Macaroni Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⣡⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢃⠇⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⢆⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⢣⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡠⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡝⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢃⠃⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⠃⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡀⣠⠤⠒⠒⠉⠉⠉⠁⠢⢙⡆⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡎⠸⡁⠀⠀⠀⠀⠀⣀⠤⠔⢹⡇⠀⠀⠀⣀⠀⡏⠢⣀⠔⠁
⠀⠀⠀⣀⠤⠐⠒⠚⠋⠙⠻⡔⣦⠀⠀⠀⠀⠀⠀⠀⣸⠉⠓⠒⠚⠛⠋⠉⠁⠀⠀⠀⢸⠟⠓⠚⢻⢡⠬⢿⡏
⣴⠡⡊⠀⠀⠀⠀⠀⠀⣀⠤⠖⠙⢦⣀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠈⣟⠀⠀⣷
⢹⡓⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⡆⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣐⠲⣤⣀⣀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣔⢏⠀⠀⠈⠉⠑⠢⢄⡀⠀⠀⠀⠀⣰⣿⠗⠉⠈⢃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠲⢤⡀⠀⠀⠀⠀⢑⠑⣄⡴⢟⠟⠁⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠉⠙⠒⠒⠐⠲⣏⢀⠎⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⠀⢀⡠⠊⠀⠀⣴⢢⡽⠒⠒⠢⠤⣀⡀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢯⣄⣠⠤⠊⠈⠣⢅⠀⠀⠀⠀⠀⠉⠑⠞⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣀⣀⠀⢘⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠆⠀⠀⠀⠀⠂⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠿⢷⣦⢠⣿⢿⣄⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⣀⣴⣿⣿⠃⠈⠛⠿⠶⣶⡿⠁
⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠿⠛⠛⢹⣿⡇⠀⠀⠀⠀⣰⡟
⣴⡟⠋⠉⠀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⣾⣿⡁⠀⠀⠀⠀⣿⡇
⢻⣧⣤⣤⣾⠟⠙⢿⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣼⡟⢿⡇⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠈⢿⣏⠁⠀⠀⠀⠀⠙⠿⣶⣦⣴⣶⠾⠿⠿⠶⠶⢶⣶⣴⣟⡀⠘⣿⡀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣴⡿⠛⠉⠉⠙⣿
⠀⠀⠻⣧⡀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣼⣿⣄⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠾⠟⠛⣿⡅⠀⣿⣦⣀⣀⣠⣴⣿
⠀⠀⠀⠈⠻⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠿⠛⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⠉⠉⠉⠉⠁⣿
⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⣀⣤⣶⠶⠶⠶⣶⣤⣄⠀⠀⣿⡏⠀⠀⠀⢀⣾⢿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣶⣿⠇⠀⠀⠀⠀⢰⡿
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄⠘⣿⣶⡶⠾⠛⠁⠀⠻⣷⣍⠙⠛⠛⠛⠛⠉⢉⣡⡾⠋⠀⠀⠀⠀⢀⣿⠃
⠀⠀⢀⣿⣃⣀⣀⣀⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠘⣿⣄⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣶⡶⠾⠟⠋⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⣸⡿⠛⠉⠉⠙⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠹⣷⣤⣀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣬⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠛⠿⠶⣶⣤⣤⣤⣴⣶⠶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢩⡍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣠⠞⣷⠀⡇⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⣇⣴⠃⠘⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⣀⣤⡀⠀⠸⡆⠈⠛⠁⠰⠚⠲⠀⠀⠔⣛⠲⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢦
⠀⠀⠀⢰⡝⠀⢱⡤⡄⠙⠲⢄⡀⠰⣽⣷⢀⡀⣈⣾⡇⠀⠘⣇⠀⢀⣠⠴⢤⣄⠀⠀⠀⠀⠀⠀⢦⠮⠈⡨⠃
⠀⠀⠀⠀⠑⢆⠀⣸⠀⠀⠀⠀⠙⢦⡛⠉⣄⣠⠍⠉⠁⠀⢠⣿⡚⢉⣴⡒⣦⠈⢻⣤⣄⡀⠀⠀⢈⡦⣤⡇
⠀⠀⠀⠀⠀⠘⢯⣿⣅⡀⠀⠀⢀⣠⣷⡀⠩⠝⠀⢀⡴⠶⠼⠷⠃⠠⣤⠌⠀⣀⣀⠠⠦⠙⠲⣄⢀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠟⢛⡇⠀⠀⢰⡯⠤⠶⢒⡒⠶⠖⠒⠚⠻⠤⠞⠛⠋⠉⣉⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠴⠞⠀⠀⠀⠘⡇⠀⠰⠧⠞⣠⢒⡒⠄⠀⠀⢒⣒⠆⠀⠻⠇⢹
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢻⠀⢀⣤⡄⢹⣿⣜⠀⠠⠀⣿⣏⠇⠀⢠⡀⠻⡀
⠀⠀⠀⠀⠀⠀⢠⡏⢠⡟⠙⡆⠸⡆⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠛⠋⠘⣟⡏⠈⠉⠀⠀⣈⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡇⠸⣧⣰⠇⢠⡇⠀⣀⣠⡴⠊⢀⣿⢀⣀⠀⠰⠽⠃⠀⠀⠀⠠⠄⠀⠘⢭⡽⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣆⡈⠁⣠⡾⠁⠚⢉⣁⡤⢾⣿⣿⣏⣚⣁⣀⣀⣴⠖⠶⢤⣤⣤⠶⠶⠶⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣶⡟⠉⠁⠀⠀⣿⣇⠉⠉⠉⠉⣿⣿⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⡿⠀⠀⠀⠀⠀⢸⠛⢲⠀⠀⣶⠛⠛⣧⠀⢰⡞⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠶⣻⣿⡀⠀⠀⠀⠀⢸⣿⣻⡄⠀⣹⠟⣛⡧⠀⠈⣷⡛⠻⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠸⢷⡴⠗⢾⡥⠖⠉⠀⠀⠀⠈⠉⠑⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⢠⠀⣆⢠⠀⠀⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠉⠩⢵⣦⠢⢬⣿⡃⠁⠀⢀⠤⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠐⠛⠛⠙⠉⠈⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⢁⡀⠀⠀⠀⠀⡠⠀⠀⠐⠀⠈⠉⠃⠠⠄⠀⠀⠐⠀⠈⠀⠀⠀⠄⠄⠀⠊⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠲⠎⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠐⠤⠀⢀⠀⠀⢢⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠠⠒⠚⠻⢌⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⢀⠀⠀⠀⠀⡀⠀⠈⠁⠢⣤⡄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠀⠀⣠⡦⠖⠈⠈⠀⠀⠀⠈⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠁⠀⠀⣠⠄
⠀⠀⠀⠀⠀⡉⢢⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠦⠷⣤⠂⠇⠀⡀⠁⠈⠀⠀⠀⠀⢰⠀⠀⠀⣤⡦⠀⠀⠈⠀⠀⠀⠀⢀⠀⡖⠀⠠⠀⠀⠂⠁⠀⢀
⠀⠀⠀⠀⠈⠀⠀⢀⠤⠀⠑⢄⠀⠀⠀⠀⠀⠉⠒⠒⠊⠠⠈⠀⠀⡄⠀⠠⠀⠠⢂⠄⠀⠘⣁⠠⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠉⠀⠀⢀⡀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠒⠉⠫⢉⡗⠀⠄
⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠁⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠀⠀⢻
⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡄⠀⠀⢢⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠄⠀⠈⠇⠀⠀⢀⠀⠀⠀⠁⠁⠀⠰⠆
⠐⠛⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣇⠀⢼⡾⠀⠀⠀⠀⠀⠀⢩⣅⡿⣠⣄⢀⣴⢠⡾⢀⡴⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠂⠘⠉⠀⢀⠀⡄⢠⠀⡀
⠀⠀⠀⣄⠀⠀⡐⠟⠋⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠘⠗⠿⠾⡼⠻⠷⠿⠶⣧⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠘⣉⣙⢞⡀⠁
⡌⢀⠀⡈⢧⠀⠃⣀⡐⠁⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠃⠀⠌⠀⡄⠌⠁⠀⠀⢀
⢇⠀⠀⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡄⠀⡀⠀⣼⡟⠲⠀⣀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠠⢄⡀⠁⠀⠀⢠⠆⠤⣄⠀⠈⠉
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣦⡟⢸⣠⣎⣵⣤⣏⣰⣧⣮⣴⣴⡏⣽⣼⣱⣦⠀⠀⠀⠀⠈⠙⠠⠄⣬⡀⠂⠀⠀⠀⠀⠈⠀⠐
⠀⠀⢤⠄⠀⠀⠐⢇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⡀⠀⠀⣀⠤⡀
⠀⢀⠈⠀⡼⠓⠀⠈⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⠀⢰⠄⣿⡀⠀⠀⠀⡐⠦⣄⠈⠲⡖
⠀⠀⠀⠈⠀⠀⠀⠀⠄⠈⣀⡄⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠁⠐⠛⠀⠀⠀⠁⢀⠴⠙⠳⠆⡐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡹⠁⢠⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠖⠀⠀⠀⠀⠠⠦⣄⡀⠀⠀⠈⠂⠀⠀⠘⢦⣄⢀⠀⠀⣀⡄⣀⠀⠀⠡⠖⠀⠐⠀⠀⠀⠀⠠⠄⠉⠑⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⣄⣤⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠑⠄⠀⠀⠀⡀⠀⠀⢀⡤⠶⠶⠦⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⡀⢠⠀⡐⠀⢰⠁⠀⠈⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⡀⠀⠂⠐⢀⣴⣅⡀⢀⢀⣐⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣦⠀⠀⠀⠁⢐⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠁⠰⠦⠀⠈⠀⠦⠀⠈⠉⣁⡉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢠⠆⡐⠀⠡⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢔⠛⠉⠲⢔⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⣶⣄⡀⠀⠀⠂⠔⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣗⡠⢀⠀⠀⠀⠀⠀⢦⠑⠐⡄⠀⠠⠂⡠⠀⢀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠒⠀⠀⠀⠑⠒⠌⠿⠆⠠⣟⣀⠘⠞
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡴⠩⢓⡲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀
⡼⠤⢅⣁⡒⠫⠥⣖⣭⡽⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡥⠒⠒⠒⠲⠭⣙⠲⢤⣀⡀
⡇⠀⠒⠠⠬⢭⣓⡲⠬⢍⣙⡒⠣⠽⣿⣷⣶⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡜⠁⢀⠀⡄⡘⡄⡰⡄⣍⢉⣹⡿⠁
⢳⡤⢤⣉⣐⡢⠤⢍⣙⡒⠲⠭⢭⣒⡲⣼⢡⣾⣷⣌⢦⠀⠀⠀⠀⠀⠀⠀⡇⣸⡄⢤⡀⣦⣘⣇⢿⣠⣷⣿⢎⡾⡇
⠀⠹⣇⣒⡾⣭⣙⣒⡶⡭⣍⣓⡲⠤⣍⣷⢸⣿⣿⣿⣏⣇⠀⠀⠀⠀⠀⠀⡇⣿⣸⣺⣷⣽⣿⣾⣿⡿⢟⡵⢏⢸⠇
⠀⠀⠈⠉⠙⠛⠾⢾⣽⣗⣗⡾⣭⣽⣒⡾⡜⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⡇⣿⣽⣿⣿⡿⠿⢛⣩⡴⠋⢱⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢾⣿⣽⣝⠿⠿⢏⡞⠀⠀⠀⠀⠀⠀⡇⢔⣋⣩⢤⠖⡞⢫⠀⠃⣂⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠓⠾⠶⠷⠷⠞⠛⠁
⠀⢀⠴⢶⢶⡒⠛⠛⠉⠉⠉⠛⠓⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢴⡄
⢀⣳⣿⣿⣿⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠈⢳⠆
⢸⣿⣿⣿⣿⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⣸⠅⠀⠀⠀⠈⠓⢦⡀⠀⠀⢠⠏⠀⠀⡀⠀⠀⠀⠘⢲
⠀⢪⡻⠿⢟⡽⠗⠚⠋⠉⠉⠳⡄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⢀⣀⠙⠲⠶⣋⣠⠴⠚⠀⠀⠀⠀⠀⢨
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⢴⡇⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⢉⣛⣭⣭⣤⣄⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⣭⣍⠳⡄⠀⣸⠁⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⡰⠋⠁⣠⠶⢤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣿⣿⣿⣧⢹⢪⡏⠀⠀⠀⠀⠀⢨⣇⠀⠀⠀⠀⠈⠀⠀⣴⠃⠀⠀⠙⠳⠦⣤⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⣿⣿⡿⣼⠞⠀⠀⠀⠀⠀⠀⠀⠼⣤⠀⠀⢀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⠭⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠒⠛⠉
⠀⠀⣀⣀⣤⠤⠶⠶⠶⢤⣄⢀⣠⢤⢤⣄⠀⣀⡤⣤⣤⡀⢀⡠⢤⣤⣄⠀⢀⡤⣤⣤⣀⠀⣀⡤⢤⣤⡀⠀⣀⣠⣀⣀
⠀⠸⡍⠀⠀⠀⢩⠉⠁⠲⣬⠋⠀⠀⠀⡨⠛⠁⠊⠀⠀⡹⠋⠀⠀⠀⢈⡿⠁⠊⠀⠀⣨⠟⠁⠀⠀⢀⡹⠛⠁⡀⠀⠈⣳
⠀⠀⡼⠂⠀⠀⠀⠄⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠁⠀⠀⠀⠠⠊⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠈⠀⡠⠊⠀⠀⠸⡇
⠀⠀⣳⠂⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠏
⠀⢰⡋⠀⠀⠔⠉⣠⡴⠅⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠀⣠⠦⠄⠀⠀⢀⣤⣄⣀⠀⠀⢀⣴⣅⡀⢀⠀⠀⠀⠘⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠓⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠓⡀⠈⠀⣰⠊⠀⠀⠒⠀⠈⢋⠑⠂⠠⣣⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠰⠴⠀⠛⠀⠐⠠⡄⠠⣀⠐⠒⢢⠍⠁⠀⠬⠒⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⢉⣀⣀⢰⠁⡀⠉⠀⠀⠀⠀⢀⡬⠇⠀⠀⠁⠀⠰⠛⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢐⠀⠉⠁⠀⠀⠀⠁⣠⠉⠀⠠⠀⠀⠀⠀⡀⠀⠑⠀⠘⠂⠉⣀⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠁⢀⠔⠊⡨⠃⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠁⠀⢈⣥⠘⢁⡀⠤
⠀⠀⠀⠀⠀⠀⠯⠠⠀⠀⢀⡎⠀⠀⠂⠀⠀⠀⢀⠀⠀⢴⠀⠀⠀⢀⠀⠀⠐⣉⠸⢂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠗⠻⠥⠄⢀⡀⠀⠀⠀⠀⠈⡛⢠⡴⠒⠁⠀⠀⠲⠆⠄⠀⠰⠀⢀⠁⢶
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠈⢀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠈⠛⡄⠀⠊⠀⠰⠄⠐⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠺⠤⠚⠂⠐⠦⢉⠦⣈⠀⠠⠀⠀⠘⣦⣀⠰⡀⠀⢀⡤⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠦⠊⡄⠀⠀⠀⠰⠏⠀⣀⠀⠀⠀⠐⠋⠠⠉⠀⠈⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠤⠒⠉⠀⠶⣤⠘⠛⠛⠉⠀⠀⠀⠀⠀⠴⠒⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢶⢁⡐⠲⠒⠀⠀⡀⠀⡈⠀⠄⠈⠁⣦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠉⠄⠀⠀⡵⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠔⣣⢀⣀⣀⠀⣀⣀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠈⠁⠈⠁⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠈⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⠤⠀⠈⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐



⣿⣿⡿⠻⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⢶⠀⠀⠤⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣦⡀⡄⠚⠁⡀⠀⠀⣨⠀⣤⠀⠘⣀⡐⠦⣔⠁⣄⡄⠗⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⢹⠀⢿⠛⠉⢁⠈⠧⡞⠙⢿⣀⣹⣾⡴⠟⠀⠀⠾⠆⡈⢃⣲⡤⣤⡸⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡯⡄⠀⣿⠴⠦⣠⡼⠀⡴⠆⠃⣠⠿⢍⣤⢤⠀⠂⢷⡦⣤⠾⠷⠴⣱⣤⠌⠻⠻⢆⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡐⢇⣀⠅⢠⣠⣋⢠⣾⠀⠠⠊⠹⣿⣟⣒⣒⠆⢰⡦⠄⢲⣹⠶⢤⣥⢾⠳⣤⣄⣾⣭⠏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠢⢭⡀⠀⢌⠙⣿⠛⠀⠁⠈⢰⣧⣄⣤⣤⠖⢋⣤⠸⢟⢧⡝⣺⠎⠽⣷⣜⣿⣟⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⢤⣀⠘⠓⠃⠠⢾⠉⠁⠚⠉⣹⠃⠈⠁⠀⣉⣠⠜⠉⠿⠷⠒⣛⣩⣽⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡛⠂⠀⠈⠁⠀⠀⠀⠐⠢⠀⠨⠥⢤⣤⣤⣤⣔⣶⣶⣶⣶⣿⣿⣿⣿⡟⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠐⣾⣿⣿⣟⣿⣿⡚⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢽⣿⣿⣿⣿⡿⣿⠏⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⢾⣷⣯⣿⣿⡷⠽⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣿⣿⣿⣿⣗⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⣿⣿⡟⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣤⣄⡀⢀⢀⡀⠀⢀⣘⣀⣨⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠊⠤⠬⠽⠿⠿⠟⠛⠛⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢿⢹⡿⡿⣿⡿⡿⣿⢿⡿⠿⡿⣿⡟⢿⣿⢿⡏⡿⡿⣿⢿⡿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣾⣶⣷⣿⣶⣷⣿⣾⣿⣷⣷⣿⣾⣾⣿⣾⣷⣷⣷⣿⣾⣿⣶⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⣤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠖⠒⠚⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠘⢿⡄⠁⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢺⠃⠀⠌⢠⠀⠀⢲⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠌⠀⡀⣠⡚⠀⠀⢨⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠠⠀⢀⢠⡇⠀⠰⡄⡄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠺⠅⠰⠂⠳⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠐⠂⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⠈⠀⣧⡈⠀⢁⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⡀⢢⠀⠀⠻⠊⢀⢩⠀⣠⡟⠧⠔⣃⢀⢌⡰⠶⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠊⢁⠀⢣⡀⢀⢨⡁⡘⣤⡇⠼⠀⢀⠈⠳⣈⣀⡘⠁⠀⠀⢠⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⢀⠇⠀⠀⠀⡀⠀⠔⠁⢈⣌⣭⣀⠈⢳⡤⢬⠞⠀⣛⠡⣒⠈⠓⠋⠹⠛⢾⣶⣂⡠⠄⠀⡀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⡄⢠⠠⠋⠀⠀⡁⢸⡚⠈⠓⠺⠭⠀⣠⡞⢊⠀⠤⠀⠀⢀⠃⠀⠀⡒⠒⠤⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢡⣆⠐⡴⢀⡄⠀⠨⠥⠳⠦⠤⣴⠖⠋⠀⠀⠀⢹⠇⠀⢠⠆⠌⣰⠞⠣⠀⡀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠾⠈⠓⠃⠋⢈⠴⢤⡄⠤⠔⠃⠈⠛⠳⠦⠤⡴⢿⣊⠁⠀⠀⠀⠆⠀⠀⠚⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠠⢀⣀⡴⠈⠀⠀⠀⢀⡠⠐⠈⠛⠀⠀⣤⠩⠶⠬⢠⠤⣤⠌⣀⠠⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠳⣔⢂⠖⠪⠉⠀⢀⠠⠀⣠⡀⢀⠀⠀⠈⢀⠜⠃⠐⠟⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡤⢀⠀⠀⠈⠣⠀⠀⠒⠀⠒⠂⠪⠍⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡴⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⠥⣐⡠⠤⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠠⣐⠂⠜⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣄⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣖⠈⠀⠀⢀⠀⣀⠈⠀⡔⠀⠆⠘⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠤⠐⠢⠄⠀⢱⡀⢀⠈⠙⠿⠀⢹⡀⢠⡀⠤⠀⡄⠆⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠓⠠⠀⠄⠂⣤⣀⣁⠈⣡⣤⠀⣀⠀⠀⠂⢀⡔⠖⠀⣣⠀⠹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠴⠀⠀⠠⢠⣤⢄⡀⠀⡍⢋⣀⡠⠈⠁⠴⠀⡐⠃⠀⡤⡀⠀⠠⠜⠈⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡖⠀⠀⠀⠁⠠⢀⠈⠀⢀⡻⠀⢄⠐⠎⡥⠀⠙⠀⠉⠀⠀⠄⠂⠀⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠋⠈⠁⠓⠁⠈⠁⠀⠠⡌⠁⠖⠀⠆⠘⠅⠀⠘⠶⠀⣀⠐⠈⠤⢀⠴⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡈⠂⡀⠠⣤⠘⠀⣤⠤⠄⠲⠀⠠⠄⠠⡓⠁⠀⠔⠲⠌⠅⠄⣸⠀⠈⢀⡀⠚⠃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠁⠀⠉⠀⠄⠀⠖⠁⠊⠒⠠⢀⡀⠷⠀⠁⠤⢡⡀⠠⢀⠀⢳⡀⠀⢀⠀⠁⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠰⠐⢇⠀⢀⠀⠀⠈⡜⠔⣄⠀⠙⠈⡂⢠⢀⠚⢁⠈⠀⢄⡀⠶⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⢆⠈⢀⠀⠠⡌⠂⡄⠓⠀⠠⠀⡀⠈⠒⠀⠀⠀⠀⠑⠂⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠘⠉⠻⠀⠠⢈⡄⠈⢡⢄⠀⠠⠔⠲⡄⠀⣀⣘⣀⠀⠰⡄⠀⢣⡀⠀⢠⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⢀⠀⠀⠀⠆⠐⠒⠀⠀⠀⠀⠀⢀⡹⠋⢙⠉⣭⡀⢄⡠⢀⠀⠉⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⡅⠤⠒⠤⠶⠤⢯⡀⢀⣀⠐⠈⠉⡀⠀⠀⢫⠰⠃⠐⠚⠁⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠐⠂⠀⣤⠀⠀⠀⠀⡀⠀⠀⠄⠘⠁⠈⢹⠀⠘⠁⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠒⢢⡄⠀⠤⠴⠀⢀⡀⠀⡀⠇⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠉⠲⠀⠄⠀⠀⠀⠀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠏⢸⠏⡼⢃⡠⣤⢀⡴⠆⣀⢤⡄⡠⡆⢀⡴⢆⢠⣄⣄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠘⠃⠉⠉⠒⠉⠛⠈⠉⠀⠃⠈⠐⠀⠈⠁⠘⠁⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠠⠎⡄⠀⠐⠂⢠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠭⠀⠀⠀⠀⠀⠐⢀⠄




⣿⣿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠉⡏⣿⣛⠋⠉⠛⢦⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⡇⢿⣍⠀⠀⠀⢈⣭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣿⡀⣧⢸⣭⣤⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣸⣧⢹⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⢣⢿⡌⣧⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⢋⡴⠋⠀⠻⣌⢧⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠷⣝⠶⣭⣛⡲⢤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⢴⣶⣶⣶⡾⣿⣶⣮⣭⣟⡲⠯⣝⡻⣿⣿⣷⣶⣶⣦⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠛⠉⠉⠀⣠⡶⣫⠷⣋⡵⢞⣭⠶⣟⣭⣷⣿⣷⣮⣝⢦⣝⢮⡻⣿⣿⣷⣄⡀⠉⠉⠛⠷⢦⣤⣀
⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⡀⢀⡼⢫⡞⣡⠞⣋⣴⡿⢿⢋⡉⠉⠟⠳⢛⠛⣻⣷⡙⣧⡻⣮⢿⡽⣿⢷⡀⣀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢾⣵⣏⡴⢟⣛⡭⠶⣚⣿⡥⠶⠶⠖⠚⣤⣤⠶⠾⢷⠘⣷⠹⡇⢿⠽⣿⡷⠟⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠾⠿⢿⣿⣶⣾⣶⣶⣶⣶⣶⣶⣬⣴⣶⠾⠶⠶⠆⠃⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣛⣛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⣛⣛⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠓⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣤⣴⠾⠿⠷⠿⠋⠀⠀⠀⠙⣷⡶⠶⠶⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠾⢇⣠⣴⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡶⠶⠶⣦⣄⠀⠀⢹⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⣰⡿⠉⣀⣤⣤⣼⠇⠀⠀⠀⠀⠀⣾⠛⢻⡆⠀⠀⢻⣦⣤⣤⡀⠙⢷⡄⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⢀⣤⡶⠿⠇⠀⠀⣿⠀⢰⡟⠁⠉⠁⠀⣠⣶⣦⣤⣴⠟⠀⣼⠇⠀⠀⠀⠀⠀⠈⣿⡄⢸⣷⠀⠀⠀⢸⣷⣤⣀
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⢿⣤⣼⠇⠀⠀⠀⠀⢻⣧⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⠏⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⣀⣸⣧⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀
⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⢛⣿⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠘⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠉
⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⢚⣛⠛⠲⣄⡀⢀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⢾⡉⠉⠓⠚⢧⡲⣛⣏⣤⠼⠋⠉⠙⠳⣄⡀⣙⣦⠶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠳⢾⡽⠚⠁⠀⣀⡤⠤⣷⠺⠏⣠⠤⠿⢥⣀⡈⣧⠤⠿⣯⢄⣀⣿⠷⣄⠀⠀⠘⡏⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢳⠀⢠⣴⡞⠸⡅⠀⠀⠙⣦⠞⠁⡴⡆⠀⣸⡋⠛⠚⠛⠒⠋⢉⣡⠴⠞⠓⠲⠾⣅⡀⢀⡟⠛⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⣝⢮⡛⠁⣩⠵⠒⠚⠛⢲⡀⠀⢸⡄⢀⡿⢃⡾⣿⠻⠙⠲⣦⣤⣴⠏⠀⣀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣤⢀⠀⠙⠳⢤⡀
⠀⠀⠀⠀⢀⡴⠋⠀⣠⡹⡼⠶⠻⢯⡙⣆⢠⠖⠋⠻⣷⠛⠉⢹⡄⢀⣏⣉⣤⣖⣦⡀⣿⠀⢘⣇⠸⢉⡇⢰⠚⠛⠲⣄⠀⣐⡆⣹⣿⢋⠔⣠⠀⠙⢦⡀
⠀⠀⠀⣰⠋⠀⢠⠰⣿⡟⠛⠓⣦⣤⣷⣼⢫⠀⠀⠀⣸⠂⠀⠀⢳⣏⢉⡽⠓⠺⠭⣝⠳⢤⣸⣉⠓⠲⠖⠋⠀⠀⠀⠙⠦⢭⡴⢋⠘⠛⠾⠥⠴⠖⠲⡝⣆
⠀⠀⢰⠇⠀⢀⡏⢸⠁⠀⢀⡴⠋⣤⣤⣽⣉⢰⠀⠀⢧⡲⢴⣖⠂⣼⠋⣩⣝⢦⠀⣸⠀⠀⣟⠻⠿⣥⣚⠉⠉⠹⡄⣼⣯⡀⢻⡺⣗⠦⠄⠀⠀⣿⡇⡿⠸⡆
⠀⠀⢸⡀⠀⠘⡷⠋⡼⢁⣼⡀⠀⠀⢠⡞⣿⣞⢦⣀⣀⡉⠲⠴⠖⣧⠀⠳⠟⠸⣧⠏⣠⠴⠛⠛⣋⣉⠉⠙⠦⡀⠙⠲⢭⣡⠿⠝⠺⡿⠥⠤⣄⡈⡞⠁⠀⡇
⠀⠀⠈⣧⠀⠀⢳⣰⡆⣞⢀⣳⡤⠤⣤⣙⡽⠞⠛⠉⠉⠙⢦⠀⠀⠸⡆⠛⠻⠀⢱⡎⠁⢀⡖⠛⠉⠉⢳⣄⣤⣧⡀⠀⢀⡞⠛⠳⣬⡭⠵⢦⣀⡽⠁⠀⣼⠇
⠀⠀⠀⢹⠳⡄⠀⠙⢧⡼⠋⠀⣠⠴⠋⠁⠀⣠⠀⡀⡤⢀⣸⣤⠤⠤⢿⡄⠀⠀⠀⢻⣴⣫⠴⢀⡴⠚⠩⠖⢒⡶⣍⢳⣯⢄⣀⡀⢹⠰⣏⡽⠋⠀⢀⠞⣽
⠀⠀⠀⠘⣧⣈⠳⣄⡀⠈⠳⢾⣁⠀⡠⢾⣷⣿⣯⣷⡾⠍⠀⠈⢷⠚⠉⠹⡄⠀⢀⡄⠙⢿⣴⠋⠀⠀⣀⣀⡈⠉⢯⠷⢳⣎⡼⣀⡼⠖⠋⢀⣠⢞⡡⢞⡏
⠀⠀⠀⠀⢿⣮⣓⠀⠙⠳⢤⣀⡈⠙⠓⠷⢯⣸⣄⠀⠀⠀⠀⠀⡼⠀⠀⠀⠹⣄⠃⢾⣙⡦⢹⡀⠀⣾⢁⣠⢹⣀⣸⡧⠴⠛⠋⢁⣀⡤⠞⠋⠴⣫⢴⣿⠃
⠀⠀⠀⠀⠸⣗⠦⠀⠀⠀⠀⠀⠉⠓⠲⠦⣤⣀⣉⡉⠙⠓⠒⠿⠶⠤⠤⠤⠤⠼⠦⠤⠭⠤⠼⠷⠶⠛⠛⠋⢉⣁⣠⣤⠴⠖⠚⠉⠀⠀⠀⠀⠈⠕⣫⡟
⠀⠀⠀⠀⠀⢻⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠲⠶⠦⠤⠤⠤⠤⠶⠶⠶⠒⠒⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣪⢿⠃
⠀⠀⠀⠀⠀⠈⣷⣌⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢛⡥⠚⣡⡞
⠀⠀⠀⠀⠀⠀⢸⡿⣟⠦⣌⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⢛⣩⡴⠞⢉⡤⠞⣹⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡦⣙⠮⣙⠲⢤⣈⠉⠓⠒⠦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⠒⠛⠉⠉⠀⠴⠚⠉⣁⡤⠞⢉⣠⢞⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢮⡳⢬⡛⠦⣌⡙⠓⠶⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⢋⣁⡤⠞⠋⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣝⠦⣍⠲⢤⣉⠓⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⣀⣠⠴⢚⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣗⢬⡙⠦⣌⡙⠒⠦⡄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠋⣉⡤⠖⣋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡳⢍⡳⢤⣙⠓⠦⣤⠀⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢋⣡⡴⢚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣍⠲⢬⣙⠒⠦⠀⣤⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣉⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⡢⢌⣙⠲⠄⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣙⡃⠲⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠴⠶⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠶⢤⡀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⢤⡀⢀⣤⣦⡄⠀⠀⡴⢶⣄⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣾⠃⠀⣇⣾⠃⢸⣧⠀⢸⠀⢸⣿⠀⠀⠀⣼⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡇⠀⢸⣿⠀⢸⣤⣾⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⠃⠀⢸⡿⠀⢸⠀⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⠀⠀⣸⡇⠀⣿⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠀⠀⣿⣧⠀⢸⠀⢸⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⡴⢶⣏⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠀⠀⣿⣿⠀⢸⠀⠘⣿⡇⠀⢸⣿⠀⢸⡆⠀⠀⠀⠀⠘⢷⣶⡿⠞⠁⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠀⠀⣿⣿⠀⢸⠀⠀⣿⡇⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⢸⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠉⠀⠀⠿⠿⠀⠸⠀⠀⠙⠃⠀⠈⠿⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠠⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⡀
⢀⡀⠀⣀⣠⣿⣿⡄⢠⡆⠀⠀⢠⡾⢋⣨⣿⠀⣾⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠚⢷⠀⠏⢻⣷⠘⣷⣾⠇⠀⢀⣿⠁⠈⠛⠉⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣤⣶⡄
⠀⠘⠀⠀⠈⣿⠄⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢀⣿⣿⢷⣦⠀⣠⣶⣶⡆⢀⣶⡿⢿⡇⠀⠀⣴⣿⡀⢀⣿⡟⢠⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⣸⡿⢁⣿⡟⢰⣿⡟⣽⠃⣼⣿⢁⣼⠇⢀⣾⠁⣿⡇⢸⣿⣵⠟⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣾⢿⡇⠘⣿⣇⠸⣿⣿⣁⣀⣽⣿⣿⣥⡶⢻⣧⣽⡿⢶⣾⠿⠿⣶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠉⠀⠈⠁⠀⠈⠛⠛⠋⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣀⣀⣤⣶⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠤⡄⢠⡖⢤⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⣄⢴⣲⡰⠿⣚⠷⣼⠢⣬⠛⢳⣦⣿⣅⠯⡬⢖⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢥⢻⡆⠰⣅⠙⣝⠋⣡⣟⣴⣷⢞⡝⢻⣧⣹⡚⠇⡞⢫⡍⠻⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠘⡄⣙⡖⢞⡠⢿⣦⣉⣷⢦⣯⣥⡛⣿⠛⡷⢻⣄⡟⣲⢿⡚⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣶⣾⣧⡘⢳⢶⣜⢏⢰⣇⢷⠤⣻⣇⣿⢣⡖⣻⣋⣧⣼⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢛⡓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡴⢦⠀⣷⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡞⣠⠏⠠⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣇⠀⠛⠋⢠⠖⠦⠀⠀⠴⠒⢦⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤
⠀⠀⠀⠀⠀⠀⢨⠃⠘⣦⠄⠈⠳⢤⡀⠀⢳⣷⢀⡀⢈⣾⡇⠀⢸⡄⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⠀⠤⠼⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠲⡀⢠⡃⠀⠀⠀⠉⠢⡙⠉⣄⣠⠅⠉⠁⠀⣤⣷⠋⢡⣖⢲⡄⠹⣤⣄⡀⠀⠀⢀⡧⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣯⣀⠀⠀⣀⣠⣽⡄⠨⠜⠀⣀⡴⠒⠾⠚⠀⠤⠦⠀⣀⢤⡀⠶⠍⠳⣤⣀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⢋⡇⠀⠀⢸⠷⠖⠒⡲⡒⠒⠒⠉⠙⠧⠐⠉⠉⠉⣩⡉⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠖⠊⠀⠀⠀⠘⡇⠀⠘⠖⢃⣖⡉⡒⠀⠀⢘⡭⡓⠀⠘⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣀⠀⢢⡀⠀⠀⠀⠀⠀⢻⡀⠠⠶⠀⢸⣷⡀⣀⣂⣸⣿⠇⠀⢠⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⣧⠀⡇⠀⠀⠀⠀⢀⠀⣹⠀⠀⠀⢀⣉⠀⠹⠝⠀⠀⠀⠀⣠⣀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⡤⠃⢀⡇⢀⣤⠴⠞⢁⣠⣿⢠⣤⠀⠙⠃⢀⡀⠀⠐⠓⠀⡀⠓⠚⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⡟⣁⣈⣤⠴⠚⢹⣿⡽⣦⠥⠤⠤⣴⡟⠉⠓⢲⣶⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⠇⠀⠀⠀⠀⢿⣇⡀⠀⠀⣠⣿⣇⠀⠀⢸⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣿⣿⠀⠀⠀⠀⠀⢸⡄⣇⠀⠀⢯⣤⣼⠆⠀⣯⣁⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣻⣯⣴⠿⠃⠀⠀⠀⠀⢸⡟⢙⣄⡴⠋⡠⠞⠁⠀⠘⠷⢤⣉⣓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣳
⠀⠀⠀⠀⢺⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣛⣿⣭⡽⠿⣷⣶⣿⡿⡿⠿⠟⣿
⠀⠀⠀⠀⢸⣿⣿⣷⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⢿⡟⣿⢸⡶⣬⠁⣌⠠⣶⣉⣐⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⡇⡟⢸⡏⠛⣭⢗⢹⣆⢗⣸⣧⣽⡧⠼⠮⣶⣛⣻⡿⠉⢯⣵⠶⢾
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣧⡦⠧⣄⣖⣑⣳⣯⣭⣽⡷⠶⠶⣛⣛⢛⣋⡩⠍⣠⠞⠁⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⠿⠿⠛⠛⠋⠉⠉⠁⠀⡠⡤⠶⠏⠸⣇⢰⡏⣷⣴⠇⠀⠀⠀⠀⢸⠅
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⣀⣀⡼⠋⢘⡀⣸⡿⠓⣬⡄⢠⡿⠀⠀⠀⠀⠀⠰⡂
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⡦⢄⡛⠰⠘⢛⡉⣴⣪⢉⣷⠞⠁⠀⠀⠀⠀⠀⠨⡂
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⡜⡁⣬⠒⡿⣩⠡⣶⣛⠵⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣤⣀⣀⣠⣶⡿⢁⠠⡃⠐⠾⣤⡍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⠿⠋⡹⠛⢉⣰⠝⢢⡣⠠⣦⡀⢪⣁⠐⠖⣆⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⠒⠊⣩⠲⠮⢍⣐⠻⠭⢀⡈⠛⢐⣇⣷⣌⣹⡿⠿⣿⣶⣄⡀⠀⠰
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⠛⣁⡠⣀⠱⢪⠈⣷⠂⠘⠛⠛⠛⠉⣤⣤⢤⠰⢶⢻⣿⣿⢻⠄⠨
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠸⠚⠡⡀⣀⡄⢸⠖⢬⡹⠭⠏⠁⠠⣀⣜⣑⡀⠃⡈⠘⣿⣿⣿⣄⠈
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠰⠰⠿⠟⠛⢒⣒⠓⡦⡙⠳⠦⣄⣈⠉⣧⣤⣁⡉⠛⡝⣿⢿⣯⠏⢐
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠸⠒⠶⠤⣤⢤⡤⠬⠇⡌⢓⣠⢀⡈⠀⡇⢙⠆⠈⣠⡾⢁⣰⠏⠀⢐
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⡂⠉⠉⣠⠀⣴⠖⠒⢋⠈⡉⢬⢓⣨⡃⣀⣴⠞⠉⢰⡿⠁⠀⠀⠠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⠄⠒⠊⡁⢀⠼⠀⢄⣂⣠⠧⡤⠔⣟⡿⠟⣁⣾⠾⠛⠁⠀⠀⠀⠨
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢰⣤⠀⢤⠆⠐⠒⠒⣖⣂⡶⠴⢓⣪⠡⣖⣻⡿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢰⣭⠤⠴⢒⣒⣿⣿⣭⣵⣶⣿⠿⠚⠉⠉⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴
⠀⠀⠀⠀⠘⢿⣿⣿⣿⢸⣿⡿⠿⠿⠿⠿⠟⠛⠉⠁⢀⣀⡀⠤⠤⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣬⣀⣀⠤⠤⠔⠒⠂⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠔⠒⠒⢒⣒⣒⠒⠒⠲⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣋⣭⣤⣶⣾⣿⡿⠿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣶⣦⣬⣍⣓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣩⣴⣾⡿⣿⠋⠉⠉⡿⠉⠀⣀⣀⡤⠤⠤⢽⣟⠛⠻⢿⡿⠟⠿⢿⣿⣿⣶⣬⣑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣩⣶⣿⣿⣿⣁⠀⢹⡄⠤⢼⣁⣴⡞⠉⠀⠀⠀⠀⢀⡨⠳⣄⠀⠹⡄⠀⠀⠈⠻⣿⣿⣿⣷⣮⡑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⣾⠟⠩⠀⡤⠀⠈⢧⣤⣱⣄⠠⠘⢇⡀⣰⡴⠤⣤⣠⠉⠀⠀⣼⠀⠀⢹⠒⠉⠙⠲⢿⣀⠀⠹⣿⣿⣦⡙⢆
⠀⠀⠀⠀⠀⠀⡰⢣⣾⣿⠃⣀⣀⠤⠤⣀⣠⠏⢀⣤⡽⠿⣶⣶⠸⠷⠖⠛⠁⠈⣑⣖⣾⡁⠀⠀⣸⢄⣀⠀⠀⠀⠈⢻⡥⠿⢿⣿⣿⣦⡳⡀
⠀⠀⠀⠀⠀⡼⣱⣿⣿⢫⠏⠁⠀⠀⠀⠀⠈⠳⣿⡀⢉⠀⠠⠀⠉⠲⣄⠀⢠⠋⠁⠀⠹⣷⠤⠞⠁⠀⠈⠳⣤⡀⢀⡠⠃⠀⠈⣿⣿⣿⣷⡹⡄
⠀⠀⠀⠀⢰⢱⣿⣿⡿⣿⠀⠀⣠⣴⢦⡀⠀⠀⣸⢿⠾⠶⣄⣀⡀⠀⠈⢷⠟⣦⠠⠖⣪⠈⠓⠶⢲⠓⢦⡀⠈⡏⠉⠀⠀⠀⢀⣇⠘⣿⣿⣷⢹
⠀⠀⠀⠀⡇⣿⣿⣿⡞⠉⠉⠉⠁⡸⠒⠉⠉⣉⣠⣿⠀⠀⠈⢿⠁⠉⠑⢿⢷⢚⣶⣾⣊⣄⠀⠀⠀⣤⡴⠳⢤⣇⠀⣀⣠⣞⠁⠈⠙⣜⣿⣿⡇⡇
⠀⠀⠀⢰⢱⣿⣿⡟⠀⠀⠀⢠⣊⣤⣄⡀⢺⠁⠀⠈⢢⣀⣠⡜⠢⣤⣴⡾⠛⣏⠀⣼⠉⠉⠉⠉⡙⡏⠀⠀⢴⠀⠙⣏⠀⢸⠀⠀⠀⢸⢹⣿⣷⣿
⠀⠀⠀⠸⡸⣿⡇⢳⡀⢀⠴⠛⠁⠈⠀⣹⠙⢳⣤⣤⣄⠀⠉⠙⢻⠋⢡⡄⠀⢹⡆⠉⢦⣀⣡⠽⢯⠘⠢⣤⠀⠀⠈⠘⡤⠋⠀⠀⠀⡼⠀⣿⡿⣿
⠀⠀⠀⠀⡇⣿⡇⠀⡷⠁⠀⠀⢂⣼⡺⣅⡤⠒⠦⣉⣙⣇⠀⠀⣼⠓⢦⣠⢤⣞⠀⠀⢸⠋⠀⠀⣸⠟⠙⠛⢷⡀⠀⠀⡇⢠⠞⠉⢾⡁⠀⣿⡇⡏
⠀⠀⠀⠀⢸⡸⣇⢰⠇⣁⡀⢀⣎⣀⣘⣿⡀⠀⠀⠉⠻⠮⠷⠾⡁⢀⡼⡷⠚⠾⠳⠦⢮⡘⠃⢰⠃⠲⡀⠀⣸⠓⠀⣄⡟⣇⠀⠀⠀⣧⢠⡿⣸⠁
⠀⠀⠀⠀⠀⢳⡹⡜⡇⠉⠀⠀⣧⠀⠊⠻⠷⣄⠀⠀⠀⠀⠀⢀⡇⠘⣆⠠⡄⡠⠀⠀⠐⠉⢦⣿⠀⠀⠀⢸⠷⠷⠦⣞⣀⡾⠀⠂⠀⡟⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠳⡝⢟⢾⠶⠊⡟⢤⡄⠀⠀⠈⠑⢦⡤⢤⣶⠯⢄⡀⢸⡏⠉⠙⢢⡀⠀⠖⠂⢿⡄⠀⠀⠸⣀⠅⠀⠀⠍⢲⡄⢀⣼⠟⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⣄⠸⡇⠀⠉⠓⠦⠬⠥⣤⠚⣿⠁⠀⠀⢳⣤⠇⠀⠀⠀⣷⣀⠀⣠⣜⠛⣆⢀⢘⡹⠦⣀⠀⠴⠆⢷⡿⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⢿⣦⡀⠀⠀⠀⠀⠈⡆⢸⡀⠀⠀⠸⡇⠀⠀⢀⣴⠥⠭⢭⡝⠉⠙⠚⠛⠉⠀⠀⠈⣆⣠⠖⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠬⣙⠳⢶⡶⠶⡋⠁⠈⢇⠀⠀⠀⠈⠛⡟⠁⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⣀⠤⢞⣩⢴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣙⠲⠬⣍⣛⠲⠤⣬⣷⣤⣀⣀⡴⠃⠀⢀⣴⣲⣄⣤⡬⠷⠒⣚⡭⠴⢚⡩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣈⠉⠑⠒⠲⠦⠤⠭⠭⠭⠭⠭⠥⠤⠴⠒⠒⠋⢉⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⡠⠤⠤⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⡼⡇⢰⠉⢳⠀⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣆⡇⡇⠸⡤⢼⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠉⠀⢻⠀⠇⠘⠇⠈⠓⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠴⠖⠒⠒⠒⡒⣖⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢛⣿⣿⠀⠀⠀⠀⠸⠖⢢⠀⠀⢸⠛⠒⠒⠶⠛⠛⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣠⡼⠟⠁⠈⢧⠀⠀⠀⠀⣈⡹⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠛⠉⠁⠀⠀⠀⠀⠀⠑⢦⣄⣀⣃⣠⡴⠏⠀⣀⠴⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⡴⠋⠉⠓⠂⠀⡄⠩⡉⢭⠒⠊⠈⢧⠀⡀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠘⡇⠀⠀⠀⠀⢰⣃⣠⡇⢸⡤⠤⠀⠘⣏⢀⣠⣤⡴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⡘⠢⠤⡄⠀⢸⠁⠀⡇⢸⣆⡠⠄⣠⡽⠽⠟⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⢷⡡⢄⣤⠮⢤⣄⠁⠀⠠⢴⡼⠁⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠙⠋⠀⠀⠀⠈⠳⠗⠛⠻⠁⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡾⣇⠀⠀⠀⠀⣤⠞⢦⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡞⠀⢻⡀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⠃⠀⠈⢳⡄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠋⠀⠀⠀⢻⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⢰⣟⡾⣏⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠈⢷⡀⠀⠀⠀⠈⣿⣷⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⢿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣷⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⣰⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⡄⢰⣿⣿⣿⣿⣷⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⢿⣿⣿⡿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⡆

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠿⣿⣶⣶⡿⠿⠿⣷⣶⣾⡿⠿⣿⣶⡄⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠻⣿⣦⣤⣤⣾⡿⠃⠀⠀⠀⢹⣿⡄⠀⠀⢀⣾⡿⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣿⡄⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⣼⣿⠿⢿⣶⣾⡟⠀⠀⠀⠀⣸⣿⠁
⠀⠀⣀⣤⣤⣀⠀⠀⢠⣿⡟⠁⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠙⣿⣧⠀⠀⢀⣠⣿⣇⡀
⣠⣾⠟⠛⠛⠿⣷⣤⣾⡿⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣄⣀⣀⣀⣠⣤⣴⣿⠿⠋⠀⠀⠀⠀⠀⠸⣿⣦⣴⡿⠟⠛⠛⢿⣷
⣿⡏⠀⠀⠀⠀⢹⣿⡉⠀⠀⠀⢀⣀⣀⡀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⣻⣿⠁⠀⠀⠀⠈⣿
⢻⣿⠀⠀⠀⠀⠀⠻⣿⣶⣴⣶⡿⠟⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠿⣷⣶⣴⣾⡿⠋⠀⠀⠀⠀⢰⣿
⠈⢿⣧⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠈⢻⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⠋
⢠⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣦
⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿
⣿⣏⠉⠉⠙⠛⠿⢿⣷⣶⣶⣶⣶⣶⣶⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⢿⣷⣶⣶⣶⣶⣶⣾⣿⠿⠟⠛⠉⠉⢉⣿
⢿⣿⠿⠿⢿⣷⣦⣤⣀⣈⠉⠉⠉⠉⣀⣀⣤⣴⣶⣿⠿⠿⠿⠿⠿⢿⣿⣶⣦⣄⣀⡈⠉⠉⠉⢉⣀⣠⣤⣶⣿⠿⠿⢿⣿
⠸⣿⡄⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⣼⣿
⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⣱⡤⠔⠚⠉⠉⠉⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⣠⠔⠋⠁⠀⢀⡤⠔⠂⠉⠉⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠔⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⠋⠀⠀⠀⠀⢀⠭⠖⠀⠈⠉⠁⠰⣦⣠⡔⢎⢠⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢁⠽⠂⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠆⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠠⠁⠀⠀⠀⠀⣇⠠⠄⢀⡀⠀⡴⠒⠀⠀⠀⢀⠔⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠛⠢⠤⠤⠤⠔⢇⢐⠎⠀⠆⠀⠀⡀⠀⠀⢂⢙⡆⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠁⠐⠦⢄⠀⢀⡜⠈⠆⠈⠀⠀⠒⡄⠀⠀⠂⣈⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢄⣀⣠⠜⠀⠀⠈⠁⠀⠀⠈⠀⠀⣤⣤⠜⠣⡔⠃⠉⠉⡀
⠀⠀⠀⠠⠰⠆⠒⠒⠒⠒⠊⢉⡳⢄⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⢹⠓⠰⠑⠂⠀⠚⠀⠀⠔⢒⠒⠄
⢇⢤⣴⠒⠒⠒⠒⠒⠂⠀⠀⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠁⠸⠠⠜⠀⠘⡆⢀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⢉⠳⢄⣀⠤⣖⡦⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠘⠑⠒⠉⢐⡔⠉⣔⡀⠢⡀
⠀⠀⠀⠀⣰⡫⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠈⢢⣀⡠⠃⠐⠁
⠀⠀⢠⠐⠉⢀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣼⡤⠊⠈⠂⠀⠀⠀⠀⠁⠀⠀⣠⠃
⠀⠀⠈⠀⢯⠀⠀⠀⢀⠀⠀⠑⡀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠔⠒⠒⠊⡅⠀⠀⠀⠀⠀⢀⡜⠁⢠
⠀⠀⠀⠀⠈⢣⠴⠋⠀⠀⠀⠀⣁⣀⣀⠤⠤⠐⢯⠀⠀⠀⠀⠀⠀⡀⠆⠀⠐⡀⢀⡀⠀⠀⠀⠈⠢⠴⢂⢱
⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢀⡔⠉⠁⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢀⡤⠁⠘⢬⠤⠋⠀⡴⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸⡦⡄
⠀⠀⠀⢸⣄⠀⠀⠀⠀⡠⠋⠈⢱⠊⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠈⠤⠀⠔⢡⠘
⠀⠀⠀⢿⠈⠓⠠⠄⠊⠀⠀⢀⡇⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠈⠣⠀⠀⢰⠀⠀⠀⡃⠀⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠖⠢⡐⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠰⢡
⠀⠀⠀⠀⠀⡆⠀⢰⠀⠀⠀⠑⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠔⢄⠀⠀⠀⠀⠀⠀⠀⡠⠐⠊
⠀⠀⠀⠀⠀⠧⠔⠃⠀⠀⠀⠀⢰⠀⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠼⠀⣀⠠⠀⡀⠈⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⡄⠃⢸
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠭⠍⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⠄⡠⣠⠃⠀⢀⡀⠀⠀⡀⠀⠀⢠⢀⠸⣘⣧⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁⡠⠒⠉⠀⡀⠄⢁⠠⢀⡠⠴⠋⠁⣧⣰⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⢀⠔⠉⠀⠀⠀⠀⠁⣠⠴⠊⠁⢠⢠⠗⢋⡹⢤⢼⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡸⠁⡠⠚⠁⠀⠀⡐⠀⣀⠔⠋⠀⡀⡄⠘⢈⡤⠖⠉⠰⣰⢠⡠⡖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⢱⠈⠀⠀⠀⠀⢀⡵⠊⠀⠀⠀⠀⢁⡠⠚⠁⠀⡀⢃⠁⣫⠼⢓⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢻⣇⠀⠀⡠⠖⠁⠀⠀⠀⠀⡠⠖⠉⢀⠀⠀⠂⢁⡤⠊⢁⢀⢠⠰⠄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠑⢾⠐⡄⠀⠀⣠⠔⠋⠀⠀⠘⠀⠀⣠⠔⠋⠀⡀⡀⠎⢀⠴⠊⡉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⠔⡋⠀⠀⠀⠀⠃⡡⠖⠋⠀⠀⠠⠀⠐⣠⠖⢁⢠⢡⠁⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠢⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⢀⡠⠊⠁⠰⠈⠨⠘⡠⢎⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⠉⠁⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠰⡀⠄⣢⠴⡋⢌⢂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠙⠁⣀⠤⠒⠉⠀⠀⡀⡄⠆⣀⠴⡎⢃⠱⣈⡴⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡉⣀⡀⡀⠀⠀⢀⡠⡔⠊⢥⠑⣈⣤⠖⠉⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡠⠄⠒⠋⠁⠂⠐⣈⡴⠞⠉⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⡤⠖⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠍⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠸⠳⡄⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣀⡤⠴⢂⡀⠀⠀⠀⠀⠀⠀⢠⠁⠃⡙⣄⠀⡜⢱⣲⡄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⢸⠘⡄⢣⡀⠤⠃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⡇⡄⡆⢂⠇⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⡄⠘⡘⠸⡰⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠁⢀⢣⠡⢃⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠰⡈⠀⡐⣢⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⢀⠀⠀⠀⢀⢁⣦⢡⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢠⠀⠄⣨⠕⠉
⠀⠀⠀⠀⠀⡔⠓⠒⠂⠀⠤⠀⠰⠦⠤⣄⣀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠘⢀⠁⠆⠀⠀⠃⢂⠆⣂⠤⠊
⢀⣀⣀⠀⠀⠓⠶⠦⣤⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⡈⡀⠀⢈⡨⠔⠋⠁
⢣⣀⣀⠈⠁⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠰⠀⠀⠰⠀⢀⡀⠔⠊⠁
⢎⠉⠙⠛⠶⠶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡆⠆⣀⣁⣤⠤⠖⠊⠉
⠈⠹⡷⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢀⠞⠉
⠀⠀⠑⠲⢦⣦⣄⣀⣀⡀⠀⠀⠀⠀⢀⠀⠆⠂⣡⠔⠁⢀⡀⢀⡀
⠀⠀⠀⠀⠈⠢⣤⣤⣤⣀⣠⡀⣀⣥⠠⠴⠒⠋⠁⠀⠔⠁⣸⡆⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⠁⠘⢠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⣶⡆⠈⠃⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢿⡟⠋⠉⠉⠙⠻⡆⢛⣛⡷⠶⢾⣛⡉⠙⣷⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⣠⡿⠶⠶⢿⣤⣠⠟⠛⠛⠒⠛⠉⣉⣿⣎⡉⠉⠻⣿⣿⣿⣿⣟⠛⠛⢷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⣾⠋⢀⣤⣤⡀⠈⢿⣦⣤⣀⣀⣤⠞⠁⠀⣈⡟⠛⠳⢾⣍⠀⠀⠈⠻⣦⠀⢻⡆⢀⣴⣶⣦⣄
⠀⠀⠀⣠⠞⠛⠻⣿⡀⠀⢻⡀⡿⠷⠿⢷⣤⠟⠁⠀⠈⠙⢷⠤⠀⣾⠿⠶⠲⠦⣄⠙⢻⣦⣤⣄⣸⠟⠛⠛⠻⣦⡀⢈⡿
⠀⠀⠀⣏⠀⠚⠋⠙⠛⢿⣷⣿⣁⡀⢀⣀⣿⣀⣤⣶⡶⣶⣤⠖⠋⠉⢹⣄⠀⠀⣸⣶⢟⣥⣤⡀⠈⢳⣶⣄⠀⠈⣷⣿⣷⣆⣤
⣤⣄⡀⢠⣤⣤⣤⣤⡴⠋⠉⠀⠉⠙⢿⡏⠁⠀⠀⠀⠉⠛⠧⠀⣰⣞⣋⡙⠻⠞⢿⣅⢉⡉⠉⠛⢆⣼⠟⣿⣠⡴⣟⣯⡿⠛⣽
⢻⣿⠛⠷⢿⣽⣿⣿⠷⣴⣿⣷⣄⡀⠘⡿⢶⣶⢶⣶⠤⠤⠤⠤⠿⠋⠉⣠⣄⡄⠀⢹⣧⣻⡄⣀⣤⠿⣞⣯⣷⠿⠛⣁⣤⣾⡿
⠀⠻⣷⣄⣀⠈⠉⠛⠻⢶⣦⣬⣍⣙⡛⠛⠿⠿⢶⣿⣤⣤⣄⣀⣀⣤⣾⣿⣛⣡⣤⡼⠿⣛⣯⣽⡾⠿⠛⢉⣠⣴⡾⠟⣹⡿⠁
⠀⠀⠙⣿⡍⠛⠲⠦⣄⣀⠀⠉⠉⠛⠛⠿⠿⣶⣶⣶⣤⣭⣭⣭⣿⣿⣿⣭⣭⣽⠶⠿⠛⠋⠉⣁⣠⣴⣾⠿⠛⠁⠀⣰⡿⠁
⠀⠀⠀⠘⢿⣆⠀⠀⠀⠉⠉⠛⠲⠶⢤⣤⣀⣀⡀⠈⠉⠉⣿⣿⣿⠉⠉⢉⣀⣀⣠⣤⣴⣶⡿⠿⠛⠉⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⢿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠶⠶⠶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⣰⠟⠁
⠀⠀⠀⣀⣀⣤⣤⡴⠾⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠉⠀⠀⠀⣠⡾⠋
⠀⠐⢿⣯⣉⠁⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠈⠉⠛⠻⠷⢶⣶⣤⣤⣀⣀⠘⣷⢀⣠⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠶⢶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠤⠤⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠛⠷⠤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⡄⠀⠀⠀⠀⠀⠀⠀⡖⠉⠨⢽⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠈⠀⠀⠀⡀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠘⢋⡄⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢀⣿⣿⣷
⠀⠀⠀⠀⢠⣾⠃⠀⢻⣿⣆⠀⠀⠀⠀⠀⣶⣿⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡻⣿⣿⠁
⠀⠀⠀⠠⣿⣯⣦⡄⠀⢿⣿⣆⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠹⢿⣿
⠀⠀⠀⣰⢏⣾⣿⣅⣀⣼⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠠⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⣏⠈⠻⣿⣿⣿⠿⠟⠋⠉⠙⠿⢶⣷⣾⠶⣤⣀⣀⣀⣤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⠳⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠴⠖⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢤⣉⣁⠂⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣉⣁⠃⠰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣍⣽⢻⣃⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠐⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣽⣿⣿⡛⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⣀⠒⠰⢶⡂⢀⡀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⠇⠀⠀⠀⠀⣠⣼⠟⠁
⠀⠀⠀⠀⠈⠻⣦⡤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣦⠀⠉⣥⠀⠀⠉⠐⢺⢆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣻⠏⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠀⠀⠀⠀⠐⠠⣀⢀⡀⠀⠙⠚⠻⠗⠀⠀⠖⠀⠟⠀⠀⠀⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⡄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣴⣆⣄⠀⠀⠀⠀⠠⣿⡅⠀⠀⠀⠀⠀⠀⣠⣾⠟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣻⣶⣴⣶⣧⠀⠛⠀⠀⠀⠀⠀⢀⡴⠛⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠐⣡⣸⠗⡹⣋⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⡶⠒⠒⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡤⡄⢘⡅⣩⣀⣌⠛⣾⣏⣸⢿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⢤⠷⠈⣯⢁⣽⡧⠤⠵⠷⠾⡵⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠁⠀⠀⠀⠀⠱⣧⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⣡⡄⣀⠁⠉⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠖⠂⠀⠀⢈⠀⡀⠀⠆⡀⣤⣠⢂⣀⡰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢻⠂⢿⠗⠋⠁⠫⣴⠒⢿⣀⣷⣦⣼⠋⠀⠼⠆⡙⢂⣦⢤⡸⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⠀⢻⠶⠶⣤⠆⠠⠶⠐⣠⠾⣉⡤⠤⠐⠰⡦⠦⠚⠷⠞⣦⡄⠙⠛⢦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⠘⢤⡄⠠⡴⣀⣰⡇⢀⠈⡙⡿⠿⠿⠷⢀⡾⠆⣸⡼⣒⣶⣶⣟⠧⣤⣾⡼⣣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣬⣒⠆⠀⣢⣈⡏⠁⣠⣀⣰⡷⣶⡶⢾⠉⣴⠀⢫⣵⣯⠟⣒⡻⢿⣿⣯⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡛⠒⠠⠍⠁⠘⠃⣀⠀⠠⠞⠀⠀⠀⢐⣒⣃⣀⣋⣭⣵⣶⣾⡿⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠆⠅⠀⠀⠀⠀⠀⠀⠁⠈⠟⡙⡿⢿⡟⣿⣿⣿⡿⣿⣿⢿⡽⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⠿⢿⣿⣿⣿⣿⣷⡾⠑⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⡮⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⡞⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣽⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⡄⠠⠠⢤⣄⣤⣥⣤⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⢻⢹⠿⢿⣿⢿⢻⢿⡿⡻⣿⣿⡹⣿⢿⡏⡿⢿⡿⣿⡿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⣀⣀⣤⢤⡀
⠀⠀⠀⢠⡞⠉⠉⠀⠀⢸⠁
⠀⠀⠀⢸⠃⢠⠀⠀⠀⡍
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣾⠀⠀⠀⠀⢰
⠀⠀⠀⡇⢠⠀⠀⢀⡿
⠀⠀⢰⠇⠘⠀⠀⢸⡇
⠀⠀⣸⠀⡇⠀⠀⣼⠁
⠀⠀⣿⠀⡇⠀⠀⣿
⠀⣸⣿⠀⣇⠀⠀⠸⡄
⣰⠇⣿⠀⣇⠄⠀⠀⠈⡒⠤⡀
⢻⡃⣿⠀⢹⣠⡐⢄⣀⠈⡁⠈⢢
⠀⣷⣿⣷⡸⠋⠀⠀⠈⠙⠙⢶⣸⡀
⠀⡽⢹⣿⣿⡀⠀⠀⠀⠀⡦⠀⢹⣿⠙⢦⣀⣀⣀⣀⣀⣠⠤⠴⠒⠒⠒⠛⠛⠓⠲⠶⢶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣄
⣸⢣⡟⠁⠈⠇⠀⠀⠰⠚⠁⠀⣸⣯⠀⢀⢩⠭⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡿⢸⠇⠀⠀⠈⠲⠤⠤⠤⠴⠶⣿⡏⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠖⠶⠶⠴⠶⠶⠾
⡇⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠴⣷⣖⣶⣶⠶⠶⠦⠤⣤⣄⣀⣀⣀⣀
⢧⡀⣨⠓⠀⠀⠀⢀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠓⠒⠀⠁⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠉⠛⠒⠒⠚⠛⠛⠋⠉⠉⠛⠛⠛⠿⢶⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣶⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠘⣤⣀⣀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠑⠆⠀⠃⡀⠀⠀⠀⠀⠀⠐⠀⡾⢷⠀⠀⠀⠹⣯⡀⠀⠁⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⠀⠀⠀⠀⠀⢁⣿⡆⠀⠀⠀⢿⣷⣤⣤⡠⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠈⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠃⠀⠀⠀⣼⡿⠁⢸⣷⡀⠀⠈⠛⠿⠿⠷⢾⠷⡦⠤⡤⠴⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⢘⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠀⣀
⠀⠀⠀⠰⠀⠀⠸⠟⠀⠀⠈⠳⣤⣤⣀⣀⣀⣴⣴⡴⠟⠋⠙⠿⢿⠿⡿⠋⢹⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⠀⢋⣄⠀⠉⡀⢋⡄
⠀⠀⠀⠀⠂⠀⢰⡆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⣠⣬⣃⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣤⣶⣦⣴⣤⣤⡄⠒⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⡗⣫⣾⠀⠀⠀⠀⠐⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠰⠟⠐⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⢀⠉⠙⠻⠟⠛⠛⠛⠓⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⣾⣿⡿⣿⠅⢀⣤⣤⠀⣤⢤⣄⠀⣀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⠀⢀⣴⣿⡿⠢⠀⠀⠀⠸⠏⢫⠤⠁⣠⣿⠀⠈⢣⡀⠀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠠⠤⠀⠀⠀⠀⢀⣼⡅⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⠀⠀⠑⠚⠒⠉⠋⠁⠀⠀⠀⠃⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⡆⠀⠀⠀⠀⢀⣰⣶⣾⡿⠁⠀⠀⠘⠁⠀⠀⢀⣀⢠⢐⢋⢭⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠙⠇⣠⣤⣤⣾⡿⠿⠛⠉⠀⠀⠀⠀⡄⠀⠀⠀⠑⠓⠛⠘⠂⠚⠛⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠈⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡄⢀⣿⣄⣠⣤⣶⣶⣿⡚⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣶⣿⣿⣿⣇⠈⠘⣿⣿⣿⣿⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⡄⠠⣿⣿⣿⣿⣯⣿⡟⢟⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⡘⣿⣿⣧
⠀⠀⠀⠀⠀⡴⠀⢸⣿⣿⣿⢻⣿⣿⣿⣿⣿⡆⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆
⠀⠀⠀⠀⠈⠁⠀⢸⣿⣿⠇⠘⣿⣿⣿⣿⣷⣧⣇⠸⣿⣿⣿⣿⣿⣿⣿⣯⡿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣏⣣⢸⣿⡏⢿⣷⣿⣿⣟⣱⣿⠀⡐⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⣿⣿⣿⣿⡟⠹⣿⣿⡇⣇⣿⣿⠈⢿⣿⠟⠈⠋⢩
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⡿⠋⠀⠀⣿⢿⣷⣿⢹⣿⣇⠀⠳⣦⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣼⣿⠏⠁⠀⠀⠀⢿⣿⣿⣿⣇⣬⠻⣆⠀⠙⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠙⠷⢤⡹⣷⣦⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠸⡄⠀⡘⡆⠀⠀⣤⣿⣿⠋⠀⠀⠀⠀⠀⠀⠑⣿⣷⣼
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠑⠤⣀⣀⣠⣴⣿⣾⣷⣄⣴⣾⣾⣖⡀⢄⣰⣽⣿⢺
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣀⣄⠄⣤⣾⣿⢟⡿⢹⣿⣿⣿⣿⣿⣿⣿⣻⡾⣿⣯⣿⠂
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣉⡀⠘⠻⠿⠿⣿⣿⣷⣾⣏⣰⣟⣽⡟⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⢻⣿⣿⣽⣧⣿⠻⠲⢦⣤⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣦⣤⣀⠈⣂⣤⣀⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣷⣦⣬⡉⠳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣷⣶⣬⡉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣷⣼⣤⡂⠄⡀⠀⠁⠂⠄⣀⠉⠚⢥⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠁⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣷⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⡂⠬⠩⠳⠦
⠀⠀⠀⡠⣒⡢⣞⠥⠂⠁
⠀⠀⠀⠇⡟⡹⠪⡳⣄⠀⠀⢠⠖⠛⠫⡑⠒⠤⣀⣀
⠀⠀⠀⡴⣴⠁⠀⠘⢎⢢⠀⠀⠀⠀⠀⢸⠀⣀⠤⠤⠊⠑⢦
⠀⠀⢀⠁⡆⠀⠀⠀⠈⡆⢳⠀⠀⠀⠀⡌⡰⠁⠀⠀⠀⠀⠀⠡⡀
⠀⠀⢠⢠⠀⠀⠀⠀⠀⠸⡀⠆⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⢸⠈⡀⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⡜⠀⢇⠀⠀⠀⠀⢠⠃⠀⠈⠲⢄⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⢀⠞⠀⢀⡈⠑⣄⠀⢰⡃⠤⠀⠤⠒⠚⠣⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀
⡞⠉⠉⠁⠀⠀⠈⠇⠸⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⡇⠀⠀⠀⠀⠀⠀⠘⡘⡆⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠇⠀⠀⠀⠀⠀⠀⠀⢡⠱⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⢰⠀⠀⠀⠀⠀⠀⠀⠈⢇⠱⡄⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠁⠲⠤⣀⠀⠀⠀⠀⠈⢢
⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈⣆⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠄⡰⠃
⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀
⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠄⣀
⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠤⢀⡀
⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠠⢄⣀⣈⡦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⠠⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣸⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⣼⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⣼⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⣆⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⣾⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣿⣿⡿⣾⣿⣿⡄⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⢹⣿⣿⣽⣿⣿⣷⣶⠀⠀⠀⠗⣠
⠀⠀⠀⠀⠀⠘⣿⣿⡾⣿⣿⣿⣿⡇⠀⠀⠀⢿⣧⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⠛⠛⠁⠀⠀⠀⠀⡙⣯⣤⣄⣀
⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⢊⣽⣿⣿⣷⡇⡀
⠀⠀⠀⠁⠀⠀⢸⣿⣿⡿⠀⡀⠀⢠⠀⣀⣴⣖⡄⢸⠁⠛⢹⣙⡏⡃⠇⠃⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⡟⣾⣾⣿⣿⣿⣿⡇⠘⠀⠘⠘⠇⠃⠱⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡸⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⣿⡛⣿⣿⣿⣾⣦⣦⣦⣠⣤⣄⣀⣠⣀⣀⣤⣄⣀⣤⣴⣤⣴⣦⣤⣦⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠴⠿⣿⣿⣿⣿⣿⣿⣧⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠟⠶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠶⢶⡎⠀⣆⠠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡄⢢⣄⠀⡀⠰⠞⠁⠉⠂⠀⢀⡇⢀⡀⠀⠰⠂⡈⢲⣄⡔⢃⣀⢀⢹⠀⣀⢀
⠀⠀⠀⠀⠶⢲⡆⢱⣿⡧⠷⠗⠂⢶⣁⣠⠴⢾⠁⠘⣧⣴⣀⣾⠟⠈⢀⣽⡄⠙⠿⠤⣄⢀⡐⢱⣶⣦⣤⡀
⠀⣠⠾⠀⠀⣼⡇⢀⡋⠀⢀⠔⠈⣁⠈⡇⠀⣨⠿⠞⠛⠙⠉⢃⢢⣀⠁⠀⢠⣶⠈⡖⡋⠉⠹⣶⣴⣈⢻⣿⡖
⡈⣿⢁⡏⠀⠸⠛⠋⠓⡶⠛⠀⡩⠛⠁⢩⡔⣏⣃⡼⣛⠓⠒⠉⢘⠿⠚⢓⢭⠙⠛⢳⠙⢾⣀⡈⠉⠉⡾⢿⡿
⣇⠱⡈⠃⣤⡄⠀⢦⣴⣁⢀⣾⡇⠀⡐⠁⠘⣿⠿⣭⣝⣽⠏⢹⡿⠢⢀⣻⣸⢛⠳⣶⡾⣿⡹⠶⣦⣼⣷⡼⢃
⠸⣦⣈⠲⢬⡄⠀⠂⣌⠉⣻⠛⠁⠀⠀⠈⠵⣷⣤⣤⣤⣴⠞⠋⣱⡀⠸⡛⢳⣼⣨⣷⠤⠶⣷⣶⣱⢿⣋⣴⡟
⠀⢹⣿⣿⣦⣄⣀⠐⠛⠶⠾⠀⣰⡏⠛⠒⠺⠋⢙⡿⠁⠈⠇⠀⠙⠁⣀⠞⠉⣿⡯⠥⠖⢛⣋⣽⣿⣿⠛⠍⠁
⠀⠀⢿⣿⡻⠄⡈⠁⠓⠒⠂⠀⠀⠤⢀⣀⣀⣙⣛⣁⣀⣀⣀⣀⣉⣡⣭⣄⣤⣴⣶⣶⣿⣿⣿⣿⠏⠊⠁
⠀⠀⠀⢯⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⠝⠛⠒⠁⣪⣽⣿⣟⢿⣿⣿⣟⣟⡯⠀⠄⠁
⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⠚⣿⣿⣿⣷⣮⣿⡯⣭⡟⠀⢠
⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠂⣽⣿⣿⣿⣿⣿⢭⡽⠁⠀⠛
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣈⣿⣿⣿⣿⣿⣿⠿⡣⢀⡴
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣿⡯⣿⣻⣿⣷⠆⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⣾⣿⣿⡿⣻⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢻⣿⣿⣯⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣂⡒⠲⠤⠤⢤⠴⣶⣶⣶⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⣤⠀⣤⣄⡤⣤⢠⠄
⠀⠀⣿⣿⣿⣧⡸⡇⣿⡟⡿⣿⣿⣿⡟⣿⢻⢻⢻⢻⡿⣿⢇⡸⣿⡟⣿⡇⡟⡟⣟⠃⣝⡀⠿⢢⣲⣿⣬⡅
⠀⠀⣿⣿⣿⣿⣿⣷⣿⣶⣿⣾⣷⣷⣷⣿⣾⣿⣾⣾⣾⣿⣷⣷⣿⣿⣾⣷⣷⣷⣾⣷⣾⣿⣿⣶⣿⣿⣿⡇

⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠀⠒⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⢠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⢀⡀
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢒⠀⠒⠂⠀⠀⠀⠀⠒⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡒⠀⠐⠀⣀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⡀⠦⣤⡤⠀⠀⣀⣀⣤⡤⠶⠔⡿⠥⠤⠤⠵⠤⠁⠀⠀⠀⠈⠀⠀⠂⠢⠔⡄
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⡰⠃⠀⠀⠀⠀⢀⠀⠸⠀⠀⠀⠀⠀⠈⠀⣤⠤⠤⢤⣤⣀⠀⠔
⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠀⠳⢤⣤⡀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⣀⠤⠝⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠈⠀⠀⠌⠦⣷⣄⣀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠄⠀⠀⢸⣷⣄⣸⣿⣷⠀⠈⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠘⢄⠉⠉⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠃⠙⠋⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢠⠞⠉⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⡰⠂⠀⠀⠀⠀⣀⣀⠂⠀⠀⠀⠀⢠⠂⣈⠴⠁⠀⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠀⠐⡀⠀⠀⠤⣀⠁⠈⠁⠒⠈⠀⠉⢠⣀⣀⣀⡤⠚⢥⢹⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠣⡀⠀⠀⠈⠑⣦⢤⣄⣀⡀⠀⠀⠈⣀⣀⡤⡆⢸⢎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢤⠀⠀⠀⠸⣦⣄⣀⠈⠉⠉⠉⣉⣀⣴⠂⢸⠃⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣌⡀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠣⡀⠀⠹⣿⣿⣿⡿⠋⠉⠉⠉⠙⠢⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢆⠀⣀⠀⠈⠻⠿⣤⣴⣶⠶⠄⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⠙⡦⡀⠀⠠⠀⠀⠒⠀⠀⠀⠠⡀⠀⠀⠀⠀⠉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠑⣄⠀⠘⢌⠲⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠣⡈⢆⡀⢀⠅⠀⠀⠀⠌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠲⢡⠁⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠈⢧⠀⠀⠀⠀⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⣓⠤⠠⠄⣀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠂⠀⠃
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠁⠀⠠⡄⠆⠄⢀⠀⠀⡀⠄⠀⠤⡐⢄⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⢠⡄⠀⡄⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣴⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣧⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣤⡄⢠⡄⢀⣤⡀⢠⣤⣄⠀⢀⣤⡤⠀⠀⣤⣤⡀⣤⢠⡄⣤⣤⠄⣤⣤⠄⣤⣤⢀⣤⢤⠀⢸⣿⡇
⠀⠀⠀⠀⢠⣀⣀⣀⣀⣿⣿⠀⠀⣿⣇⣿⡇⢸⢿⡇⢸⠀⠛⠀⠘⣧⣴⡄⠀⡷⠘⠃⣿⣼⡇⣿⣤⠀⣿⣤⠈⢷⡌⢸⣧⣄⠀⢨⣿⣇⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠈⢿⣍⠉⠉⣿⣿⠀⠀⣿⢻⡏⡇⣼⠶⣧⢸⣀⣶⠀⢸⣇⣸⠀⠀⣇⣰⠆⣿⢸⡇⣿⣀⡀⣿⣀⡠⣆⣹⢼⣇⣀⠀⢸⣿⡏⠉⠉⣽⡟
⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⣿⠀⠀⠁⠈⠀⠁⠁⠀⠉⠀⠉⠁⠀⠀⠉⠉⠀⠀⠈⠉⠀⠁⠀⠁⠈⠉⠁⠉⠉⠁⠉⠁⠀⠉⠉⠀⢸⣿⡇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⢠⡿⠃⢿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠇⠘⣿⡀
⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠉⡻⢿⣿⣿⣿⣶⣶⠶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⡶⣶⣶⣾⣿⣿⡿⡋⠁⠀⠀⠘⣷⡀
⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠀⣿⠇⢿⡏⢹⣿⢸⣿⠙⣿⡇⣿⡇⢿⡟⢸⣿⠸⣿⠁⣿⠃⢻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⠀⢸⡇⢸⡏⠈⣿⠀⣿⠀⢿⡇⢸⡇⢸⡟⠀⣿⠀⢘⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣬⣀⠀⠇⠀⠟⠀⢻⠀⢸⠀⠸⠇⠀⠇⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣀⣀⣀⣀⣀⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⣀⡤⠶⠞⠛⠉⠉⡿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡇⠀⠠⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⣾⠀⡆⠀⠀⠀⣶⠂
⠀⠀⠀⠀⢠⡟⢠⡇⠀⠀⢸⣿
⠀⠀⠀⠀⢸⡇⢸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠃⠸⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢩⠀⣶⡆⠀⠀⣿
⠀⠀⠀⠘⢸⠀⣿⡇⢰⠀⢹⡄
⠀⠀⣰⠇⣼⠀⢿⢇⠀⠂⠀⠉⠢⣄⡀
⠀⢸⣯⣠⣿⠀⢸⡄⠢⣄⠆⠀⠰⣦⡍⠲⣄
⠀⠀⢷⢈⣿⢄⠀⣷⡧⠌⠳⠶⣤⣾⣤⣆⢸⡄
⠀⠀⠸⣿⣿⢻⢆⡏⠀⠀⠀⠀⠈⠉⠙⢿⣾⣃⣀
⠀⠀⢠⡟⢹⣿⣿⢆⠀⠀⠀⠀⠀⣰⡆⠀⢹⣿⡍⠳⣄⣀⠀⠀⣀⣀⣀⣤⡤⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⢷⢶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⡿⠁⠏⠁⠈⠹⠀⠀⠀⠀⠴⣫⠀⠀⢸⣟⠁⠀⡎⢍⣉⡉⠩⠭⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⢸⠀⠀⠀⠀⠱⣄⣀⠀⠀⣀⣀⣰⣿⣿⠀⠀⡇⠈⠈⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣤⣤⣤⠤⣤⣤⣤⣀⣤⣤⣄⣠⣀⣀⣀⣀⣀⣀⣤⣤⡿
⠀⢸⠇⢸⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⢿⡇⠀⣠⣁⣀⣀⣀⠀⣀⡀
⠀⢸⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠡⠬⣯⣉⣉⣛⣋⡉⣛⣓⠒⠶⠶⠦⢤⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠘⣧⣀⡴⠈⠀⠀⠀⢀⣠⣤⣐⣖⣤⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢹⡿
⠀⠀⠀⠉⠛⠛⠒⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠿⠿⣽⣶⣶⣦⣤⣄⣀⣤⣄⣀⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⣤⣤⣠⣤⣤⣤⣤⣴⣶⣶⣲⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⢴⣶⣶⡾⠿⢿⡯⠭⠭⠭⠭⠭⠭⠭⠉⠉⠉⠙⠓⠒⣒⣒⣲⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡟⣟⠉⠰⣞⣋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡁⣉⡷⠂⠈⠙⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠋⠿⠳⣦⣭⣥⣤⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣬⠭⠥⠶⣞⠫⠤⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⢀⣀⣨⡟⠳⢶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⡶⠟⢿⣄⣀
⠀⠀⣀⣴⠞⠛⣉⣤⣄⡀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣿⣟⣉⣹⣿⣿⣿⣷⣿⣷⣠⡍⠉⠛⠶⣄⡀
⢀⣾⠋⣠⣴⡾⠟⠉⠙⠛⠿⣶⠀⣀⣤⣤⣀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢉⣁⣀⣀⣀⣤⣬⣽⣿⠿⠿⠛⠋⢀⣴⣶⣦⡈⠻⣆
⣼⠃⠀⠹⢿⣷⣾⣭⣦⣤⢶⡛⠛⠳⢤⡀⠉⠳⡶⠓⢶⣤⣤⣶⡛⠛⠛⢶⡄⠈⣉⣉⣉⣉⣁⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⡄⠸
⡏⠀⣤⣄⠲⢬⡿⠛⣿⣛⠛⣿⢶⣶⣾⠟⢻⡳⢾⡴⠋⣁⠀⣠⠽⠛⠛⠛⢛⣿⣏⠳⠾⠿⠿⣿⠛⠛⣛⡿⠛⠉⢿⣿⣿⣧
⡇⠀⣿⣿⢠⡀⠘⢯⠉⠉⠙⢷⠴⣿⣷⣀⡀⠀⠀⠹⡏⢩⠟⠁⢀⣠⣴⣶⡿⠟⠋⠙⢶⣠⣤⢼⡟⠛⠛⠶⡖⠒⢼⣿⣿⣿
⣷⣤⣿⣿⠀⢷⠀⠘⣗⣤⣀⣤⣷⡇⠀⠖⠙⣦⣤⠤⢧⣼⣞⠍⠉⠉⠙⠻⣧⠴⠒⠉⣩⠿⠛⠉⠙⣏⣢⠀⠘⡷⢼⣿⣿⣿
⡏⠉⠙⠻⠶⢶⣤⣼⣋⣀⣀⠀⠀⠉⠲⡷⠊⠁⠀⠀⠀⠁⠽⢧⡴⠊⠛⠛⠛⣄⣀⣴⠃⠀⢠⠶⠒⢿⠋⠀⢀⣗⣸⣿⣿⡿⠾
⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠶⠶⠷⠶⢿⣿⣿⣷⣦⣶⣾⣧⣤⣤⣤⣤⣾⣷⣾⣦⣶⠾⠷⠶⠾⠛⠛⠛⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠁⢨⣍⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⠃⢠⣾⣿⣧⠀⣴⣿⣿⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⡞⢳⠄⣿⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⢿⡿⢠⣿⡿⣿⣿⢸⣿⣧⡄
⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡏⣠⡟⢀⠟⠀⠀⠀⠙⣦⠀⠀⠀⣴⣿⣿⢠⣶⠂⣶⡆⣰⣤⣤⢀⣬⣭⡄⢙⣛⣁⠀⢀
⣇⠀⠀⣠⠶⣄⠀⠀⢸⡇⠘⠛⠋⢀⣤⣄⠀⠀⢀⣀⡈⢷⡀⢸⣿⣁⡀⣸⡿⢿⣿⢁⣿⡷⠆⢸⣿⡭⠁⣾⣯⡙⢠⣿⡿⠿
⣿⠀⢸⣏⠕⠈⣧⢤⠀⠳⢦⡀⠀⢈⣶⣌⠀⠀⢉⢢⡝⠈⢷⡘⠿⠿⠃⠛⠃⠚⠋⠘⠛⠻⠃⠿⠿⡶⢠⣮⣿⡇⢸⣿⠻⠃
⣿⠀⠀⠉⢶⣀⣠⡇⠀⠀⠀⠙⠳⡌⣿⡿⠠⠄⠸⢿⣇⠀⠸⣇⠀⣀⣤⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠻⠿⣿
⣿⠀⠀⠀⠐⠻⣿⣟⡀⠀⠀⠀⠀⢙⣆⠐⣶⣶⠂⠀⠀⠀⢴⣿⡋⢡⣖⣒⡦⠈⠷⠤⣄⡀⠀⠀⠀⠀⠀⢀⡴⢲⣦
⣿⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣾⣿⣿⡆⠈⠁⢀⣴⠞⠓⠚⠋⠁⠰⣶⠀⣠⠤⣤⣒⣶⣉⠷⣦⡀⠀⣻⠛⠀⡱⠟
⣿⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⣭⣄⣠⡾⠁⠀⠀⢿⠛⠛⢋⡳⣟⠛⣋⣀⠈⠛⠒⣩⣭⡁⠠⣶⠈⣷⢐⣿⠶⡞⠁
⣿⠀⠀⠀⠀⢀⣶⠋⢁⣀⠀⢤⡀⠀⠀⠀⠀⠀⠸⡇⠀⠘⠓⠁⢿⣥⢬⠃⠀⠀⣶⣲⡀⠀⠈⠀⣿⡟⠋
⣿⠀⠀⠀⠀⢸⡇⢸⡟⠉⣷⠈⣷⠀⠀⠀⠀⠀⠀⠻⣄⠐⠛⠀⠸⣿⡷⢤⣭⡄⠻⠏⠁⠀⠙⠃⠀⢯⡀
⣿⠀⠀⠀⠀⠈⢧⡈⠻⠶⠋⢀⣿⠀⢀⣀⣀⣤⠆⢀⡟⠀⠀⠀⣠⣤⠀⠈⠉⠀⣠⡀⠀⠰⣯⠟⠀⣈⡧
⣿⠀⠀⠀⠀⠀⠀⠙⠶⣤⣴⡞⠃⠘⢋⣉⣩⡤⣶⣿⣿⠲⠗⠀⠈⢁⣤⡶⣤⣀⣤⣤⠶⠖⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠟⠉⠉⠀⠀⢹⣿⡙⠛⠛⠛⠙⣿⡏⠀⠀⠈⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⢀⣄⢠⣿⡼⢿⣿⠀⠀⠀⠀⠀⠀⡿⠳⡄⠀⢠⡾⠛⢻⡆⠀⢰⣟⣉⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠷⣦⣄⡀⠀⠈⠙⠾⠿⠶⠿⠿⠀⠀⠀⠀⠀⠠⣿⡿⣇⠀⢀⡿⠛⣹⠇⠀⠈⠻⠧⠤⠭⠽⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾
⣿⠀⢸⣯⠙⠻⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠲⠯⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⢿⣿⣿⠀⢸
⢹⡄⢸⣿⡟⠛⠛⢧⣤⣜⣽⡟⠛⠳⠶⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠾⣿⠟⢿⣿⣥⡜⢣⣿⣿⡏⠀⣸
⠈⣷⠀⢿⣧⡤⣤⡀⡽⣿⠉⠉⠓⠶⣄⢸⡇⠀⠙⣿⢩⠁⢹⡿⣿⢿⣬⣉⣛⣩⣴⣁⠀⢀⠾⣏⣴⣿⡽⢯⣤⣿⣿⡟⠀⢀⣿
⠀⠘⣧⡈⠿⠀⣈⡙⠓⠿⠶⢤⡀⠀⠈⢻⡇⠀⠸⣍⣞⢦⠈⢦⡀⠉⠀⠀⠉⠉⠁⢈⢶⣏⡠⠞⠙⣦⣠⣾⣿⡿⠋⠀⢠⡾⠃
⠀⠀⠈⠳⣄⡀⠀⣉⠛⠲⠦⣤⣽⣀⣀⠈⢷⢀⠀⠈⣿⡗⠒⠋⠉⣰⠖⠢⠤⠶⠒⢉⣼⡟⢠⣶⣾⣿⡿⠟⠉⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠈⠛⢶⣤⣉⡒⠦⢤⣀⣉⠉⠐⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⣀⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣦⣭⣉⣛⠓⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢀⣼⠟⠛⠛⠛⠷⣤⡀⠀⢰⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⣿⣦⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢠⡿⠁⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⢸⣯⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣀⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠶⣦⣄⣀⡀
⠀⠀⠀⢀⣾⣛⣭⠁⠉⢿⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⢶⣤⣤⡄
⠀⠀⠀⣸⡿⠋⠁⠀⠀⠀⠹⣧⡀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣷⡶⠟⠋⠀⠀⣀⠀⢰⠄⠀⣶⠀⠐⣦⠀⠉⠳⡄
⠀⠀⠀⠈⠻⣦⣀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⡼⠃⠀⣿⠀⠀⢹⡀⠀⠘⣧⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠉⠀⠀⠀⠀⠀⠶⠀⠀⢰⡏⠀⠀⢸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠀⠀⠒⠒⠒⠒⠈⠉⠉⠉⠉⠉⠉⠉⠀⠒⠒⠒⠲⠤⠤⢤⣄⣀
⠀⠀⠀⠀⣀⠤⠔⠂⠀⠩⠀⠂⠀⠀⠀⠀⣀⣤⣤⣄⡀⣀⣤⣤⣀⣀⣠⠴⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⢀⡴⠋⠁⠀⠀⠀⣠⡶⠶⣶⣤⣀⣠⠞⠋⣡⠖⠛⠛⠇⡀⠀⠹⣿⣄⣤⣤⣀⠀⠻⠋⠙⢷⣶⡞⠛⠷⣦⡀⠀⠀⠙⠲⣄⣀
⢠⡟⠀⠀⢀⠀⣤⣶⠋⠐⠀⠀⠀⡙⠃⠀⠀⠇⠀⠀⡀⠊⠁⠀⡴⠛⠀⠀⠀⠈⡇⠐⠒⠦⠀⠙⠿⡄⠀⠊⠋⠳⣤⠶⠶⣬⡻⢦⡀
⢸⡇⣀⡞⠛⠻⠒⠛⠆⢀⣠⠴⠂⠀⠀⡠⠤⠲⠴⣍⠉⠙⠀⢸⠁⠀⢀⡴⠒⠒⠃⠚⢤⣠⡤⠄⠀⣠⠴⠶⠦⠀⠘⠦⢀⣸⣷⠨⡗
⠘⣧⠈⠻⠦⣤⣀⠀⠠⡀⠀⣠⠇⠀⠈⢀⡤⠤⣄⢸⡆⢀⣠⣄⡁⠐⠚⠂⠀⠘⢄⡀⠀⠀⣰⠀⠞⠁⠀⣠⠴⠒⠒⠒⣶⡴⠗⢠⡏
⠀⠹⡄⠀⠀⠀⠈⠉⠓⠾⠯⣥⣄⣠⣤⣬⣄⠀⠈⠈⡴⠉⠀⢀⣙⠂⠀⢠⠖⠋⠙⠻⠉⠉⠁⠀⠀⣀⣠⣧⡤⠴⠞⠋⠁⠀⠀⡎
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠙⠛⠛⠛⠓⠒⠶⠿⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠠⠐⠶⠒⠒⠩⠛⠉⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠄⢀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⠦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⠴⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣑⡀⠉⠉⠉⠉⠋⠙⠉⠉⠙⠉⠉⠙⣒⣈⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠁