Candy crush Emojis & Symbols

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣩⣭⣍⢹⡏⢉⡭⢭⣍⢹⡏⢉⣭⣭⡉⢹⡏⣭⣭⣭⡍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣹⢾⡇⣿⠀⠀⣹⢾⡇⣿⠀⢈⡷⢸⡇⣿⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣛⣛⣋⣸⣇⣈⣓⣞⣋⣸⣇⣈⣛⣛⣁⣸⣆⣛⣛⣛⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡤⢤⡄⢸⡏⢀⡴⢦⡄⢸⡇⢀⡴⣤⠀⢹⡇⣤⠴⢤⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡀⢀⡿⢸⡇⢸⡇⢀⡗⢸⡇⣿⠀⢈⡷⢸⡇⣿⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣭⣭⣥⣼⣧⣤⣽⣯⣤⣼⣧⣬⣿⣯⣥⣼⣧⣭⣭⣭⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡶⠶⣶⢸⡇⢠⡶⠶⣄⢸⡇⢀⡴⢦⡀⢸⡇⣰⠶⢦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣇⣀⣻⢸⡇⢻⣄⣀⡿⢸⡇⣿⡀⢈⡗⢸⡇⢿⡀⣸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣭⣭⣭⣼⣧⣤⣭⣭⣤⣼⣧⣬⣭⣭⣤⣼⣧⣬⣭⣥⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡶⠒⣶⢸⡇⢀⡴⢷⡄⢸⡇⣶⠒⢲⡆⢸⠃⠰⠒⣶⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣇⣀⣿⢸⡇⢻⣄⣀⡿⢸⡇⣼⣀⣸⡇⢸⡅⢿⣀⣼⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠭⠭⠥⠼⠧⠤⠭⠭⠤⠼⠧⠤⠭⠥⠤⠼⠧⠤⠭⠥⠴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⢦⡀⠀⠀⢀⡴⠋⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢙⠦⠴⡋⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣇⠀⠀⣸⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣇⣀⡤⠖⢋⠏⠹⡙⠲⣤⣀⣸⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠔⠉⡠⢀⡰⠃⠀⠀⠘⢆⡀⠀⠉⠢⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⣀⣀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⣀⡹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡧⢄⢸⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢰⡧⡄⢹⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡏⠀⠀⢸⠀⢸⡄⡇⠀⠀⠀⠀⠀⡰⠋⢸⠀⠀⠀⣼⠀⢸⢸⠀⠀⢹⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣾⠀⠀⠀⢻⠀⢸⢸⠀⢀⠀⠀⠀⡰⠁⢠⠏⠀⠀⠀⣿⠀⡸⢸⠀⠀⠀⣷⠈⣧
⠀⠀⠀⠀⣠⠖⢋⠉⣧⣸⡇⠀⠀⠀⠘⣟⣡⠏⠀⠈⠢⣀⠀⠧⠔⠃⢀⡠⠂⠀⠸⣗⣡⠇⠀⠀⠀⢸⣇⣼⠍⡙⠲⣄
⠀⠀⣠⢊⡠⠊⠁⠀⡾⣹⠁⠀⠀⠠⠂⠉⠑⢄⠀⠀⠀⣏⠉⠙⠋⠉⡏⠀⠀⡠⠂⠉⠃⠄⠀⠀⠀⠈⣏⢷⡀⠈⠑⢄⠑⣄
⠀⣰⡣⠊⠀⠀⢀⡼⠁⡿⠀⠀⠀⠰⢀⣀⠀⠌⠀⠀⠀⠘⢄⣀⣀⠜⠁⠀⠀⠣⢀⡀⣀⠆⠀⠀⠀⠀⢿⠈⢯⣀⠀⠀⠑⢜⣆
⢠⡟⠀⠀⣠⡴⠋⠀⢰⡏⠓⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠚⢹⡆⠀⠙⢦⣄⠀⠀⢻
⠘⠧⢖⣫⠵⠒⠛⠉⡩⠛⠉⠳⡄⠀⠀⠉⠉⠉⠛⢛⡖⠒⢒⡶⢶⡒⠒⢲⡛⠛⠉⠉⠉⠀⠀⢠⠚⠉⠛⣍⠉⠙⠒⠮⣝⡲⠼
⠀⣰⠋⠀⠀⣀⣠⣤⣇⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⢸⡥⠞⡵⠊⠑⢮⠳⢬⡇⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣸⣤⣄⣀⠀⠀⠙⣆
⠀⠻⡄⢰⡋⠁⢠⡟⠈⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⢻⡄⠈⢙⡆⣠⠟
⠀⠀⣈⡷⠝⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠫⢾⣁
⣰⠋⠉⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠙
⠓⠒⠛⠛⠲⠤⣄⣀⠀⠀⠀⠠⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠑⠤⠔⠋⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠄⠀⠀⠀⣀⣠⠤⠶⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣤⣀⣀⠀⠉⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠊⠉⠉⠉⠉⠀⣀⣀⣤⠤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⢶⠶⡶⠶⠶⢶⠶⡶⠒⠒⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⢸⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⣿⠀⠀⣿⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣠⡤⠴⠚⠋⠁⠀⠀⠈⠙⠓⠦⢤⣄⣨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠛⠛⠛⠿⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠿⠿⠿⠿⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠰⠿⠿⠟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠙⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠋⠀⠀⠀⣾⣦⠀⠈⢻⣷⡀
⠀⠀⠀⠀⣼⡿⠋⠀⠈⠙⠻⣿⣦⣀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⢿⣧
⠀⠀⠀⣸⣿⠁⠀⠀⢀⠀⠀⠈⠙⢿⣷⣤⣿⣿⠀⠀⢸⣿⠀⠀⠀⠙⠃⠀⠀⠀⠀⠺⣷⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⣿⡇⠀⠀⠸⣿⡇⠀⠀⠀⠀⠙⠻⣿⣧⣄⠀⠘⠛⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠈⠉⠀⠀⣶⣶⣶⠄⠀⠀⣿
⠀⠀⠀⣿⣧⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣄⡀⠀⠀⠀⢸⡿⠃⠀⠀⠀⣠⣤⠀⠀⠈⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢸⣿⡄⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣤⣀⠀⠀⠀⠀⠰⣿⠏⠀⠀⠀⣀⡀⠀⠀⣸⡿
⠀⠀⠀⠀⢻⣿⡄⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣷⣦⣄⡀⠀⠀⠀⠰⡿⠿⠛⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠈⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⡄⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⣠⣴⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠁
⠀⣀⡀⠀⡀⠀⠀⠀⠀⢀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠳⢾⣅⣈⣷⠄⠀⠀⠀⠀⠀⣿⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢹⡏⠀⠀⢀⣠⣤⣤⣤⣇⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣸⠇⢀⣴⠟⠁⠀⠀⠈⠙⣷⡤⠴⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⠙⣷⣤⣤⣤⠶⢋⣴⠟⠙⠇⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠏⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⢷⣄⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⢷⣄⠀⠀⠀⠀⠀⠙⣷⠞⠁⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢷⣄⠀⠀⣠⠞⣁⣤⣤⣄⣼⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣇⠀⠀⠀⠀⠀⠉⣠⠞⢁⡾⠋⠀⠀⠀⠙⣷⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠋⠉⠉⠉⠙⢷⣤⣤⣤⡴⠞⠁⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⣤⠼⢷⣄⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢠⡟⠀⠀⠀⠀⠀⠀⠹⢦⣠⡏⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⣭⣭⣍⠉⣿⠉⣩⣭⣭⡉⢹⡏⢉⣭⣭⣍⠉⣿⢉⣭⣭⣭⡍⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⡆⣿⢸⣿⣿⣿⣿⢸⡇⣾⣿⣿⣿⡆⣿⠀⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠿⠿⠟⠀⣿⠈⠻⢿⠿⠋⢸⡇⠘⠿⠿⠟⠀⣿⠐⠿⠿⠿⠗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⣛⣛⠛⠛⣿⠛⢛⣛⡛⠛⢻⡟⠛⢛⣛⠛⠛⣿⠛⣛⣛⣛⡛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣿⣿⣷⡀⣿⠀⣾⣿⣿⡆⢸⡇⣰⣿⣿⣷⡀⣿⠈⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣿⣿⠟⠀⣿⠀⠻⣿⡿⠃⢸⡇⠻⣿⣿⡿⠁⣿⠠⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⣿⠶⠶⠶⠶⠶⢾⡷⠶⠶⠶⠶⠶⣿⠶⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⠆⣿⢀⣾⣿⣿⣆⢸⡇⢠⣾⣿⣦⠀⣿⠀⣾⣿⣷⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡄⣿⠘⣿⣿⣿⡟⢸⡇⢿⣿⣿⣿⠃⣿⠀⢿⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣬⣭⣭⣭⣤⣿⣤⣬⣭⣭⣤⣼⣧⣤⣭⣭⣥⣤⣿⣤⣬⣭⣥⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣶⣶⣶⡄⣿⠀⣠⣶⣦⡀⢸⡇⢴⣶⣶⣶⡆⣬⠀⣠⣴⣶⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⡀⣿⠰⣿⣿⣿⡷⢸⡇⢸⣿⣿⣿⠀⣿⠐⣾⣿⣾⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣘⣛⣛⣛⣁⣿⣀⣙⣛⣛⣁⣸⣇⣙⣛⣛⣋⣁⣿⣀⣘⣛⣋⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⡄⠀⢀⣴⡶⠀⠀⠀⢀⠂⠀⠀⠀⠀⣔⣀⠄⠀⠀⠀⠀⢀⢂⡀⠀⠀⠀⢰⡂⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣄⡀⠀⡀⠀⠀⠈⢉⣁⣄⣀⣀⢀⡄⠤⢀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣄⠀⠀⢠⡀⠀⣰⡀⠰⣀⢸⣿⠍⢽⡇⡾⠃⠂⠲⢘⣿⣿⣿⣿⣿⣾⡃⠀⢘⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡀⢀⣤⠞⣷⠀⠐⡃⠓⠉⢀⣀⡀⠘⣿⡆⣸⡷⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠗⠈⠈⣦⠀⠃⠒⠢⢟⣩⣁⠞⠙⠁⠈⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠑⡈⠶⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠛⠉⣸⣿⣿⣿⣿⡟⣿⣿⣿
⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡸⣿⣿⣄⠀⠀⢠⣿⣿⣿⡿⠏⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣾⣿⣿⡏⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⡄⠀⠀⠀⢲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿
⢠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⢿⠟⠀⠀⠀⠀⣾⣿⣿⣿
⠸⠱⠼⠻⠉⠁⠀⠀⠀⠀⠒⠂⠀⠀⣿⡇⡀⠀⠙⢣⡀⠀⢠⣀⠀⠀⠀⠄⣀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣤⠤⣄⠀⣀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⣄⣀⣀⣤⡀⣠⠞⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠌⣟⠉⠀⢹⣷⠞⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠟⢹⡶⢶⠛⢍⠛⢦⣸⡷⢦⣤⣀⠰⡆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡴⠚⡟⣰⢠⡟⠀⠀⠳⣬⣑⡀⢛⣃⣴⠟⠙⠷⣯⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣧⢀⡴⢯⣄⣚⣠⡵⠋⠀⠀⠀⠀⠀⠉⠉⠋⢉⣤⢤⣄⠀⠈⢳⣾⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢨⡟⠁⠀⠀⠀⠀⠀⠀⠀⡤⠚⠙⠲⣄⠀⠀⠘⠁⠀⠈⠳⡄⠀⢻⣆⡼⠁⠀⠀⣀⣤⠤⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠳⣦⡟⢀⡴⠶⣄⠀⠀⠀⠀⠘⢇⡀⠀⡠⠏⢀⣼⠁⠀⠀⠀⠀⠁⠀⠀⣿⠀⠀⣠⢞⠥⠖⠚⣩⢟⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡟⠀⡞⠁⠀⠈⠃⠀⠀⣦⣀⠀⢉⣉⣠⠴⠋⢹⢀⠤⠒⠤⠀⠁⠢⡀⣿⣄⣰⡏⠁⢀⡤⠊⣡⡾⠁
⠀⢀⣤⠴⠶⠶⠶⠦⣄⠀⠀⠀⠀⣼⠁⣠⠴⢒⣐⠦⡄⠀⠀⣿⠈⢹⠉⢩⡇⠀⠀⢸⢤⠠⡀⢀⡜⠀⢠⠇⣿⠆⢈⣽⡾⠵⠶⠟⠉
⠀⠻⣤⣀⠙⠒⠒⠦⣌⢳⣄⣀⣀⣿⠰⠁⠀⠁⡀⢙⢾⡆⠀⣿⣠⣤⡤⠾⠃⠀⠀⢸⠈⢧⣉⣁⣀⡴⠋⠀⣿⠴⠿⠛
⠀⠀⠙⢧⣍⠑⠒⠒⢚⣻⡏⠉⢺⡏⠀⠳⢄⣀⣀⣠⡾⠀⠀⢹⣤⣤⣤⡀⠀⠀⠀⢸⠀⠀⠹⢍⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠉⠛⠒⠚⠛⠻⢬⣶⢶⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠘⣇⠀⠇⠙⢧⡀⠀⣾⠀⠀⠀⠀⠙⠒⢒⣾⠿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠹⣆⠀⠀⠘⡇⣰⠇⠀⠀⣀⣠⡴⠞⡟⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⢀⡤⠒⢉⡴⠂⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⠴⢦⣤⡀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣤⣿⣯⡶⠞⠋⠉⠁⠀⢄⣷⡀⠀⠀⣼⠃⠉⠓⠶⠤⣤⣇⠀⠀⠀⢣⡘⠛⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠃⠀⠀⠀⢻⠖⠶⢶⠶⠶⠒⠛⠟⠛⣫⠯⣄⣀⣿⠀⠀⠀⡠⠊⠀⠙⠒⠻⢥⣤⣤⡤⠶⠖⠋⠡⡀⠀⣀⣤⡉⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡀⠀⠀⢀⡾⢠⣴⡁⠀⠀⠀⠀⢱⠄⠑⠓⠺⣝⢅⡀⡠⠎⠀⠀⢀⡔⠀⠀⠀⠀⠈⠳⢦⣄⣀⡀⠈⠉⠁
⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣠⠟⠉⠳⣦⠶⠛⣡⠋⠀⠉⠢⢀⠀⣠⠃⠀⠈⠒⠤⠚⢀⠜⠑⠤⣀⣠⠊⠀⠀⠀⠀⠀⠀⢀⣠⡼⠛⠁
⠀⠀⢸⣄⣉⡉⠉⠉⠙⣦⣞⣁⣤⠶⠟⠁⢀⡜⠁⠀⠀⠀⠀⠀⡽⢇⡀⠀⠀⠰⡏⡳⣦⠀⠀⠀⢠⠋⠑⠢⢄⣀⣠⣴⠞⠋⠁
⠀⠮⣀⡀⠀⠇⠀⠀⠀⢹⢹⠏⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠂⢄⣀⡟⠓⠋⠀⠀⣰⣁⣤⡴⠶⠛⠋⠉
⠀⠀⣇⣠⠞⢠⠖⠶⠚⠁⠻⠦⣤⣤⣴⣁⣀⣈⣂⣄⣀⣀⣎⣀⣠⣤⣤⣤⣤⠾⠿⠶⠺⡟⢻⠉⠉
⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⡸⡄⠀⠀⠀⢸⡇⢸⣠⡴⠖⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠾⡇⢳⡀⠀⠀⢸⠃⠘⠋⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠙⣦⠀⣟⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠖⠚⠛⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢰⡀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⢄⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡠⠀⠢⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣈⣀⡀
⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⠀⡟
⠀⠀⣰⠟⠁⠀⣀⡤⠶⠶⠶⠶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡝
⠀⣰⠏⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣸⡇⠀⢸⣇⣀⣀⣀⣀⣀⠀⠀⠀⡏⠀⠀⠀⢀⣼⡇
⠀⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠻⣤⣿⠉⠙⠋⠉⢻⡆⣠⠞⠋⠉⠉⠁⠀⢸⣿⠉⠙⣟⠉⠙⣯⠀⢰⣿⠃⢴⣶⠊⣻⣿
⠀⣿⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣶⡄⠀⢹⣿⠀⠀⣤⠀⠀⣿⠃⠀⣠⡴⢶⡆⠀⢸⣿⠀⠀⣿⠀⠀⣿⢀⣿⡿⠂⣄⣀⡉⠙⣿⣇
⠀⢹⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⡇⠀⢰⡏⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⣇⣼⣿⣧⡐⠿⠿⠿⢀⣾⣿⡄
⠀⠀⠹⣆⠀⠀⠙⠳⠦⣤⡤⠶⢿⡀⠀⢾⣿⠆⠀⢸⣿⠀⢸⣿⠀⠀⣷⠀⠀⠻⣤⣼⡇⠀⠸⣿⠀⠀⠏⠀⠀⣿⣿⣿⣿⠿⢓⣒⠻⢿⣿⣿⣷
⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⣈⣷⣀⠀⠀⢀⣀⠀⠀⠀⢸⣿⠀⢀⣟⠳⣄⡀⠀⠀⠀⣀⠀⢰⡀⠀⡀⠀⠀⣿⣿⣿⡏⠀⣸⣿⡇⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠀⠉⠛⠛⠋⠉⠙⠛⠛⢛⡿⠛⠉⠙⠷⠟⠉⠉⠻⣟⠉⠙⠛⠋⢛⡇⠀⢠⣿⣿⣿⣇⠀⢿⣿⡇⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⣾⣷⣦⣶⣿⡆⠀⣿⠀⠀⠀⢀⣼⠃⠀⣼⣿⣿⣿⡿⣶⣬⣭⣴⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠉⠁⠀⠉⠉⠛⠳⣤⣈⢷⡀⠻⣿⣿⣿⡿⠃⣰⠏⠀⣀⡴⠟⠁⢀⡼⠋⣿⣿⣿⣷⠀⢰⣶⡄⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡴⠶⠒⠲⠶⣤⣀⠀⠉⠻⠿⠦⠈⠛⠋⢠⠾⠷⠶⠛⠉⢀⡠⠖⢻⡇⠀⣿⣿⣿⣿⠀⢸⣿⡷⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠙⠓⠶⣤⣤⣤⣤⡴⢦⣤⣤⣤⠤⠶⠚⢻⡇⠀⢸⡇⠀⣿⣿⣿⡟⠀⠸⠟⣁⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⡷⣿⠛⠛⣿⠛⠛⣷⣰⠞⠋⠉⢻⡇⠀⠘⠛⠛⣿⣿⣿⣿⣿⠉⠹⡿⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⡇⠀⢠⣤⣼⡇⠀⢀⡄⠀⢸⣿⣿⣿⡟⣴⠀⠱⠆⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟⣿⠀⠀⣿⠀⠀⣿⢧⡀⠀⠹⣿⡇⠀⢸⡇⠀⢸⣿⣿⣿⢃⣭⡄⠀⢺⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠙⠳⢦⣤⣤⣤⢶⡇⠀⠀⡇⣿⠀⠀⡿⠀⠀⣿⠈⢻⡆⠀⠸⡇⠀⢸⡇⠀⢸⣿⣿⣶⣶⣿⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⢐⡇⠀⠀⡇⢿⡀⠀⠀⣀⠀⠉⠉⠉⠁⢀⣼⡇⠀⢸⡇⠀⢸⡿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠛⠛⠛⠛⠛⠃⠈⠛⠶⠚⠉⠛⠓⠒⠒⠛⠋⠙⠛⠛⠛⠛⠶⠶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⠤⠒⠐⠃⠀⠀⠙⠃⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⡀⠀⠀⠀⠀⣀⠔⠋⡇
⠀⠀⠀⡠⠂⠁⣠⠴⠒⠋⠉⠉⠉⠓⣦⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡄⠒⠢⡈⢆⢀⡤⠚⠁⣠⡄⡇
⠀⠀⡔⠁⣠⠞⠁⠀⠀⠀⠀⢀⣀⡀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢥⠀⢧⣀⡠⠃⡘⠘⢀⡔⠋⠀⠂⡇⠀⠀⠀⡠⠔⠒⠒⠒⠲⣄⡀
⠀⡸⠀⣰⠋⠀⠀⢀⡴⠚⠉⠉⠉⠉⠛⠰⠖⠒⠒⠢⠤⠈⠉⠉⠉⠓⠀⠀⠀⠀⠚⠤⠐⢸⠀⠀⢰⡇⢧⣄⣤⠊⢀⠔⠒⠒⠢⢤⡀⠙⢦⣤⣤⣀
⢀⡇⠀⡇⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠶⣄⠀⡖⠲⠶⠖⠒⢦⠀⢀⡤⠖⠛⠛⠀⠀⢸⡧⠤⠤⡤⠴⢶⡄⠀⢖⣠⣤⣽⣶⣶⣶⡒⢌⠢⡀
⢸⡇⢸⡅⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⢀⣀⠀⠈⢿⡇⠀⠀⠀⠀⠘⡷⠋⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⡄⠀⠀⡟⡰⠁⠀⠀⣞⣱⠄⠀⠈⢳⢱⠈⡆
⠸⡇⠈⣇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡽⠋⠉⠙⠀⠀⢸⡇⠀⠀⡇⠀⢰⡇⠀⢀⡞⠁⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⣷⡇⠀⠀⠀⣈⣥⡀⠀⠀⢸⢸⠀⡇
⠀⢷⠀⠹⣄⠀⠀⠙⢦⣀⣀⣀⣠⢤⡏⠀⢀⡴⢦⠀⠀⢸⡇⠀⠈⡇⠀⢸⡇⠀⠘⣇⠀⢸⠀⠀⢘⡇⠀⠀⡇⠀⠀⣿⡇⠀⠀⠐⢧⣀⠀⠀⠀⢸⣼⠀⡇
⠀⠈⢧⡀⠘⠷⣄⠀⠀⠀⠉⠉⠀⠀⢳⡀⠀⠙⠉⠀⠀⠘⠁⠀⠀⡇⠀⢸⣧⡀⠀⠈⠉⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠠⣄⣈⡗⠀⠀⢸⡏⠀⡇
⠀⠀⠀⠑⢦⣀⠈⠙⠲⠦⠤⠤⠤⠴⠚⠻⠤⣤⡤⠖⠦⠤⠤⠤⠴⡧⠖⠚⠳⢍⠶⠦⠤⢤⡴⠲⢤⣽⠶⢤⡆⠀⠀⣿⡇⠀⠀⠀⠈⡁⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠋⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡠⢤⣀⡤⢤⡀⠀⢳⠀⠀⠀⠀⡸⠁⠀⢰⣿⡇⠀⠀⠀⡼⢻⡀⠀⠀⢸⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠤⠖⠚⠛⠛⠛⠒⠲⠤⣄⣸⡀⠘⡇⠀⠈⠀⢀⠟⢀⡟⠀⠀⣠⠞⠁⠀⣠⠏⣿⡇⠀⠀⣸⠷⠶⢷⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡞⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠉⠳⢤⡘⠦⣀⠴⠋⣠⡮⠤⠖⠋⠀⠀⣠⢾⠁⠀⠏⡇⠀⠀⠀⢀⣀⡀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⡞⠀⠀⢀⡴⠋⠁⠀⠈⠉⠓⠦⣄⣀⠀⠀⢈⣀⣠⣄⣈⣁⠀⣀⣀⣤⢴⠚⠁⢸⡀⠀⡇⡇⠀⠀⣴⠋⠈⠉⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⢠⠖⠒⢮⣉⡭⠭⠥⡤⠤⠤⡌⢉⡭⠶⠲⢾⠀⠀⠸⠷⠶⡇⡇⠀⠀⢻⣀⢈⣹⠄⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⡇⠀⠀⡇⠀⠀⣧⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠈⠉⠁⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⡇⠀⠀⡇⠀⠀⣿⡀⠀⠀⢻⣾⠀⠀⢠⠀⠀⡇⡇⠀⠀⠀⢠⢶⡀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⢧⠀⠀⠈⠳⣄⡀⠀⣀⣠⣼⠀⠀⢸⡇⡇⠀⠀⡇⠀⠀⡏⠳⣄⠀⠀⢹⡀⠀⢸⠀⠀⡇⣧⠀⠀⢠⠯⠬⢷⠀⠀⠈⣿⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠳⣄⠀⠀⠈⠉⠉⠉⠀⢸⠀⠀⠸⡇⡇⠀⠀⠁⠀⠀⠛⠶⠞⠀⠀⢸⡇⠀⢸⡇⠀⡇⢿⣀⣀⣉⣀⣀⣈⣁⣀⣠⡿⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣈⠙⠶⠤⣤⣤⠤⠶⠾⣤⠤⣤⠇⠱⣄⣀⡴⠲⠤⣤⣀⣀⣤⠴⠻⢦⣤⡼⢇⣀⣘⣤⠴⠖⠚⣛⣒⣒⡒⠒⠒⠒⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠶⠖⠢⠤⠤⠴⠊⠑⠢⢤⡤⠖⠢⠤⠤⠤⠤⠴⠊⠢⠤⠤⠶⠤⣈⣀⣀⡤⠊⠁⠈⠁⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣄⠀⠀⠀⠀⣠⠴⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⢲⣄⣠⠞⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠎⠁⠉⢳⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣈⡧⡤⢤⢼⣁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠤⢶⠋⠁⡴⠁⠈⢦⠈⠙⡶⠤⣟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠊⠁⠀⠃⡠⠊⠀⠀⠀⠀⠳⣄⠐⠄⠈⠓⠄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢀⣀⣀⣀⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢀⣀⣀⡠⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢰⣁⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡀⠘⡆⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⡟⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠛⡄⠀⠀⠀⣸⠃⠘⡀⡇⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢊⣹⠃⠀⠀⠀⡇⠀⢸⢠⠃⠀⠀⠀⠀⠀⢠⠏⠀⢰⠁⠀⠀⠀⡇⠀⠀⠇⡇⠀⠀⠘⣏⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⠏⢠⡟⠀⠀⠀⠀⣷⣀⠌⡸⠀⢀⠆⠀⠀⢀⠎⠀⣰⠃⠀⠀⠀⠀⣿⣀⡸⢰⠃⠀⠀⠀⢻⡄⠹⣦⢄⣀
⠀⠀⠀⠀⠀⣀⠴⠋⡡⠔⢘⣧⣼⠇⠀⠀⠀⠀⠹⣤⡴⠃⠀⠀⠈⠢⣄⣈⠒⠊⣁⣀⠴⠊⠀⠀⠘⢦⣠⠏⠀⠀⠀⠀⠸⣧⡾⠑⠠⢈⠙⢦⡀
⠀⠀⠀⢀⡴⢃⠔⠋⠀⠀⢬⠏⣿⠀⠀⠀⢀⠈⠁⠀⠁⢂⠀⠀⠀⠘⡄⠀⠹⠉⠀⣸⠀⠀⠀⠄⠉⠈⠁⢢⠀⠀⠀⠀⠀⣿⢹⡡⠀⠀⠑⠢⡙⢦
⠀⠀⢀⡞⡐⠁⠀⠀⢀⣨⠏⢠⡇⠀⠀⠀⠘⠄⣀⢀⡀⠎⠀⠀⠀⠀⠳⣄⡀⣀⡴⠃⠀⠀⠈⢆⡀⠀⢀⠔⠀⠀⠀⠀⠀⢹⡄⠳⣅⡀⠀⠀⠈⢎⢳
⠀⠀⣸⡏⠀⠀⢀⣤⠟⠁⠀⢸⠛⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣠⠴⠖⠻⡇⠀⠙⠿⣦⡀⠀⠀⢹⣇
⠀⠀⢿⣀⡤⢖⣋⡥⠴⠖⠒⢛⠶⠒⢦⡄⠈⠉⠉⠛⠒⠒⠶⠶⣤⠤⠤⠤⣤⣤⠤⠤⠤⣤⠶⠶⠒⠒⠛⠉⠉⠀⢠⠴⠒⠶⡛⠒⠒⠦⢬⣙⡲⢤⣀⡿
⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢰⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡤⢚⠥⠬⡓⢤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠘⡄⠀⠀⠀⠈⠙⢶⡄
⠀⠀⢠⡏⠀⠀⣠⠴⠒⢹⡟⢦⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢰⠁⠀⠀⠈⡆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡼⢻⡉⠒⠦⣄⠀⠀⢹
⠀⠀⠀⠻⣄⡸⣅⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣨⢇⣰⠏
⠀⠀⠀⣀⣬⠟⠂⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠐⠻⣤⣀
⠀⢠⠞⠁⢁⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡈⠈⢳⡀
⠀⠘⠶⠒⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠀⠀⠀⠀⣀⣠⡤⠶⠛⠛⠒⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⣀⠀⠀⠈⠉⠉⠁⠒⠒⠒⠒⠒⠢⠤⠤⠴⠒⠒⠒⠒⠒⠊⠉⠉⠁⠀⢀⣀⣠⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠶⠖⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢸⡇⠀⠁⢸⡅⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠃⠈⡇⠀⠀⢸⠀⠸⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⢀⣠⠇⠀⠀⠾⣄⡀⠀⠀⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⡤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡐⠛⠒⠉⠀⢸⡁⠂⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⢀⠔⠂⠐⠤⠴⠡
⠀⠀⠀⠀⠀⠀⠀⡄⡠⠀⢩⠄⠀⠀⠀⠈⠉⠀⠒⢄⠀⢊⡠⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢋⡂⠀⢰
⠀⠀⠀⠀⠀⠡⢀⡘⢀⡀⠀⠀⠀⠀⣀⠐⢀⠀⠀⠀⠀⠈⡀⢀⠀⢈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠙⠘⠁⠀⠈⣀⠠
⠀⠀⠀⠀⠘⠢⢤⠁⠈⠀⠀⠀⡦⢄⠤⣴⣿⠀⠀⠀⠀⠀⠛⢉⡖⠀⢸⠑⠂⠤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡞⠉⣹⠋
⠴⠂⠉⠒⣄⡀⡀⠀⠀⠀⠀⠀⢧⣤⣤⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⢀⡆⠀⠓⣖⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠿⠟⠁⠀⠀⠀⠓
⠢⠀⠀⠀⢼⡉⡃⠀⠀⠀⠀⠀⠸⡉⠉⠻⣿⠀⠀⠀⠀⠀⠐⡀⠀⠀⠳⠄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠎⠢⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠄⣀⡟⠀⠀⠀⠀⠀⠀⠉⢃⡰⠁⠄⠄⠀⠀⠐⠊⠀⠀⠄⡀⠀⠘⣀⠈⢀⡀⠀⡂
⡖⠀⠈⡄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣩⠒⠠⠀⠀⠀⠀⠀⠒⢊⡑⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢔⣁⠀⣈⣀⡤⡇
⠁⠤⠐⠣⢅⠈⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠒⣲⣤⣦⣄⠀⢠⠊⠁⠈⠉⢧⡀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠊⢙⡐⠏⠁⠋⠁⠐⠡⡀⠈⠆⠀⡠⠊
⠀⠀⠀⠀⠀⢈⠃⠈⠀⠀⠀⠀⠀⢀⡠⡄⠾⠿⠿⡍⠹⢷⣻⣤⣶⣤⣀⡸⠋⢀⡐⠀⠀⠀⠠⠃⠊⠀⠀⠈⠀⡀⢀⠄⠀⠀⠀⣿⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠮⢀⡰⢆⣀⣀⠔⢩⠊⠀⠀⠀⠰⣿⣧⠀⠀⣠⡇⢘⠹⣿⡄⣀⢀⡘⠀⠀⢁⢀⠂⠀⠀⡰⠷⠀⢱⠀⠀⠀⠰⠞⠉⠣⡀⡌
⠳⡄⠀⠀⠀⡠⠴⠁⠀⠉⠁⠀⠀⠑⠢⢤⣄⢲⣌⠁⠀⠀⠿⠗⠀⠁⠘⢂⠀⠈⠑⠀⠀⠬⠁⠀⠀⡴⠃⠁⠀⠈⡁⠀⠀⠀⠀⢠⠤⠓⠓⠒⠒
⠤⣙⡂⠂⢲⠗⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⡀⠀⠈⠑⠺⢖⣂⠀⠀⠈⡄⠡⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠡⠊⠀⠀⠈⠁
⠀⢹⡇⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⣷⠀⠀⣠⡤⠀⠙⡍⠐⠒⠁⠀⢇⣀⠀⠀⠀⡰⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠂⠤⣄⣀⡠
⡴⠏⠸⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⢔⠹⠀⠀⠀⠀⠀⣈⠝⠓⠊⠀⠀⣀⡌⠀⠀⠀⠀⠀⡀⢠⠁⠀⠀⠀⠀⠀⠙⠲
⠀⢀⠆⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡄⠀⠀⠀⡌⢥⠠⠀⠀⠀⠂⡦⠜
⠴⠃⠀⠀⢈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⢯⠀⢀⣠⠴⠧⠼⠦⠤⢤⠀⢸⠁
⢀⠀⠀⠀⠈⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠰⡾⠛⠁⠀⠀⠀⠀⠀⠀⠨⠠⠆⠀⠀⠀⠀⠀⠖⢲⣀⣄
⠀⠀⠀⠀⠀⠈⠣⢤⠂⠀⠛⢁⣀⠄⠀⠀⠀⠀⠀⠈⢿⣶⣾⣿⠀⠀⠀⠀⠐⢦⠖⠃⠀⡠⠒⠒⠢⡄⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠀⠀⠘⠤⡖⠀⢀⠀⠱⠶⢲⢀⡄⠀⠀⠀⠙⠿⢃⠄⠀⠀⠀⣀⣈⠃⠀⠀⡁⠀⠀⠀⣽⢠⠃⠀⠀⠀⢸⡀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⡇⠀⠀⠠⠀⠀⠀⠀⠑⠚⡇⠀⣠⠀⠀⠁⠈⠒⠀⠀⠀⠀⢀⠀⠀⣄⣠⠎⠅⠀⠀⠀⠙⠦⠤⠞⠁⢀⡝⠀⠀⠀⠀⠀⠷⠤⡄⠀⠀⢀⠔⢻
⠀⢇⠀⠀⠦⠤⠀⠀⠀⠀⠀⠙⠈⢡⣀⣠⡂⠀⣠⠀⠀⣠⠀⢸⠣⠔⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠑
⠀⠸⡀⠀⠀⠐⠒⡂⠀⡀⠀⠀⠀⠀⠈⠀⠓⠚⠉⠢⠔⠁⠉⠁⠀⠀⠀⢀⠶⠒⠼⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠴⠋
⠀⠀⢧⠀⠀⠀⠀⠉⠉⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⡠⢣⡧⠎⡜⠀⠈⠑⠲⠤⠄⣀⣀⣀⣠⠾⠙⠉⠁⠈⢉⠃⠀⠀⡀⠀⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠘⢛⢃⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠒⢒⠓⠓⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⢉⢁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠂⠀⠐⠚⠘⠘⣤⡀⠀⠀⠄⢀⣀⠀⠀⠀⠀⢰⠶⢀⣠⡴⠄⠁⠀⠀⣍⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⡤⠆⠲⡄⠀⣌⡓⠀⠤⠔⠒⠒⠉⠉⠉⠀⠈⠉⠉⢉⠙⢒⠤⢤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⡀⠀⢀⠀⣀⣀⣷⠀⠁⠀⠀⠀⠀⠀⢀⡀⠄⠤⠶⢶⡟⠛⠁⢀⣠⣧⡬⢄⣀⠈⠁⠒⠆⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠨⠁⢀⡾⠀⠀⠀⠀⢀⠀⣈⣒⡤⢓⣂⠄⢐⡀⠄⢈⡀⠠⠥⠀⠠⢉⡉⠥⠄⠌⠐⣀⡠⠽⠧
⠀⠀⠀⠀⠀⡍⠀⠀⠐⠊⣳⢸⠀⠈⡀⠈⠀⠀⢈⢉⠉⢰⠒⣶⣌⣘⠳⡖⡭⠐⠚⠭⠤⣍⡉⠚⢯⠥⢞⡩⠤⣀⠈⠠⣄⣲⣤⠶⠍⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡀⠀⠀⢀⣈⣁⣸⣄⣌⠂⠤⠤⠤⠤⠤⠆⠹⠒⠀⠀⢆⠻⡇⢈⠁⠀⠈⠁⠀⠈⠑⠒⠠⠔⠠⠀⠐⠀⠈⠁⠤⣐⠤⣐⡢⢀⣀⣵⠠⠔
⠀⠀⠀⠀⠈⠁⠒⠒⢺⠙⠉⠐⠒⢜⠂⠀⠀⠀⠀⢀⠁⢾⣣⠄⠀⠰⣒⡟⢛⠾⠛⠴⠖⠢⠾⢷⣶⣦⣴⣄⡀⠇⠴⠖⢒⣉⡁⠥⠔⠒⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠥⠬⠼⠦⠤⣀⣀⣀⣠⡴⠋⠉⠉⠋⠉⣕⠖⠅⠿⠁⠀⠀⢀⠀⠀⠈⠈⠉⠓⠑⠠⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠉⠀⠀⠈⡍⠁⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⢔⡲⠈⠐⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣂⣥⣾⡷⠛⠁⠀⠀⠀⠀⣠⣭⡒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠙⠲⢿⡛⠻⢥⡀⠀⠀⠀⢀⣤⣮⡥⢋⡴⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢐⣠⣭⣿⣶⣤⣀⠀⠀⠀⠈⠙⠲⢽⣦⣴⣾⠿⣛⣥⣺⢵⣚⣭⣶⡆
⠀⠀⠀⠀⠀⠀⣀⣠⢤⢲⣻⠿⠟⠋⠉⠘⢦⡉⠛⢦⣄⡀⠀⠀⠀⠈⣉⢲⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠐⠠⢉⡛⠋⠁⠀⠀⠀⠀⢀⣠⣤⣿⣷⡶⣞⣻⣷⡆⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢄⡀⠀⠀⣊⠕⡢⢄⡠⢶⣯⡥⢞⣛⣭⣶⣿⣿⣿⣽⡇⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⢷⣶⣍⡂⠀⠉⠓⢶⣾⣿⣿⣿⣿⣿⡿⢿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠑⢤⡀⠨⡛⢿⣷⣤⣀⢸⣿⡿⢿⣻⣭⣷⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠈⢹⣾⣭⣶⣿⣿⠿⣛⣭⣷⣿⡿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠢⣀⠈⡳⢦⣸⡿⢟⣛⣭⢶⣻⣿⣿⣿⡿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡂⠙⠿⣟⣭⣾⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⢸⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠉⠑⠒⠒⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡚⠛⠉⠉⠉⠉⠒⠤⣔⣲⠶⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⣉⣉⣽⡶⠆
⠀⠀⠀⠀⠙⠛⠿⣯⣉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣽⣗⡢⢄⣀⠀⠠⢀⡀⠈⠉⠓⡓⠤⢤⣀⣴⣾⣯⣷⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⣿⠒⠦⣌⡙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠈⢙⣛⣛⣈⣉⣲⣤⣤⠝⠒⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆
⠀⠀⠀⠀⠀⢸⡷⠦⣄⡉⠙⠲⢤⣉⡛⢒⣛⣛⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⡀⣻⡿⠿⠿⠿⠿⠯⠅⠀⠐⠒
⠀⠀⠀⠀⠀⠈⣗⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠠⣟⡒⠤⣀⠀⠀⠀⠀⣹⣟⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⢍⡓⠦⢍⣀⠒⠠⠄⠙⣩⠵⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠈⠁⠀⠉⠓⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣍⣙⠒⠒⠖⠋⣱⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠐⠒⠛⢣⣄⡀⠀⠈⠐⠛⠷⠆⠀⠀⠀⣀⣠⣤⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⢟⠂⠤⣀⠀⠀⠀⠀⠀⠈⠙⢋⣉⣐⢤⡶⠒⠋⠀⣻⣿⣿⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⣤⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠉⠒⠲⠶⣾⣿⣿⣿⣿⣿⣽⡇⢀⣀⣤⣿⣿⣯⣴⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠈⣉⡒⠾⣿⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠤⣀⠀⠈⢿⣿⣿⣿⠿⠟⢛⣳⣯⠛⠉⢁⣼⣿⣯⡽
⠀⠀⠀⠀⠀⢈⡀⠠⢤⣴⣿⠢⠬⣭⣿⣿⣿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠿⢤⣀⡈⠀⠒⠛⠉⢀⣴⣾⣿⣿⡿⠒⠚⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠬⢭⣛⣿⣊⣁⡒⠺⣿⡿⣿⡀⠤⢤⣴⣿⡆⠀⠀⠀⠀⢸⡏⠑⠒⠤⢍⣀⡐⠀⠀⢼⣻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢀⣑⠒⠶⣿⡟⠢⢬⣽⣿⣿⣿⠌⣙⣻⣿⣛⣧⠄⠀⠀⠀⠈⠣⠄⣀⠀⠀⠀⠉⠉⣒⣭⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠬⢉⣛⣿⣛⡁⠒⠲⢿⣯⣿⡓⠲⢾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠒⠶⠚⠁
⠀⠀⠀⠀⠀⠐⠓⠶⢾⣿⣧⠬⢐⣒⣶⣿⣿⡅⠙⠛⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠲⢾⣿⣿⠿






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢴⡶⢫⢻⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣭⡍⢩⡍⡉⠉⡿⠉⡍⢩⣷⣿⣿⣿⠿⡟⢸⣿⠟⣥⣯⣭⣭⣿⣿⣿⣿⣿⣿⣶⠸⣧⠻⠴⠛⠚⢻⢀⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣣⠾⠛⠓⠈⠁⢀⠈⠉⠁⠈⠉⣉⠝⣡⡖⢁⡇⡟⣵⠋⠀⢋⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠓⠀⢸⢸⢿⡵⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠁⠀⠀⢀⣤⠠⢄⠀⠀⠀⠀⡜⣠⣾⣿⢃⡼⢱⡿⣿⠀⠀⢸⠀⠀⠀⠀⣄⣠⣤⣠⢤⠀⠈⠀⠀⠀⠀⡜⡜⣼⣏⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢎⡴⠁⠠⠄⠀⠀⠸⣌⣉⠴⠀⠀⠀⢸⣵⣿⣟⣡⢃⡆⣼⣼⣿⡄⠀⡼⠀⠀⠀⣸⢻⣿⠿⢯⠏⠀⠀⠀⠀⠀⡰⢱⠡⣽⣾⣏⡝
⠀⠀⠀⠀⠀⠀⡠⢣⠎⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠘⡻⣿⡿⢁⢾⡇⣿⣾⡿⠁⡴⠁⠀⠀⣆⠀⢀⠄⣀⡀⣤⣤⣤⣴⡖⣰⢣⢣⡜⣽⣿⡿⠁
⠀⠀⠀⠀⠀⡔⣱⣿⣶⣶⣶⡖⠰⡆⣴⣠⣞⣪⠉⡥⣤⣤⣤⣿⡟⢠⢋⣾⡇⣿⣧⣶⡧⢤⣤⢤⣤⢀⣤⣤⠄⠤⢤⡥⣭⠵⠒⠺⢃⣯⢻⣰⣿⡿⠁
⠀⠀⠀⠀⢾⢤⠴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦⣤⣤⣭⣉⣉⣉⣹⣡⣏⣤⣼⣄⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣭⣭⣭⡴⠶⠒⣒⣛⡿⣱⣷⣿⡿⠁
⠀⠀⠀⠀⢘⡿⣿⡿⢗⣒⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡷⠤⢤⣬⣿⣿⣋⠈⠀⡐⠒⠲⠶⠶⠶⢴⣶⣿⣽⣿⠃
⠀⠀⠀⠀⠸⣯⣭⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣽⢿⣯⠿⠿⠿⠿⠿⠿⠦⠶⠶⠿⢿⣾⣿⣿⣿⣿⣿⢿⣻⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⣲⠶⠤⢤⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠉⠉⠀⠀⠰⡅⢃⠴⣣⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠲⠭⠙⠛⠫⠷⢦⣄⠀⠀⣠⣾⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⡿⠥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡐⠌⠊⠁⠀⠣⡠⠀⠐⢉⠝⣓⡶⢤⢠⠐⣸⣿⣿⠿⠏⣆⣴⣾⡆
⠀⠀⠀⠀⠀⣠⠐⢊⣥⠞⠁⠛⠀⠀⠀⠀⠀⠈⠉⠉⢉⢥⡪⣾⣿⡀⣳⣯⣿⢍⣡⣾⣿⣿⢏⡇
⠀⠀⠀⠀⠀⣾⢛⠒⠤⣼⣒⠤⣁⠀⡀⠤⣤⠄⢤⣲⣵⣿⣿⣿⡿⢐⣿⡛⠈⠀⡉⣿⡾⣻⢏⡀
⠀⠀⠀⠀⠀⡷⠈⠹⠷⣒⠭⠹⣶⣯⣠⣚⣭⣶⣽⣾⣿⣿⣿⡿⢟⣋⣀⡀⢠⢴⡃⣿⣿⠿⣤⠉⠹⡖⠤⢄⡀
⠀⠀⠀⠀⠀⠑⠢⠤⣐⡢⠭⣝⡂⠝⡓⠮⣿⣯⣷⣿⠿⠋⢉⣁⡠⢴⢻⣻⢮⠷⢻⡿⠖⠚⠹⣧⢤⡐⢋⣵⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣗⡲⢬⣙⡒⢧⣿⣿⡋⠭⠃⠀⠀⠀⡔⣵⣿⣿⠲⣱⡋⠀⢀⠔⠀⠀⠁⢚⠻⠿⡿⢿⡀
⠀⠀⠀⠀⠀⠀⣤⠒⠩⠍⠁⣂⡐⠀⢍⡛⠑⠁⠀⣀⢀⣀⡠⣪⣾⣿⣿⣿⣼⠁⠀⠒⠁⠀⠀⠀⠤⠀⠀⠀⠃⠰⣨⠉⣲⡄
⠀⠀⠀⠀⠀⠠⣗⠂⠈⠩⠥⠐⣂⡈⠓⠲⠤⢔⣉⣐⣊⢔⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣀⢕⡤⢖⡫⢔⣷
⠀⠀⠀⠀⠀⠀⢿⣊⡠⠬⠍⠁⠐⠒⢒⣀⣤⣬⢐⣶⣂⣭⣾⣿⣿⣧⣤⡠⠤⣤⠄⣀⠀⢀⡀⠠⣐⡮⢝⣪⣵⣾⣿⣾⢿⡃
⠀⠀⠀⠀⠀⠀⠉⣶⢖⠶⡮⢭⠥⡤⡥⣤⢶⢖⡶⡶⣲⢻⣿⡫⡃⠀⠙⠻⣖⠬⣙⣠⣭⣶⣦⣟⣾⣿⣿⡿⣟⣊⣥⣒⣿
⠀⠀⠀⠀⠀⠀⠈⡯⠁⠑⠊⠂⢄⣈⡘⠐⠑⠠⠊⠄⠔⠔⡠⣻⣮⡀⠀⠀⠉⠯⢃⣬⣭⣍⣬⣿⣻⢿⣷⣾⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠈⢻⢦⡉⠭⠽⢓⣾⡿⣿⣿⣿⢿⠶⠄⡀⠀⠰⣷⡶⣶⡷⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⢯⢍⠑⢾⣻⣷⣿⣿⠟⠋⠁⠀⠀⠀⠑⠒⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⠃⠐⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠢⠰⢀⠄⡠⡀⢀⠀⠀⢐⠅⡨⢀⠀⡠⠀⠔⠁⠀⢀⠔⠡⠊⠀⢀⢀⠑⡡⠂⢀⠔⡁⡠⢀⢔⢕⡔⡰⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠡⠪⠀⠅⠨⠀⠕⡨⢂⠔⠀⡨⠀⠀⡠⠪⢀⢀⠔⡡⠂⠂⠐⠁⠊⠌⠐⠁⠃⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠈⣿⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⣴⠶⠿⠿⠿⢿⣤⡀⠀⠀⡀⠀⠀⠀⠀⣉⣉⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⢿⡿⢋⠀⠰⠄⠀⠀⠒⣈⣉⣤⣤⣴⣶⠶⠿⠟⠛⠋⢿⣇
⠀⠀⠀⠀⠀⠀⣈⣤⣴⣶⠿⠛⠋⠁⠀⢀⣉⣉⣥⣤⣶⡶⠾⠛⠛⠿⢿⣭⡁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⠉⣡⣤⣤⣶⡶⠿⠿⠛⠛⠉⣹⡟⡁⠀⢐⣦⣀⠀⠀⠈⢻⣆⠀⠀⡀⢀⣀⡀⡀⣿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⣩⣥⣤⣤⣤⣤⣤⣬⣭⣬⣤⣤⣭⣭⣬⣥⣤⣤⣥⣭⣤⣤⣥⣭⣭⣥⣥⣭⣭⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣿⣟⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿⠛⠉⠉⡉⠉⠙⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡿⠀⠀⢀⡀⠀⠀⠀⣼⠋⠀⠀⣠⠾⡗⣦⠀⠀⠈⢿⡄⠀⠀⠀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⣿⡟⠀⢠⣶⣦⠀⠀⢸⡏⠀⠀⠀⠻⣶⣇⡉⠀⠀⠀⠘⣷⠀⠀⢠⣶⣄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣿⣷⠀⠈⠛⠋⠀⠀⢸⣧⠀⠀⠀⣤⡌⡟⢻⡆⠀⠀⢠⡿⠀⠀⠈⠛⠋⠄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠙⠲⡷⠛⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣠⣀⣀⣀⣀⣀⣀⣀⣹⣷⣦⣄⣀⣁⣀⣤⣾⣟⣡⣄⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠒⢉⡁⢰⣶⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠋⣉⡠⠤⠖⠒⠋⠉⠈⢇⠀⠿⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠚⣉⣁⠤⠤⠶⢊⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠘⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠂⣉⣉⡤⠤⠔⢂⠟⠋⠁⢀⣤⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣧
⠀⠀⠀⠀⠀⡔⠒⢈⠉⢠⡤⠤⠒⠊⠉⠁⠀⠀⠀⡔⠁⠀⠀⣴⣾⣿⡿⣷⡆⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⡀
⠀⠀⠀⠀⠀⢱⠀⠘⣢⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⣿⡁⢹⣷⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠘⡆⢀⠥⠔⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠻⣿⣾⣿⣦⣤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹
⠀⠀⠀⠀⠀⠀⢡⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⢻⣷⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠀⠏⡇
⠀⠀⠀⠀⠀⠀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢠⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠰⡇⠀⢧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠐⠿⣷⣶⣿⣿⡿⠋⠀⠀⣠⠋⠀⠀⠀⠀⣀⣠⠤⠄⠓⠀⣉⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠈⠛⠁⢀⣠⣞⠥⠤⠒⠒⢉⣁⠤⠤⠖⠒⠈⠉⠀⣳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡲⠶⠶⠒⠊⣉⣁⠤⠔⠒⢺⠋⠁⠀⠀⠀⠀⠀⢀⠞⢁⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢴⠀⠙⡆⠀⣀⣀⠤⠄⠒⠚⢉⣁⠠⠤⠶⣶⣿⣿⠟⠁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⢸⡄⠈⡳⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⠇⠀⢉⣉⡁⠤⠔⠒⠋⠉⠓⢤⣀⠀⠀⠀⠈⠉⢀⣀⣴⣋⡠⠤⠤⠒⠒⠂⢋⣉⣉⡡⠤⠤⠰⡖⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠧⢲⠊⠙⡍⠀⠀⠀⠀⠀⣀⣀⣀⠠⠬⠽⠛⠒⠊⢉⣉⣁⡠⠤⠤⢲⠖⠂⠉⠉⠉⠀⠀⠀⠀⣀⣀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡷⠀⠻⠒⠒⠊⣉⣁⣤⠤⠤⢤⠒⠒⠊⠉⠻⠟⠉⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠦⠤⠖⠲⠶⠬⠭⠥⠤⠤⠤⠤⠤⠤⠭⠶⠦⠤⠤⠤⠤⠶⠮⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠨⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢿⡿⣿⣿⣶⣶⣦⣤⣤⡄⢠⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣘⣿⣯⣲⣦⠀⠀⠀⠀⢀⠄⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇⠈⣧⠀⠀⢠⣿⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⢿⣿⣿⣆⣿⡇⢠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣽⣿⣿⣿⣿⣿⠷⠚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⣩⣿⣿⣿⣾⣶⡶⢲⣾⡑⢝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⣾⣿⣿⣿⣿⠟⣸⠃⠈⠻⡿⣄⠁⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⡀⠋⢠⡄⣤⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⢀⣴⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣽⣯⠀⠀⣿⣿⡟⡇⣿⠿⠛⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗⡀⠀⢿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡇⠀⠀⠛⢹⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠀⢠⣤⣿⢸⡟⣿⣿⡄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢈⣹⣻⣿⣿⣷⡶⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⢀⠠⠀⠀⠀⢀⣿⣿⣼⣧⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣤⣮⣿⣿⣿⣿⣿⣿⣷⣂⣀⡤⠖⣾⣿⣏⢻⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⢷
⠀⠀⠀⠀⢶⣾⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣽⣿⠿⢛⣁⣀⣀⣿⣿⣷⡬⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠛⠛⣿⣯⣍⣉⣉⣉⡙⠛⠛⠻⠿⡯⠔⠚⠋⠉⠉⣙⡻⣿⣿⣧⢀⡀⢰⣁⠀⠀⠀⡆⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠐⠿⠿⠿⣿⣿⣿⣻⣻⣶⣶⣦⣤⣄⣀⡀⠐⠉⠁⣀⣿⣿⣿⣧⡬⠙⠿⠿⡿⠀⣂⣠⡤⠞⠋⠁
⠀⠀⠀⠀⢸⣶⣦⣤⣀⣀⡀⠊⠉⠉⠛⠛⠻⠿⣿⣯⡤⠴⣚⣉⣽⡿⠿⣿⣿⣿⣿⣿⣻⣟⠁⡿⠟
⠀⠀⠀⠀⠙⠿⠷⠾⣯⣿⣿⣿⣶⣶⣦⣤⣀⣤⠼⠗⠊⢉⣉⡠⠼⠁⠀⠀⣌⠁⠀⠀⢠⡿⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣧⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⡼⢽⡧⠀⠼⣏⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣻⡗⢀⡚⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠷⢦⣯⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⡤⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣒⣒⣢⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠄⠀⠀⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡵⠋⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡺⠛⠛⠓⠶⣤⠀⠀⢸⡟⠲⠦⠤⠤⠴⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣋⠀⠀⠀⠀⣀⣼⡇⠀⣿⣝⠷⠶⠤⠤⠶⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⣉⡙⠛⠛⢋⣹⡿⠃⠀⢻⣍⡙⠛⠛⠛⠋⣿⡟⠀⠀⠀⣀⣤⠴⠚⣋⣥⣙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣥⣍⣉⣛⣫⣽⣿⠀⠀⠀⠀⠈⠙⠛⢛⣛⣫⣥⣤⠶⠚⠋⠉⠀⠀⠉⠁⠀⠉⠓⠌⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣀⣀⣤⠾⠛⢀⣀⣀⣤⡤⠶⠒⠛⠻⣿⣿⣿⣷⣄⠐⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⣷⠈⠻⣿⣿⣿⣷⣄⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠟⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠈⠻⣿⣿⣿⣿⣦⡛⠀⠀⠀⢀⣠⡴⢚⣩⡴⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡛⢦⡀⠈⠳⣄⡀⢄⡀⠀⠀⠀⠉⠻⠷⣦⣬⠙⢿⣿⣿⣿⣦⡴⢞⣫⡵⣞⣫⠵⢶⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡛⢦⡙⢦⣄⠈⠛⢦⡙⠶⣤⣤⠤⠤⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠿⢛⣋⡭⠶⣚⣻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢦⡙⢦⡙⠷⣄⠀⠙⠶⠶⠶⣒⣛⣯⠽⣷⣿⡿⢿⣿⣿⣿⠶⣛⣭⠵⠖⠋⢩⡴⣞⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⢦⣙⢦⣈⠳⠶⠖⢛⣋⣭⠵⠖⣛⣭⠴⢖⣻⣿⣿⠟⠋⠁⠀⠀⠀⠀⣿⣜⣃⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⢦⣝⠷⠶⢚⣋⣥⠴⢞⣫⡭⠶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⢻⣤⣉⠙⠛⢋⣉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠷⣚⣫⡥⠖⠛⠉⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⣿⠦⣤⣍⣉⣩⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠒⠁⠀⠀⠈⠙⣆⠀⠙⠶⣤⣤⣤⣤⡤⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⢤⣤⠤⠶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣤⡤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⠿⢿⣿⠟⣣⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⣵⣶⣶⣶⠞⣢⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣡⣾⣿⠿⣋⣵⣾⣿⠟⣋⡛⠿⠿⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣋⣼⡿⢋⣵⣾⣿⠟⣋⣴⣿⣿⣿⣿⣿⣷⡌⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢛⣥⣾⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢟⣡⣾⣿⣿⣿⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢟⣩⣶⣿⡿⢛⣥⣿⣿⠃⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢠⣾⠟⣫⣴⣿⡿⢟⣡⣶⣿⣿⣿⣿⣄⠙⠛⢉⣉⠙⢿⣿⣿⣿⣿⣿⠿⣋⣴⣿⡿⠟⠉
⠀⠀⠀⢀⣴⡿⢱⣿⣿⣿⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢨⣿⣿⠿⣋⣵⣾⣿⠟⠉
⠀⠀⠀⣾⣿⣿⡘⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⡀⢺⣿⣿⣾⣿⠟⠋
⠀⠀⠀⠻⣿⣿⣿⣌⢿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⠿⠋
⠀⠀⠀⠀⠈⠙⢿⣿⣦⡹⣿⣷⡜⢿⣿⣿⣿⣿⣿⡿⢟⣩⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡜⢿⣿⣮⣥⣤⣭⡛⣩⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠐⠈⠉⠀⠰⠀⢀⠂⠀⢶⡔⠡⠐⡄⠀⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠁⣀⠐⣄⠈⠲⣦⠀⠀⠆⠀⠀⠀⢀⠈⠀⡐⠀⠈⠂⠀⠀⠄⢮⣱
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠘⠂⠀⠈⠁⢀⣀⠀⠀⠄⠡⠀⠀⠀⠁⠀⠐⠀⠀⢀⠈⠱⡃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⣀⠑⢐⣀⣀⠠⠀⢠⠁⠁⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠱⡄⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⣀⣁⣤⣼⡶⠂⠀⠀⠀⠈⢐⡄⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠀⡀⡀⠀⠈⠀⠀⠀⠀⠄⠀⠈⠉⠘⠿⠋⠊⣀⠀⠘⠀⣄⠀⠁⠀⠀⡀⠀⠀⠀⢠⠐⠀⠤⠀⠀⠀⠀⢐⠀⠀⢀
⠀⠀⠀⠀⢐⠀⠀⠀⡄⠀⠀⠀⠀⠒⠃⠉⠀⠀⠀⠁⠐⠡⠀⠀⠀⠀⠂⠀⠈⠘⡤⢔⡊⠁⠘⠠⠀⠀⠀⠂⠀⠀⠈⠠⡀⠘
⠠⠀⠌⠴⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠁⢈⣦⠞⠡⠀⠉⢦⡀⠀⠈⠁⠀⠀⠠⠑⠂
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢈⣠⠄⠀⠀⠀⢠⠈⣂⠀⠀⠀⠀⠀⠀⠀⣴⡟⠣⠀⠀⠀⠀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠒⠂⣤⣀⣀⣀⠀⠀⠀⠠⠀⠀⠐⠂⠀⠂⠀⠀⠁⠀⢀⣴⣾⡏⠁⠀⠀⠀⠀⠀⠉⠉⠙⢦⠀⠀⢀⠀⡄⠀⠤⢀⠠
⠀⠀⠀⠀⠈⠙⠛⣿⣿⡆⠀⠀⠀⠀⠐⠠⠄⠂⠀⠐⠒⠠⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣰⣶⠶⣶⣶⣦⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⠉⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡁⠀⠀⠀⠀⠀⠀⢀⣴⣴⣶⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⢦⣤⠀⢰⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⣿⣷⣜⣧⣾⣵⠀⢠⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣤⣶⣾⣿⣿⢿⠟⠛⠷⣤⣿⣶⣦⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢉⣾⢻⢏⡇⠞⠈⡠⡀⠀⠆⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠸⣿⠛⠘⠀⣴⠀⠀⡀⣤⣾⣤⣤⣤⣤⡔
⠀⠀⠀⠀⠀⢀⣤⣲⣖⣂⡖⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠈⠀⠀⢿⡷⠖⠋⠉⠅
⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⢠⣶⡀⢀⡀⢰⣿⣀⣤⣤⣤⡾⠁
⠀⠀⢸⣿⡿⢿⣿⣿⣿⡇⡇⠈⣄⣀⡀⠀⠀⠀⠀⣠⣼⠏⠀⠀⢀⣴⣿⣿⢿⠿⠟⡩⣥⠀⠀⠀⠀⠘⡄
⠀⠀⢘⠛⠀⠈⠈⢠⢸⡇⡇⠀⢻⣀⣀⡀⢠⣴⣿⣿⠋⠀⠀⠀⠸⣿⣅⣿⢰⣄⡀⣠⣿⣤⣤⣤⣴⣶⡇
⠀⠀⣼⣀⣧⣧⣼⣾⣿⣇⢳⠀⠸⣿⣛⣿⣭⣽⣿⠇⠀⠀⠀⠀⠀⠙⢿⣿⣼⣟⠙⠉⠉⠉⠉⠉⠉⠉⢱
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⢻⣿⠿⠿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡇⢧⠀⠘⡇⠀⠀⢸⡃⠀⠀⠀⠀⠀⢠⣶⡄⣿⠀⣿⢘⣿⡄⠀⠀⠀⠀⢤
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡸⣄⠀⠙⠀⠀⢺⣵⣄⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣾⠿⠁⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣷⣻⠀⠀⠀⠀⣄⣿⣿⣿⣶⡄⠀⠀⠀⠀⠻⠉⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠆
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣦⣤⣤⣤⣄⡀⣀⣀⠀⢀⣀⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁


⣾⣷⠿⠿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⣭⣭⠿⠀⠀⠀⢠⠈⠡⠤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠠⢜⠀⠀⠶⠖⣿⠍⠡⠤⠤⢵⠀⢚⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣉⣿⣉⠘⣛⣛⣽⡇⠀⢒⣚⡿⠀⠥⠵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢤⣷⠀⢈⣁⣀⢽⡇⠈⣉⣭⣿⡀⢒⣲⡧⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⡤⢄⡐⢒⡲⠒⠚⠓⠒⠛⠂⠀⠂⠤⢾⡃⠀⠶⣺⣯⠄⣉⡥⣿⢉⣽⡇
⠀⠀⠀⠀⠘⠙⠓⠻⢶⠀⠈⠀⠀⠀⠀⣀⣠⠴⠖⠒⠈⢉⠉⠈⢻⣽⡻⡤⠤⣶⣷⢴⣿⣧⡆⢀⣤⣤
⠀⠀⠀⠀⢀⡀⠀⢈⢹⠀⠀⠀⠀⠀⠀⡿⠿⠷⢤⣬⣦⡶⣰⣭⣿⣶⣒⣖⣒⣲⣾⣽⠿⠿⣯⣽⣿⣿⠷⠂
⠀⠀⠀⠀⠈⠙⠊⠛⠻⢦⣀⠀⠀⠀⠀⣏⠂⠀⠀⠀⠀⡏⠁⠉⠈⠉⠩⣏⠉⠉⠾⣁⣐⣐⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠤⠹⠷⢶⣦⣄⣀⣇⣠⣤⣶⣾⠽⠏⠂⠐⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⢀⡤⠴⠶⠦⠤⢤⣖⠢⣤⣀⡀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠉⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣾⣶⣾⣾⣷⡀⠀⠀⠀⠀⠀⣠⠴⠶⡿⠷⠦⣄⡀
⠀⠀⠐⠦⠀⠀⠀⠈⢳⣀⣈⣉⢀⠞⠀⠀⠀⣀⠴⠚⠁⠀⠈⠉⠉⠉⠉⠀⠙⠢⣄⠀⠀⠀⠈⢦⣀⣀⣀⣀⡜⠁⠀⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠼⢿⠿⢿⠿⣄⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⠿⢿⡿⠿⠿⢷⡀
⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢀⡤⠶⠧⢤⠀⠀⠀⠀⠀⠀⠈⢷⠁⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⡴⠁⠀⠀⠀⣠⠤⣄⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣠⠦⡄⠀⠀⠀⠈⢢⡀
⠀⠀⢸⠁⠀⠀⠀⠀⢧⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣅⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢙⠆⠀⣇⢀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⡏
⠀⠀⠘⡄⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠛⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠩⢞⡦⢄⣀⣀⣀⣀⣀⣀⣀⣠⣼⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⡯⣀⡀⠀⠀⠀⠀⢀⣠⡔⣋⣀⣀
⠀⠀⠀⠀⠀⠞⠁⠼⠋⡽⢋⠜⢋⠔⢁⠔⢁⠞⣩⢟⡿⢛⡿⠋⣹⠟⣹⠋⡹⢋⡽⠁⠎⠰⠋⠞⠙⢫⠟⡽⠁⠞⠙⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠈⠀⠀⠁⠀⠁⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢻⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⣴⣾⣿⣷⣌⡻⣆⠀⣀⠠⠄⣀
⠀⠀⢄⠀⠀⡠⠄⢸⣿⣷⣏⢷⣽⣿⣮⡇⠀⠀⠀⠈⣷⠞⠉⠑⠢⣄⠀⢀⡀
⠀⠀⠀⠑⠄⣈⠀⣸⣿⡟⣟⣸⢿⠇⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣼⠋⠁⠉⠑⣄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⣶⡿⠄⠛⠠⠤⠄⣀⠼⠄⣄⡀⠀⠀⡏⠀⠀⠀⠀⣸⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠛⠙⠛⡟⠀⠀⠀⠀⠀⠸⠁⠀⠀⠠⠁⠀⢸⠁⠀⠀⠀⢠⡏⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⠀⠲⡀⠀⠀⠀⠀⠰⠧⣀⣴⢇⡜⠀⡟⠀⠀⠀⢀⡞⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠀⠲⣤⣀⣀⣀⣤⣴⠋⠀⢸⡇⠀⠀⢠⡞⠀⠀⠀⣴⣷⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⣿⡿⡟⠹⡿⢶⢶⣿⣷⣴⢶⣯⣀⣀⣠⣾⣽⣏⢻⣾⣿⡿⠋⣡⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠞⠁⠃⠀⠀⠈⡇⠛⢿⡀⠀⠉⢍⣍⠙⢿⣯⣻⣫⣾⡿⠀⣮⡈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⢻⢢⠈⠻⣿⣿⣿⡇⢸⣿⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⡄⠀⠀⠀⢡⡀⠙⠹⣿⠀⠘⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⣀⡀⠀⢀⣀⣼⣣⠀⠈⠀⠀⣀⠀⣟⠦⣀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠙⠛⠛⠛⠋⠥⢤⣤⣤⣤⡼⠋⠦⠖⠚⠙⠓⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⡀⠀⠊⡽⢿⣝⠓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡘⠳⠶⠾⠋⠈⠉⣀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠙⠛⠛⠻⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠓⠒⠶⠾⠿⠃⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣇⣀⡀⠀⠀⠲⠶⠶⠶⠶⠟⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣦⣴⠟⠛⠉⢙⣧⠀⢤⣤⣤⣤⣤⣤⠐⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⠲⠶⠶⠶⠶⠶⠾⢿⣿⡇⣄⣀⣀⣀⣀⡄⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠐⠲⠶⠶⠖⠃⢘⣿⡃⣀⣈⣉⣉⣉⣥⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠙⠛⠛⣛⠁⢸⣿⠃⢠⣀⣉⣉⣉⣤⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⣉⣉⣉⣉⡀⢸⣿⡀⢀⡉⠉⠉⠉⡁⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣉⣉⣩⡀⢸⣿⡇⠈⠉⠛⠛⠛⢋⣘⣿⣦⣤⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⣤⣄⣈⣿⣧⠴⠶⣶⣚⠛⠉⠉⠀⠀⣀⠤⠄⢀⣉⡛⠳⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣃⣤⠤⠴⠶⣾⣛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠙⠶⣶⣬⣀⡀⠉⠛⠛⠑⠠⠄⣀⣌⣭⡙⠻⠷⣶⣤⣄⡀
⠀⠀⠀⠒⠒⠋⠉⣉⠶⢤⣐⣪⠭⠴⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣤⣀⠐⣀⠼⠶⠶⠞⣀⣀⡤⠤⠀⣥
⢸⡀⠐⠦⡀⠀⠳⣍⣹⣷⡷⢄⡀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⣿⡴⠖⢚⣋⣩⠭⠖⣒⣋⢉⣿
⠸⣧⣀⠀⠈⠓⢤⡀⠈⠉⠓⢲⠞⣍⡛⢶⣤⠤⠒⣊⠡⠤⠉⠂⢀⣀⣠⡤⠶⠖⠛⠉⠉⠀⢸⡇⠀⠀⠄⠒⠊⣉⣡⡤⢼⣿
⠀⣇⠈⠳⢤⡀⠀⠈⠓⢦⣀⠀⠳⣬⣿⣧⡿⠴⠚⣁⣤⣴⡶⠟⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⠴⠒⠋⠉⣁⣠⣤⣾⣟
⠀⣇⠙⠦⣄⠙⠳⣄⡀⠀⠈⠙⠲⠄⣀⣤⡴⠾⣛⡉⠁⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠤⠶⠒⠛⢋⣉⣥⡤⣾⣟
⠀⠋⠙⢦⣈⠑⠦⡀⠙⠦⣄⠀⠀⠰⡿⢖⣚⣩⡤⠴⢒⣋⣭⠤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡤⠶⣖⡻⠭⣙⣠⣤⣽⣿⠿
⠀⠀⠳⣦⡈⠓⠀⠈⠐⠀⠈⠙⠢⢤⣿⣉⣭⡴⠶⠛⠉⠁⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣭⣽⣶⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⣀⣠⣤⡶⠂⢸⡇⠀⣀⣀⣤⣴⣶⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠈⣿⡤⠴⣒⠿⢛⡉⠁⣀⣤⣼⣷⣿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⢸⣿⣠⡤⠶⣚⣭⣶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⣏⡥⠖⠛⠉⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⡤⠶⢒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠲⠤⣀
⠀⠀⠀⢸⠦⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡤⢾
⠀⠀⠀⢸⠀⠀⠉⠉⠉⠛⠓⠒⠲⠖⠲⠶⠶⠶⠦⠴⠶⠖⠖⠲⠒⠒⠲⠛⠋⠋⠉⠁⠀⢸
⠀⠀⠀⢸⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠀⢸⠛⢦⡀
⠀⠀⠀⠈⠑⢲⠦⢤⣄⣤⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⡆⠀⢀⣀⣀⣈⣀⣀⣤⣤⣴⠶⠿⠖⢻⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠙⠉⠉⠛⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣄⣸⢧⣠⠴⢻⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢸⠿⢿⣖⣲⠾⠦⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⠥⠤⠴⠶⠶⠚⢒⣋⣩⡴⠋⠀⠀⢸⡆⠉⠠⡙⢆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠉⠙⠉⠛⠒⠖⠒⠲⠒⠒⠶⠒⠒⠖⠒⠒⡖⠚⠛⠋⠉⢩⠁⠀⣇⠀⠔⠈⠀⢻⡐⡀⠈⠢⠳⣄
⠀⠀⠀⣠⠴⠒⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢈⠀⠀⠙⡄⠀⠀⠠⠀⢳⡐⡀⠀⠀⠌⢦⡀
⠀⠀⠀⡷⠤⣌⣀⡉⠒⠶⠤⣤⣤⣄⣀⣀⣃⣀⣘⣀⡀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣄⣤⡴⣤⠖⠛⠻⡖⠁⠀⠀⠀⢳⡀⠀⠀⠀⠢⠱⣄
⠀⠀⠀⡇⠀⠀⠉⠉⠉⡋⠛⠒⠒⠒⠒⠖⠛⠻⠟⠛⠻⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⣿⠀⠀⠀⠹⣄⡠⠒⠁⠀⢹⡄⠄⠀⠀⠐⠘⢦
⠀⠀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⡀⠀⠀⠹⡄⢀⠄⠊⠁⠘⣆⢂⠀⠀⠈⠈⢣⡀
⠀⠀⠀⠈⢳⠶⠦⣤⣤⣇⣀⣀⣀⡀⢀⡀⠀⢀⡀⠀⢘⠀⠀⣘⣀⣀⣠⣠⣤⣦⣶⣚⣯⡥⠞⡇⠀⠀⠀⠘⣇⠀⢀⠠⠐⠉⢧⡠⡀⠀⠀⠂⠳⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠙⡋⠉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠈⢷⡁⠀⠀⠠⠈⠳⡄⢀⠀⠀⠠⠹⡄
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠳⡔⠁⠀⠀⡠⠘⢦⠠⡀⠀⠡⠹⡄
⠀⠀⠀⠀⠀⡿⢵⣒⡲⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠶⣒⣋⡭⣗⠀⠀⠀⠀⠀⠀⠀⠙⢦⠐⠀⠀⠀⡠⠳⣄⢀⠀⠁⢹⡀
⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠙⠒⠒⠒⠶⠶⠭⠭⠭⠭⠭⠭⠭⠭⠤⠶⠒⠒⠖⠚⠙⠋⠉⠁⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠔⠁⠀⠀⡈⠷⣕⠠⠀⢧
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠐⠉⠀⡠⠘⠳⣤⡼
⠀⠀⠀⠀⠀⠉⠒⠶⠤⣤⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣠⣤⠤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁