⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠌⠀⠐⠀⠞⠀⠀⠘⣷⠀⠀⢠⡀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠄⠘⠐⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢥⢀⠠⠴⠁⠀⢀⢐⡣⡈⠀⠀⠈⠀⠀⠀⠀⡀⠀⠔
⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠄⠂⠀⢸⠀⢠⣅⡀⠀⠀⠀⠀⠀⠰⢃⠌⡔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠓⠀⢠⠀⠀⠈⢁⠈⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣠⢤⢢⣤⣬⠀⡀⠂⠀⠀⡀⠀⠀⠉⠀⠢⠀⠠⠊⠜⢁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⣈⠠⣀⠁⠀⠀⢀⠈⠁⠠⠀⠀⠀⠈⠈⠀⠤⠀⠂⠐⠀⠈⠠⠤⠂⠠⠄⠤⠠⠄⠤⠤⠤⠤⠤⠴⠂⠀⠠⣀
⠀⠀⠀⠂⠐⠂⠀⠐⠂⠒⠀⠲⡂⡰⢲⣰⡒⡖⠀⠀⠀⠀⠀⠀⡀⢂⠀⠈⠈⠁⠂⠀⠀⠉⠀⠀⠀⠉⠉⡉⠁⠀⠊⠀⠃
⠀⠀⠀⠀⠀⠀⠴⢮⡉⣶⣄⠀⠀⠁⠐⠛⠉⠀⠀⠀⢀⠀⠀⠀⠘⠄⢣⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⠀⠐⠠
⠀⠀⠀⠀⠀⢀⢘⣙⠽⢥⣼⡇⠀⢀⠀⣀⠀⠀⠠⡄⠁⡈⠠⠋⢠⠈⢆⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠁⡄
⠀⠀⠀⠀⡀⠙⠾⠹⢲⡆⠘⠃⠀⠀⢠⣯⣝⣹⡏⠀⡘⠁⠐⠗⠈⡁⠀⢃⠠⡀⠐⠀⠁⠀⢠⠀⠀⠈⠀⠀⠄⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⢀⡀⠀⠸⣼⣼⡿⠀⠌⠀⠀⠀⠀⠈⠉⠀⠈⢢⠑⡀⠀⠀⠐⠈⢀⠀⠀⠄⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠠⠀⠀⠀⠠⠀⠀⠀⠖⠈⠂⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠄⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠑⠀⠐⠂⠐⠀⠄⠀⠸⠀⠀⢀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⡐⠁⠀⠀⢊⠀⠀⠀⠀⠄⠀⡀⠲⠀⢄⠀⠀⠻⡌⠆⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠈⠔⠃⠀⠀⠀⠢⠐⠀⠀⠄⠈⠁⠀⠀⠈⠁⠀⠀⠈⠄⢂⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠈⠀⠁⠒⠈⠀⠔⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠉⠛⠒⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡷⣄⡀⡀⠀⠀⠀⠀⠈⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢈⡛⠿⠷⠷⣧⣠⠀⡀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠰⠥⠃⠀⠀⠀⠈⣝⠳⠷⠦⣥⣠⡠⣀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣠⣤⣤⡤⠤⣌⡁⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡴⠋⠊⠁⠀⠈⠉⠒⠙⢦⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢸⡇⣀⠤⢤⠀⠀⡴⠶⢤⡼⠀⠀⢠⢖⡦⠘⢮⡰⣠⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⣀⠀⠀⠛⠗⠚⡾⠀⠀⣿⠛⠋⠁⠀⠀⠀⠁⠀⠀⠀⠙⢮⣓⠂⢤⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⡌⢳⡀⠀⠀⢰⡁⣀⣀⢈⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠈⠉⠓⢦⡴⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠒⠛⠀⡇⠀⠀⠀⠙⠒⠛⠋⠀⠀⢀⡤⢂⠍⠀⠀⠀⠀⠈⠉⠛⢦⡄⠀⠳⡗⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠰⠧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠒⠁⠀⠀⠀⠀⠀⠁⠀⠹⡆⠀⣸⠄⠸
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠠⡀⠀⠀⣠⠃⠀⠀⠀⠤⠴⠀⠀⠀⡎⠀⠀⣠⡀⠀⠀⠀⢰⠁⢀⠄⠀⠀⢿⢰⡗
⠀⠀⠀⠀⠀⠀⣰⠃⠳⠖⢃⡠⠖⠁⣠⠤⣀⣀⠀⠀⠀⠀⠸⡇⠀⠀⡀⠀⠀⢀⡀⠀⠉⠁⠀⠀⠀⡾⣸⡤
⠀⠀⠀⠀⠀⣰⠛⠒⠂⡽⠛⣖⣄⢸⡄⠉⠉⠙⣻⠀⠀⠀⠀⢷⡔⢉⠄⠀⠐⠒⠃⠀⠀⠰⡅⢀⣴⠃⡿⣿
⠀⠀⠀⠀⣰⠃⠀⠀⠐⣇⠀⠻⠿⠟⠀⢀⡞⡉⠁⠀⠀⢀⠀⠈⢿⣥⡂⠀⠀⠀⠀⠀⢀⣀⣤⠞⠁⢰⣧⠿⢶⢦
⠀⠀⠀⢠⠃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⠿⠿⣧⠀⠀⠈⠀⠀⠀⠉⠛⠛⠓⠒⠚⠛⠋⢉⣀⣀⣠⡾⠑⠀⠆⠮
⠀⠀⢠⠏⠀⣠⠄⢄⠀⠈⠳⣤⣀⠀⠀⠠⣂⡴⠃⠀⢀⣀⣀⣤⣤⣤⣶⣶⢶⠾⠿⠻⠛⠟⠙⠁⠁⠀⠀⣀⣀⣀
⠀⢀⠏⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⣉⣩⣭⣵⣶⣿⢿⠿⠻⠛⠋⢋⣈⣀⣡⣤⡤⠤⠶⠶⠒⠚⠛⠛⠉⠉⠉⠉⠉
⢀⡞⠀⠀⠀⢀⣀⣠⢤⠴⠖⠚⠛⢋⣙⣁⣠⣥⠤⠶⠖⠒⠛⠋⠉⠉⠁
⣾⡄⠒⣊⣉⣩⣥⠥⠴⠶⠒⠛⠋⠉⠉
⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣧⣤⣿⣙⡐⠲⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠙⠒⠲⢤⣷⣠⣾⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠀⠀⠀⠀⢠⣄⡀⠀⠀⠈⠉⠙⠷⢿⡅⠈⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⢀⣤⣴⡾⠛⢿⣿⣟⣷⣆⣘⠁⠀⠀⠈⠛⢿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢁⡤⢬⣿⣿⣟⠛⣿⣛⣿⣿⣿⣏⣀⣀⣠⡀⠀⠀⠈⠻⣴⣷⡞⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⡿⠻⣶⣦⡀⠀⠀⠈⠳⣶⡏⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⡌⠣⣤⡀⠀⢀⣿⢿⣟⣹⣿⣧⣀⠀⠀⣿⣿⣷⣶⣿⣿⣿⠂⢀⠀⠀⣸⠿⠟⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣿⣷⠀⠈⠙⠳⣾⣷⣿⣿⣿⣷⣾⣿⣧⣤⣿⣿⣿⣿⣿⣿⡟⠀⠈⣱⠆⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣻⣿⣿⣏⠀⠀⢀⣠⣿⣿⡈⢿⣿⣿⣿⣿⣿⣧⠤⠝⠓⠟⠛⠛⢓⡴⠂⠡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠟⠛⠛⠛⠉⠁⠀⠛⠍⡛⣿⣿⣿⣿⣿⡿⠿⠿⢦⠀⠀⣀⠤⠆⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣤⡤⣶⣾⣷⣶⣦⠀⠉⠁⠉⠉⠀⠀⠀⢀⣠⠃⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣣⠀⠀⢀⣀⣼⣿⣿⣿⣤⣿⣿⣿⣆⠀⠀⠀⠀⣀⠶⠛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣶⣶⣦⣀⠉⣿⣏⣹⣿⣿⣿⣿⣛⣀⡤⠐⠈⠡⠂
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡙⣿⣿⣶⡼⠿⢿⣿⣿⡿⠏⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⣽⣿⣿⣿⠿⠿⠗⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠠⢪⡞⣡⣶⡏⣸⢁⣨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣭⠴⠒⣛⣛⣛⣂⠀⠀⠀⠠⢏⣾⣿⣿⡇⠋⣈⣤⣤⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣡⣴⠾⠟⠛⠛⠛⠛⠻⠷⣶⣄⣸⣿⣿⣿⣣⣾⣿⣿⡏⡾⠀⢀⣀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⣏⠁⠀⠀⠀⠀⣴⣦⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⢷⣇⣤⣭⣭⣶⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⡿⠛⠀⠀⠀⠀⠼⠛⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢟⡿⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⣦⣀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣟⣷⠟⣡⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣸⡿⠏⠀⠀⠀⢰⣿⣷⢸⣿⣿⣧⡀⠀⣾⣿⣿⣿⣻⣿⣯⣥⣤⣀⡀⠀⢤⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠐⠛⠋⠋⢸⣿⣿⣿⣷⠀⣿⣿⣿⡿⠿⠛⠛⠛⠛⠿⣿⣦⣄⠉⠢⡹⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⣿⡿⠀⠀⠀⣴⣦⡄⣦⣀⠀⠀⢀⣿⣿⣿⣿⣿⣇⡿⠋⡡⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠙⣎⠆
⠀⠀⠀⠀⢀⡎⢠⣿⠁⠀⠉⠉⠀⠀⠀⠰⠿⠛⠁⠹⣿⣷⣶⣬⣍⣉⣙⣻⣿⣟⣄⠈⡄⢀⠀⠀⠁⠀⠀⠄⠀⠀⠘⢿⣷⡀⠘⡆
⠀⠀⠀⢀⡞⢀⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡿⠿⠛⠁⡃⠀⣤⡉⠲⠤⣄⣀⠀⡀⠀⠀⠀⠠⠀⠈⢿⣷⡀⠘
⠀⠀⠀⣾⡇⣸⣿⣿⠇⢠⡿⠗⠀⠀⢀⣤⡄⠀⠀⠈⣿⣿⠟⠋⠀⠂⠘⠃⡇⠻⣿⣷⣄⠀⠸⣍⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠻⡇⣿⡏⠁⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠀⢸⣿⠃⠀⠀⠠⠀⠀⡄⢄⠀⠙⢿⣿⣄⠀⠈⡟⠗⠀⠀⡀⠀⠀⠀⠀⢹⣿⡄⢠
⠀⠀⠀⠀⣇⢹⣧⢠⣿⡷⢀⣤⣶⠀⠀⠀⢀⣀⡀⣿⣿⠀⠀⠀⠀⠀⢠⠀⣀⢇⠀⠀⢻⣿⣧⠀⢳⠃⠐⠃⠀⠀⠀⠀⠘⠀⣿⣧⠈⡇
⠀⠀⠀⠀⠘⠈⢿⣆⠁⠀⠈⠛⠉⠀⠀⠰⠿⠿⠃⢻⣿⡀⠀⠐⠊⠀⠀⠀⠁⠀⡑⢆⠀⠻⣿⣇⠀⡄⠶⠀⠁⠀⡀⠀⠀⠀⣿⣿⠀⣿⢳
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣾⠿⠆⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠓⢄⡈⠻⣆⠡⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠸⠂⣀⠘⠁⢈⡲⣝⠆⢃⠰⠆⠀⠀⢀⠀⠀⣿⣿⠀⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠤⣍⣉⣉⣉⣀⣀⠀⠙⣿⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⡂⣀⠀⠀⠀⠐⢀⣿⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠀⠀⠀⠈⠻⣿⣦⣄⠀⠈⠀⠀⢀⠀⠀⠀⠛⠁⠀⠆⢉⢉⠀⠀⠀⠀⣼⣿⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⣼⡿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣦⣤⣀⣀⠀⠀⡀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣉⠙⠛⠿⠿⢿⣿⣿⣷⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡉⠓⠢⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⠙⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠛⠛⠛⠁⠀⠐⠂⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⣠⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⡀⠀⠀⠀⢠⣶⣿⣿⣿⣶⡄⠀⠀⠙⢷⣄⣠⡾⠋⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠁⠀⠀⠀⠘⠿⣿⣿⣿⠿⠃⠀⠒⠀⢀⣹⣿⠇⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⢁⣀⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠋⠁⠀⠘⢿⣿⣿⣿⣿⣿⡶⢶⣄⠀⣠⣶⣤⣤⣾⠷⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠤⠀⠀⠀⠀⠀⢩⡿⢋⣀⣠⣴⣿⠀⣿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣾⠏⣠⣤⣤⣄⠀⠀⣠⣤⡀⠀⣿⠟⠛⠋⠉⠀⠻⠶⠟
⠀⠀⠀⠀⠀⠀⢸⣇⣘⣋⣤⣴⣿⡇⢸⡏⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⢸⡇⢸⡇⠈⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⡾⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠛⢦⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢀⡄⠉⠁⠀⠙⠛⠛⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠾⢷⡾⠃⣤⠀⠀⠀⣀⡀⠀⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⣀⡀⠀⠀⠙⠛⠛⠛⠟⠛⣦⠀⣀⡀⠀⠀⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⠉⠉⠙⠓⠀⠀⠶⣤⡄⠀⠀⠻⠞⠙⣧⣤⡶⠻⣦⠀⠀⠈⠙⠛⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣤⣀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠈⠉⣷⣀⡀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣄⡉⠻⠖⠀⠀⠀⢀⣀⠛⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⣠⠿⠃⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠙⢦⡀⠀⠛⣶⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠉⠀⠀⠀⠻⣦⠐⢿⣤⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⣀⣤⠶⠂⣠⡼⠃⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠞⠛⠋⠉⠁⣠⡾⠋⠀⣀⣠⣄⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠆⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡤⠶⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣤⠞⠋⠁⠈⠉
⠀⠀⠀⠀⠀⢠⡾⠁⠰⠄⠀⠃⠀⠀⠀⣀⣀⣠⣤⣤⡴⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣠⠟⠁
⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣤⠶⠞⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⠟⠁⢠⡾⠃
⠀⠀⠀⠀⠀⢻⡎⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⣀⠈⠀⠀⣠⡾⠁⢀⣴⠏
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣤⡾⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠓⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠛⠛⠛⠛⠋⠁⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠃⠀⠀⣀⣀⣀⣤⣤⣤⣤⠴⠶⠶⠞⠛⠋⠉⠀⢀⣀⣀⣀⣀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⣤⠶⠶⠶⠖⠛⠛⠋⠉⠉⠁⠀⢀⣀⣀⣠⣤⣤⡤⠶⠶⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠹⣦⣀⣀⣤⣤⣤⠤⠶⠶⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠈⠉⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠑⠁⠀⡀⣀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠀⢀⠀⠆⠘⠢⠑⣤⣄⠀⠀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠋⠀⠨⡆⠈⡇⠸⠀⡠⠔⢡⠁⡦⠀⠠⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡳⠀⢀⣤⠜⠈⢃⣛⣍⠤⠒⠁⣰⢍⡛⡙⢻⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢤⣠⡃⢀⣸⠀⢀⡼⣣⣄⣀⣤⠤⣔⡃⠿⠕⣁⡾⢇⡠⠒⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡷⢹⠛⢙⡎⣦⡏⠀⠀⠀⠀⠀⢘⠙⠒⠚⠋⢀⠞⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⣠⠛⠦⠦⠵⠚⠁⢧⣄⠀⠀⠀⣀⡼⡠⠤⠜⣁⣡⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠚⠷⠖⠙⣯⠁⠀⠀⠀⣀⠀⡠⠶⠄⠛⠛⢉⣈⠭⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢊⣀⡘⠆⡄⠀⢾⣁⠤⠂⡀⡜⣉⣚⡥⠤⠖⠒⠉⠁
⠀⠀⠀⠀⢀⠀⢀⠀⣠⢤⠤⠞⠒⣎⡠⠤⠒⠋⠉⠁
⠀⠀⠀⠀⠈⢁⡠⠊⣈⠥⠔⠊⠉
⠀⠀⠀⠐⠄⠠⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠙⠒⠲⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠛⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠙⠖⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⢀⢠⣀⠀⡀⡇⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠚⠓⠻⢾⣇⣡⠐⢀⣀⡀⠀⡸⠀⠀⡀⠀⠀⠀⠀⢀⡠⠈⠉⠙⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⠈⠉⠓⠮⠿⣿⣇⡇⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣉⣉⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢀⠔⢢⡀⠀⠉⠙⣤⡀⠟⡀⢠⢀⡏⠀⠀⠀⢀⡾⠋⠁⠀⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠐⡕⡄⠀⠈⠀⢹⣧⠀⠀⡞⠀⠈⠙⠷⣼⣸⡇⠐⠀⠀⡾⠀⠀⠠⠀⠐⠂⣀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠕⠀⠀⠀⠐⢐⡀⠀⡄⢸⡇⠀⠀⡇⠀⠀⠺⠆⠀⠉⠳⣇⣰⡀⡇⠀⠰⠒⠀⠐⠂⠉⠴⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢘⠃⠠⢸⠀⠀⠱⡘⢧⡀⠀⠱⡀⠀⠀⢎⡱⠀⢠⡈⠙⢷⣻⡄⠀⠀⠐⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠤⠃⠀⠯⠃⡸⠈⠀⠀⠀⢱⣢⠟⠀⠀⠱⣔⠠⣄⡀⠀⠈⠁⢀⣤⡽⠳⣄⠀⠀⠀⠈⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠠⣖⠁⠁⠐⠀⠀⠀⠀⠀⢀⠀⠀⠈⠑⠒⠞⠛⠛⠶⠒⠁⠀⠀⡬⢳⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠶⠖⠓⠊⠁⠀⠀⣀⣤⣴⠚⠛⢦⣀⠀⠀⠀⢀⡤⣄⣀⣀⣤⠴⢶⠀⠈⠀⢸⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⣒⣤⣄⣨⠃⠀⠀⠛⠢⣄⣌⣥⡄⠐⠟⢁⣤⠤⣋⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠠⣤⣤⡄⠀⠀⠀⠀⠁⠒⠉⠀⠉⠉⠁⣀⣤⡤⢤⣄⣀⠀⡠⠊⠀⠀⢸⣦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀⡀⠛⣄⠀⠘⡀⠀⠀⠀⠀⡠⠖⠋⢴⡶⠀⠀⠀⡈⠛⠁⠀⢀⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⠉⠙⠮⠤⠞⠀⠀⠃⠀⠀⢀⠞⠀⠀⣠⠀⠀⠰⣒⡾⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠒⢲⡆⠀⠀⢠⣤⣄⠀⠀⠀⢊⡀⠸⠇⠀⢐⡶⠋⠁⠀⣀⣺⡆⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠴⠒⠢⠃⠀⠐⣅⠀⠈⢷⣄⠀⠘⣇⠀⠀⠀⠈⡔⢢⣀⣠⠏⠀⢣⣄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠤⠤⠤⡀⠀⠀⠈⠆⠂⢈⣾⠀⠀⠙⣡⢊⠔⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠑⠈⢦⡀⠀⢰⣲⠝⠚⠀⢀⠞⠁⠸⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠤⡀⠈⠀⣧⠀⠈⠀⠀⠀⢀⣉⠀⠀⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢛⡁⠀⢸⡟⠀⠀⠀⠀⣰⠃⣸⣆⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡄⣄⠙⣡⣴⠟⠁⢀⢔⣀⡴⢃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠈⢕⣪⠔⠁⠀⠔⢡⡏⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠉⠉⠀⠀⠔⠆⠀⣼⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠔⣂⠤⠊⢀⡄⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠊⠁⢀⡴⠞⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠋⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠉⠙⠲⠦⢤⣀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⠔⠒⠲⠒⢄⠀⠀⠈⣧⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢧⣄⡄⢠⣶⡴⠀⠠⠐⠙⢄⡄⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠂⠀⠀⣁⣈⡇⠀⠀⠀⠀⠀⣀⡉⠒⢧⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠭⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢃⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⠆⢀⠄⠀⠀⠒⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⣷⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⢂⠒⣄⡈⠉⣑⠆⠀⠈⣇⠀⠀⠀⠀⠀⠀⣠⢿⣷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠘⡄⠉⠁⠸⠶⡄⠀⠀⠈⠳⠦⠤⠤⠖⢊⣁⡼⠉⠙⣯
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠘⠢⠤⣤⣖⣥⣤⡴⠶⠶⠚⣛⣋⣉⣩⠥⠤⠤⠤⠚
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠤⠤⣖⣚⣫⠭⠭⠔⠒⠒⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊⠉⠉