Elephant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠈⠒⣦⣤⣤⣤⣀⣀⡠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠓⢄⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠉⠢⡈⠙⠳⠒⠚⠉⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢨⠀⠀⣰⠀⠀⡀⢀⠀⠰⡀⠈⣦⠆⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢠⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⢠⠀⠀⢸⡇⠀⠇⠀⠰⡡⠊⣤⣄⢳⢀⡏⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⣠⣴⡟⠀⠤⢤⡀⠈⠀⠀⠀⠀⣸⢞⠇⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣧⣿⣿⠀⠐⠒⠦⠄⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠉⠁⢙⣟⡏⠀⠀⠒⠤⡀⠀⣠⠄⢠⣿⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣠⠔⣿⣿⡟⠒⠤⠤⡀⢠⣾⣧⢄⡸⣿⡆⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⣀⣀⠤⠖⠋⢀⣠⠟⠋⢿⣐⠠⠀⠀⣾⡿⡇⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣼⡀⠀⠀⠀⠀⠀⠀⢰⠀⢠⡇
⠀⠈⠓⠒⠒⠒⠊⠉⠀⠀⠀⣼⠮⢭⣥⣠⣿⡵⢃⣼⣿⣿⣿⣿⡛⢶⡦⢾⣤⣤⣤⣤⡜⠸⣿⠇⠀⠀⠀⠀⠀⠀⡏⣀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠯⠷⠌⣿⡶⠿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣠⠈⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡄⠀⣼⠁⠀⣿⣿⣿⣿⣿⣿⠙⠿⠿⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⢀⡟⠀⠀⢹⣿⣿⠿⠿⢿⡄⠀⠀⡇⠀⠀⠀⢀⣀⣼⣀⣀⣤⣴⠟⠛⠉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠦⢀⡾⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢰⠁⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢰⢹⡇
⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠃⢈⣰⠟⠁⠀⠀⠀⠀⢸⣧⠀⠀⢠⠀⠀⠃⠀⠀⢸⣿⡿⠋⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠧⣤⣤⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⢠⠁⠀⠀⢀⣼⠋⠀⠀⠀⢋⠹⣿⡆⠀⠀⠀⡄⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⡀⠀⠀⣾⠃⠀⠀⠀⠀⠸⡄⢿⣧⠀⠀⠀⡇⠀⢰⡏⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠤⠀⠈⢷⠈⢀⠄⢻⣶⡄⠀⠀⠀⢀⠁⢸⡿⠀⢀⡀⢱⠀⠈⢇⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠀⠀⢨⡇⠀⠀⢸⣿⣿⠀⠀⠀⠈⠓⠚⡇⠀⠠⠄⠀⢧⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⠀⠀⣸⢿⣷⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⣧⣠⣤⣤⣤⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⣠⠴⠶⠦⣤⡤⠖⠒⢄⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠘⣁⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⡎⠀⠀⡀⠘⠢⣄⠀⠈⠣
⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⡐⢄⡂⢄⢢⡘⣦
⠀⠀⠀⣿⣾⢏⡠⠀⣠⠔⠡⢾⣿⣡⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⢿⣖⠈⡂⣤⡘⢮⠃
⠀⠀⠀⠸⣯⠞⢠⣞⠁⢊⣴⣿⣿⣯⡻⠛⠀⠀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣷⡌⠳⣝⢦⡱⡄⠁
⠀⠀⠀⠀⠿⣶⡿⢑⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠹⣾⣿⣿⣿⣿⢝⢦⡙⣷⡝⡆
⠀⠀⠀⠀⠀⠙⠇⣼⠇⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡡⣵⡈⠿
⠀⠀⠀⠀⠀⠀⠀⠙⢲⣟⣿⣿⣿⣿⣿⠁⣤⠀⠀⣀⡂⠀⠀⡇⠈⣿⣿⡿⣿⣾⣿⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⣼⣿⡟⠐⣿⡀⠀⣒⡆⠀⠀⣤⠄⡘⢿⣿⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠁⠀⣰⡇⠀⠯⠄⠀⢀⣿⣦⠀⠈⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣀⣤⠤⠀⠈⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢙⠘⠿⣯⠁⠀⠀⠀⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⡄⢠⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣧⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠘⢆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠈⣷⠀⠀⠀⡀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⡀⠀⢀⠤⠔⠒⠚⠛⠃⠒⠢⠤⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠘⠿⢿⣿⡻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠦⢤⣀
⠀⠀⠀⠁⠈⡃⠀⠀⠀⠀⠀⠀⢙⣀⡀⢰⣄⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡂
⠀⠀⠀⠀⡀⠁⠀⢄⠀⠀⣰⣿⣸⠏⠁⣰⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢦⡀
⠀⠀⠀⠀⠆⠀⠀⢀⣳⣤⡍⠉⢠⢆⣴⣿⣿⣷⡄⢠⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢷
⠀⠀⠀⠀⠀⠛⠻⠟⠟⠋⠀⠀⠉⠀⠀⠀⠀⠘⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠶⠾⠯⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠃⠀⠀⠀⠀⣰⣾⣄⣀⠀⠀⢀⣴⣶⣿⣧⠴⠀⠀⠀⠀⠀⢰⣿⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⣴⣿⣿⣾⠿⣾⣶⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⡀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠉⠉⠉⠛⠛⠋⠉⠉⠙⠻⣶⡀⣤⡀⢸⠅⢱⡀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢹⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠘⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⠻⠀⣠⣶⡴⠃⡀⠀⣤⣦⣤⢤⡤⠀⠀⠁⠀⠀⠶⠶⢦⣉⣡⣠⠼⡿⢿⠿⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠑⢄⡀⠀⠀⠀⢃⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠁⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡠⠠⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠀⠢⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠀⠀⠀⠀⠀⢀⠁⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠱⠀⠀⠀⠀⠀⠈⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠄⠠⠀⠀⠀⠌⠀⠀⠀⣤⠲⣦⠀⠀⠀⠀⠀⣠⡶⢢⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⡐⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡐⠀⠀⠰⠀⢃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠊⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠀⠀⢰⣄⠀⠀⡀⠀⠈⢰⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⢀⠔⠃⠠⠄⢀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀⠀⢀⠄⠈⠉⢀⠀⠀⠀⠂⠈⠐⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⠀⢔⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡐⠃⠉⠄⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠋⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠑⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠁⠸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠀⠢⠘⠀⠑⠀⠒⠀⠀⠀⠈⢀⠀⠀⠀⠇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢠⡇⠀⠂⠀⢀⠂⠒⠀⠚⠇⠈⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⢣⡀⠀⠀⠀⠀⣀⠀⠈⠆⠀⠀⠊⠀⠀⡄⠀⢀⠄⠀⠤⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠓⠲⢤⡀⠀⠀⢀⣠⠤⠴⠒⠒⠒⠒⠒⠲⠤⣄⡀⠀⠀⢀⣠⡤⠤⠶⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠒⠒⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⣠⡀⠀⠀⠀⠀⠙⠦⣄⠀⠀⢈⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠺⡁⠙⠦⣄⣀⠀⠀⠀⣀⣩⡗⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⡀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠳⣄
⠀⠙⢆⠀⠈⠉⠉⠙⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⠤⢤⣀⣀⣀⣀⡤⠔⠋⠁⠀⠉⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⣀⣀⣀⣀⡤⠤⠖⠚⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠙⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢻⣸⡇⠀⠀⠀⠀⠀⢀⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠁⣀⣀⣠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⠊⠀⠀⠀⠀⠀⠐⠟⠠⠌⣹⣻⣿⡯⡾⠻⠄⠉⠁⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣨⣖⣶⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠁⠠⣾⣿⠃⢹⣿⡟⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⢨⡄⠀⡐⠢⠀⢨⠀⢛⣀⣠⣾⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠈⠁⣒⠒⢠⣆⠀⠀⣾⠋⣽⣿⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⡧⠁
⠀⠀⠀⠀⠀⢀⡡⠈⢉⢿⡽⠀⢀⣿⣶⣿⠈⠀⠀⠀⠀⠀⠀⠈⠂⢀⣠⡶⠊⠀⠰⣆
⠀⠀⠀⠀⠤⠥⠐⠲⢤⣷⡧⠀⣸⣿⣟⣿⡆⠀⠀⠀⠀⠀⠀⣀⣤⣾⠋⠀⠀⠀⠀⢢⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠰⡒⣉⢐⠿⠟⠁⣠⠟⠉⠀⡇⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠁⠀⠀⠀⠀⢠⣾⠟⣆
⠙⠒⠀⠁⠈⠙⡓⢶⡶⠒⠈⠀⠀⠀⠀⠐⣶⣾⣾⣿⣿⣿⣿⡿⡌⠀⠀⠀⠀⠀⠀⠀⢸⡔⠀⠀⠀⠀⠀⠀⢀⠉⢃⠀⠀⠀⠀⠀⠀⣹⡏⠀⢠
⠀⠀⠀⠀⠀⠰⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⡉⠃⣻⣿⣿⣷⣿⠻⠿⡀⠀⠀⠀⠀⢠⠀⠈⡗⠄⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡏
⠀⠀⠀⠀⠀⠈⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⠋⣿⣿⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⢹⣂⠀⠀⠀⠀⡄⠃⢇⠀⠀⠀⠀⢀⠔⡞⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⣿⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠈⢻⣿⣿⡀⢄⠀⠀⠀⡼⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠈⠀⢢⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⣻⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢯⣷⠈⠀⠀⡼⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡏⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢠⠂⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⡠
⠀⠿⠦⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⡀⠀⠀⠀⠐⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⠄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣷⠊⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⢧⠁⠀⢤⣱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠉⠉⠉⠀⠀⠁⠀⠀⠀⢻⡀⠂⠀⠀⠉⠁⠠⠀⠀⠀⠀⣡⠣⠒⠀⠀⠀⠀⠀⠀⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠁⠐⠐⠈⠉⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠠⣀⠄⠐⠀⠈⠉⠐⠂⠤⡀
⠀⠠⠆⠀⠀⠀⠀⠀⠀⢄⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠂⠐⠐⠂⠠⠤
⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⡂⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢛⠋
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠂⠔⠀⠀⠀⠀⠀⠀⢠⢤⡁⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⠀⠀⠈⠖
⠀⠀⠀⠀⠀⠀⠃⠂⢀⡀⠀⠊⡁⠀⠀⠀⠀⢠⠋⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠀⠂⠀⠀⠀⢀⡏⠀⢠⢀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⡄⠀⠀⠀⠈⠐⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⣀⠄⠀⠂⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠄⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠠⠄⠰⡎⠀⠀⠀⠀⡘⠀⠀⡂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠃⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠀⢀⠀⠀⠘⡀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⢠⠀⡆⠀⣀⢀⡲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠘⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⡆⠀⡆⢦⠶⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⢠⡈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⠦⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⡄⠚⠀⠀⠀⠀⠀⠀⠰⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢦⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣷⡄⠀⠀⠀⠀⠀⣠⣶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢨⣾⠈⣷⣤⠀⠀⠀⠀⢋⢸⣿⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢹⢧⡁⢸⣿⣷⣿⠏⠀⠀⠀⠘⢿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠙⣿⣿⣿⣿⣆⠀⠀⠀⢄⣻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡷⢾⣿⣿⣿⠁⠀⠀⠀⠀⣸⡘⢿⡋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠄⣟⣰⣿⠒⠀⠀⠀⠀⢹⣷⣼⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠰⡧⢾⣷⡧⠀⠀⠀⢀⣼⡗⢰⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠀⢴⣾⣿⣗⡀⠀⣀⢠⣿⣿⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⣮⡋⣿⣏⠶⠀⠈⢸⣿⣿⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⢰⠟⡝⠛⣿⠀⠀⠀⣾⣽⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢷⣦⡧⠀⣿⠰⡟⠀⣿⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡇⢸⣿⡇⠀⣿⠄⣦⢠⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⣇⠀⣿⠋⠀⢹⠀⣍⢸⡇⣺⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣀⡇⠀⠺⠁⠀⠸⠀⠀⡀⠸⢦⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⣰⡇⣤⣴⣂⣀⡄⢠⢸⣷⣦⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠁⠀⢨⠅⠀⠀⠈⠶⠿⠯⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⣠⡀⠉⠓⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⡠⠒⡄⠀⠀⡴⠁⠀⠀⣠⠔⠠⠚⠁⠈⠓⠤⣀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⣰⠊⠉⢈⡽⠅⠴⠃⡠⠊⠀⠶⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠈⠑⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⡏⠀⠀⠳⣄⣀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢷⠀⠂⠀⠀⠀⠐⠀⠀⠀⢀⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠜⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠈⠢⣄⣀⣀⣀⣀⣀⣀⠔⢁⣴⢁⡤⠤⢼⠀⠀⠀⠀⣠⠞⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣀⣠⣔⡩⠖⠉⠈⠁⠀⠀⠀⠣⠤⠒⠯⢤⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣀⣀⣥⠀⠀⠀⢰⠁⠈⠉⠒⠒⠤⠤⠤⢤⣤⣤⠤⠤⢤⠤⠤⠤⡄⠀⠀⠀⠀⡎⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠣⡀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠀⠀⢱⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⢤⣀⠤⠜⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡎⠸⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⠁⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⢀⠤⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⢀⣀⡀⡜⠀⠀⡧⢄⣠⣄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠈⠉⠁⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠒⠶⠀⠒⠉⠉⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠰⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠊⢹⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡀
⠀⠀⠀⢀⠀⢻⡀⠜⢀⣴⠇⣠⣾⣧⣀⣼⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠓⠤⣤⡤⠦⠶⠞⠛⠛⠉⢛⣿⡀⠀⠀⠀⠀⠠⣄⣤⣤⣄⣠⡞⠁⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣄⠀⠀⠀⠀⣿⢿⢿⣿⣯⠀⠀⠀⠀⠀⢀⣾⡿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⢼⠁⠀⠈⠉⠛⠳⠀⠀⢀⣤⣿⣿⣧⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠉⠝⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠄⠘⠇⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠀⠀⠉⠚⢆⠇⠀⠀⠀⣴⠋⠀⠀⠀⣀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⠛⠛⠙⠛⠓⠈⠁⠙⠙⠛⠛⠀⠘⠘⠛⠛⠛⠀⠐⠛⠛⠙⠓⠛⠛⠛⠙⠛⠒⠂⠆

⠀⡴⢚⣉⠉⠲⣄
⣼⢰⠋⠉⠣⠀⠈⠳⣤⣀⠀⢀⣠⣤⠶⠶⠶⠲⠶⠶⠶⣤⣄⣀
⡇⡎⠀⠀⠀⠳⢄⣀⣨⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⢀⣠⡤⠖⠚⠛⠉⠉⠙⠛⠶⣤⡀
⣇⠇⠀⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠶⠟⠒⢋⣩⡤⠴⠶⠒⠒⠛⠓⠲⣤⡀⠈⢿⡄
⢻⢠⠀⠀⢠⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣄⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⣿
⢸⣼⡆⠀⡟⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣸⣀⡀
⠀⡟⣷⣀⡇⡜⢉⡇⠀⠀⢀⣶⠀⠀⠀⠀⢀⠖⠢⢄⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠏⠉⠛⢷⣄
⠀⡇⢃⡹⠀⣇⢿⡇⠀⠀⢸⢻⠀⠀⠀⠀⡌⢠⣘⣾⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠙⣷⣀
⠀⠹⡌⠣⣀⢈⣟⣀⡈⠁⢸⢸⡄⠀⠀⠀⠙⠬⠿⠛⠓⠒⠀⠀⠀⢀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⢿⢷⡄
⠀⠀⢻⢦⣌⡟⠁⡀⠉⠀⠘⡄⠳⣄⠀⠀⠀⠀⠀⠐⣲⣤⠀⠀⠀⠈⢷⠀⠘⣇⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⡄
⠀⠀⠀⠑⣼⠉⠈⠉⠃⠀⠀⠙⣆⠈⣳⣤⣠⣤⠶⠋⠁⠘⠀⠀⢀⣴⠛⣧⠀⠈⠳⠶⠒⢉⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠹⡄
⠀⠀⠀⠀⣿⠒⠒⠲⠀⠀⠀⡴⠋⠉⠉⠉⠀⠀⣀⣤⣦⡤⠴⠚⠉⠀⠀⠙⠷⣦⣤⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠳⢬⣶⡤⢤⢤
⠀⠀⠀⠀⣿⠤⠤⢄⠀⠀⣼⠧⠤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡈
⠀⠀⠀⠀⢿⣀⣀⣀⠀⢰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠸⡇⣀⡈⠀⢸⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⣿⠉⠉⠁⢸⠀⠘⣧⡀⠀⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢸⡉⠉⠀⢸⡀⠀⠈⣷⣤⡈⠳⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠈⡏⠉⠂⠘⡇⠀⠀⢹⡄⠉⠓⠛⠓⠶⠤⡤⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⠒⣿⠉⢧⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣏⠈⠁⠀⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⢠⣏⣉⡁⢰⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡰⠓⠂⠄⠀⡼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⡗⠀⠀⠀⠀⠀⠀⠀⣟⣁⡐⢂⣀⡼⠃⡾⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠻⠖⠻⠦⠼⠃⠀⠀⠀⠀⡿⠄⡠⡀⣀⠀⠀⢻⠀⡟⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠉⠀⠀⣧⠛⢂⠄⠄⠀⠀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠦⢴⣤⠵⠖⠋⢠⣇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣃⠴⡄⠀⠀⠀⣀⡼⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⣤⣤⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠻⠋⠉⠉⠉⠉⠿⠿⢿⣿⣿⠟⠋⠉⠉⠉⡉⠉⠛⢿⣿⣿⠿⠿⠋⠉⠉⠉⠙⠻⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⣀⣀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⣄⣀⡀⠈⠉⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⡴⢛⣿⣷⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣠⣾⣿⡟⠷⣄⠀⠀⠉⠻⣷⡄
⠀⠀⠀⣠⣴⡿⢋⡄⠀⠀⠈⠁⠠⠚⣻⣿⣿⣷⣿⣤⣤⡴⡠⢃⠄⠀⠀⠀⠀⠀⠀⠀⠈⠢⠰⣤⣤⣼⣾⣿⣿⣿⠛⠢⡈⠁⠀⠀⠢⣌⠻⣦⡀
⣠⣶⣿⣿⡭⠞⠉⠀⠀⠀⠀⠀⢀⠴⢋⣿⣿⣿⣿⣿⠟⠁⠀⠁⣀⡤⠀⠀⠀⠀⠠⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣍⠳⢄⠀⠀⠀⠀⠀⠈⠓⢮⣿⣷⣦
⣿⡟⢉⡡⠄⢀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣼⣿⣿⡟⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢹⣿⣿⣧⡈⠣⡀⠀⠀⠀⠀⠀⠠⡀⠐⢬⣉⠛
⠸⣿⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣿⣿⣿⣤⣄⠀⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⢀⣤⣼⣿⣿⣍⠙⠄⠀⠀⠀⠀⠀⠀⡀⠈⠳⢦⣈⣹
⠀⢻⣿⠁⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⢉⣼⣿⣿⣷⡙⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⣴⠟⣷⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⢹⡟
⠀⢸⣿⡟⠁⠀⡠⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣿⣿⣷⣉⢻⡟⠡⠊⠀⠀⠀⠀⠀⠀⠉⠂⠙⣿⢊⣽⣿⣿⡟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣿⡇
⠀⠀⣿⣆⣠⠎⠀⠀⢀⠆⠀⠀⣰⠟⣼⠃⣸⣿⣿⡃⠨⣿⠁⠀⠐⠀⠀⠀⠀⠀⠀⡐⠀⠀⢿⡭⠈⣿⣿⣷⠀⠹⡙⣧⡀⠀⠐⢄⠀⠀⠙⢦⣀⣿⠃
⠀⠀⠘⣿⣧⡀⠀⣰⠃⢀⠀⣼⠏⢰⡏⢠⠿⣿⣿⣷⣤⣿⢠⡶⠂⠀⠀⠉⠉⠁⠀⠈⢲⣄⢾⣄⣼⣿⣿⡿⠇⠀⣧⠘⣷⡀⢀⠈⢧⡀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⢿⣿⣧⣴⣃⣾⡏⢀⡿⠀⠀⣼⢿⣿⣿⣿⠇⣿⣇⠄⠀⠀⠀⠀⠀⠀⠀⢀⢻⡄⣿⣿⣿⣿⢷⠀⠀⢸⡆⠘⣷⣌⣷⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡿⠀⢸⡇⠀⠀⠀⢸⢿⣿⡿⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢾⣿⡿⢿⠀⠀⠀⢨⣷⠀⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣾⠃⠀⠀⠀⠈⠘⠛⣷⣾⣿⠆⣀⣤⡤⠶⠶⠦⠀⠀⠀⣿⣷⣼⡟⠇⠈⠀⠀⠀⠀⣿⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⣶⣦⡀⢀⠀⠀⢠⡿⠟⣿⡟⢉⣀⠀⠀⠀⠀⠀⠀⢀⣿⡟⢿⡇⠀⠀⢀⠀⣸⣴⣿⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠈⠙⠻⢿⣷⣦⣼⠃⠀⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⢿⣴⣶⡿⠟⠋⠀⣿⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⠀⠀⠀⢀⣼⠏⠀⠀⣸⡟⠋⠉⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠈⢿⣦⠀⠀⠀⢀⣿⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⡀⠀⣠⡿⠃⠀⠀⣰⣿⠷⠒⠒⠀⠀⠀⠀⠀⣰⡿⣿⣧⠀⠀⠈⠻⣷⣄⣠⣾⡟⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠙⠿⢿⠯⠄⠀⠀⣰⣿⣇⠤⠀⡀⠀⠀⠀⠀⣰⡿⠁⣸⣿⣧⡀⠀⠀⠬⣿⠿⠟⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣁⢀⡀⠀⠀⠀⠀⣰⡿⢁⡾⠉⣿⡿⣿⣆⡀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⣤⣤⣴⡾⠟⠁⢸⡏⣀⠀⠀⠀⠀⠀⣰⣿⣤⣾⢃⠀⣿⣇⠈⠙⠿⣦⣤⣤⣤⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⣾⡏⠀⠈⠀⠀⠀⣰⡿⣿⠡⣴⣋⢀⡟⢻⣆⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⣿⠘⢿⣤⣈⣉⡾⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠉⠀⠀⠀⢸⣿⣇⠀⣿⣿⡯⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠁⠀⠀⠸⣇⠻⣶⣿⣿⠑⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⣁⡀⠀⠀⠹⣦⡉⠀⠸⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠈⠙⠒⠄⠒⠋⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣀⣀⠀⡀⠀⣀⣀⣴⡾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⣉⣻⣋⣙⢛⣟⢋⣿⢟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣤⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠙⢻⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⡟⢁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⢀⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣚⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⡶⠖⠋⠉⠉⠙⢢⣤⣀
⠀⠀⠀⢀⣠⠤⢤⣤⡠⠊⠁⠀⠀⢬⣭⣿⣿⣦⣆⡀⠀⠀⠀⠙⠌⠢⣀
⠀⠐⠉⠁⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠟⡥⢤⣤⡀⠀⠀⠀⠈⢳⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢰⣽⣄⠀⠀⠀⠀⠈⡀⡀⠀⠀⠀⠀⢣⠀⠀⠊
⠀⠀⠀⠀⠀⢳⡀⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⡀⠀⡈⠻⣿⣷⣷⣦⣀⡠⠀⠑⠁⠀⠀⠀⡎
⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣘⣀⣀⠉⠉⠉⣉⣡⠔⠁⠀⠀⠀⠐⡐⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿⣷⡶⣿⣄⠤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡗⠀⠀⠀⣠⣿⣿⠋⠀⠀⠈⠁⠀⠀⢠⣿⣿⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠅⠀⠀⠀⠀⢐⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⢀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣸⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠄⡹⠋⠀⠀⠀⠈⠉⠒⠢⣄⡀⠀⠀⠀⠀⢀⣠⠔⠒⠉⠀⠀⠀⠀⠙⢏⠢⡀
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠾⠛⠉⠉⠉⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠢⡀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁
⠀⠀⠹⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠐⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠂⢙⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠎
⠀⠀⠀⠈⠀⣤⠂⠀⠄⠀⠀⠀⠀⢣⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⡸⠀⠀⠀⠀⠠⠀⠐⣤⠔⠁
⠀⠀⠀⠀⠀⠘⠢⠾⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⠷⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠈⢧⡜⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠃⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣶⣶⡼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣹⣄⠀⠀⠀⠀⠀⠀⢠⡏⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡰⠁⠸⡀⠀⠀⠀⠀⠀⡎⠈⢄⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⠀⠀⠃⠀⠀⠀⠀⢰⠀⠀⠀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣄⡀⠀⠐⠀⠀⠀⠀⡇⠀⢀⣠⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡈⠉⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠐⠀⠒⠒⠀⠒⠒⠒⠒⠒⠒⠉⠉⠉⠉⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⡰⢶⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢇⠛⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠈⠀⣈⡙⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠃⠀⠀⠀⢀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠉⠁⠀⠀⠀⠀⡎⠀⢀⡠⢀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⣸⠈⡉⠓⠀⠀⠷⠚⠋⠁⣘⡽⠀⢸⣀⣀⡤⠦⠤⠤⠖⠋⠀⠀⠀⠀⠀⢸⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⡇
⣀⡤⠤⠒⡀⡏⢨⠍⢁⠤⠂⢀⠜⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠙⠒⠋⠉⠀⡇⣠⠖⢁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⢸⠃⠀⠀⣇
⠀⠀⠀⠀⠀⣏⢩⡭⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⣸⠉⢦
⠀⠀⠀⠀⠀⢿⢒⡂⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⡼⠀⠀⢀⡏⠀⠘
⠀⠀⠀⠀⠀⠸⡌⠅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⡞⠠⠤⣄⡤⠔⢲⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢣⠀⠀⠄⢄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡇⠀⢸⡀⠀⠀⠰⡇⠀⢣⠀⠀⡙⣿⠀⠀⡼⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠁⠀⢀⡜⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡇⠀⠈⡇⠀⠀⠀⡇⠀⢸⠀⠀⡇⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣷⠀⠀⠀⡇⠀⡞⠀⠀⡇⢸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⡆⠀⠀⢹⠀⠀⠀⠀⢈⠀⡀⢠⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⠃⠭⠚⠠⣧⣰⣄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠮⠧⠤⠂⠀⣰⠃⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠻⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠘⠀⠀⠀⠀⠀⢤⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠸⣶⠀⢀⡤⠤⠤⣀⠀⠀⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠵⣂⣉⣉⠛⠅⠀⠷⠁⠀⠀⠀⠀⠀⠀⠀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⡄⠀⠀⠀⠀⠀⠀⢋⠥⠤⢄⡙⠄⠀⠀⠀⠀⠀⠀⢀⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠁⡿⣻⣶⠶⣀⡀⡂⠀⡀⠐⠒⢌⡠⠀⣤⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡝⣽⣿⠀⢰⠂⣰⢳⣶⣶⣦⢼⣷⣷⠸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⡇⢀⢰⣿⢸⣿⣿⡷⢸⣿⡿⠂⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡿⣧⠸⣸⣿⣿⣿⣿⣧⣼⣿⣿⣆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⠐⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣿⣿⡟⠉⠉⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡏⢸⣿⣿⣇⠀⠀⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡇⢸⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⣶⡃⠀⢿⣿⣿⡇⠀⢠⣟⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠿⠇⠀⢹⣿⣿⣯⠀⠘⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⣿⣿⡀⣾⢏⡟⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⣶⣒⣿⣳⠘⠽⣟⠿⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣤⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⢻⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⡟⢁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣚⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠐⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢷⣦⢦⣤⣟⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣰⠆⠀⠀⢀⣶⠀⠀⢤⣓⣦⣤⣤⣾⣿⣿⣅⡀⠀⣦⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡁⢸⣥⣀⡀⠀⠀⠙⡆⠀⠀⢿⠟⣿⠏⠀⠀⠀⠙⠳⢦⡐⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡁⠸⠟⠀⣨⣉⡉⢻⣿⡷⠐⠆⠀⠡⠀⠀⠀⠀⠀⠀⣄⠉⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢁⡊⠉⠉⠛⠛⠛⣿⡇⠉⠀⣠⣶⡀⠀⠀⠀⢲⡀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠊⢐⠚⠀⠀⢀⡀⠈⠙⣿⣿⣿⣿⣷⣄⠀⠀⠻⢿⠈⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡀⠀⠀⠀⠀⠀⢿⡀⠀⣾⣿⣿⣿⣿⣿⣧⡀⢀⣨⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣆⠀⠀⠀⠀⢐⣾⢳⠀⢹⣿⣿⣿⣿⣿⣿⣁⣰⣿⠉⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠄⠠⡀⣀⢨⣿⡿⢶⣾⣿⣿⡿⠿⠁⣹⣿⣟⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣿⠷⠂⣰⣟⣺⣿⡇⠰⣿⣿⣿⡷⣦⢀⣿⣿⣿⡷⠂⠀⣠⢤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠸⣟⠓⣚⡾⢿⣿⣿⠃⢸⣿⣿⠟⠀⠀⡀⠙⣿⣷⣦⣶⣿⣇⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣿⣑⣠⣿⡿⠟⢁⣠⣿⣿⠁⠀⠀⢀⣿⣿⣆⡀⠈⠛⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣾⣯⡶⠖⣶⣾⣿⣿⣿⣿⣶⡄⢀⢾⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢻⣿⣿⡇⣿⣿⠟⠁⡼⠀⢻⣿⣿⣿⣿⣿⡟⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠈⣿⣿⣧⣿⠏⢠⡔⠀⠀⠀⠹⣿⣿⢸⣿⣷⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢹⣿⣬⡋⢰⣿⠀⠀⠀⠀⠀⢿⣿⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡀⠀⠀⠘⣯⠀⣸⣺⡏⠀⠀⠀⠀⠀⢸⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢰⣿⣦⣉⢷⡁⠀⠀⠀⠀⠀⢸⡟⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⣿⣿⣿⠷⢶⡇⠀⠀⠀⠀⠀⠀⣿⡅⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⢠⣿⡿⡍⢀⣸⠇⠀⠀⠀⠀⠀⣰⣿⠇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣠⣮⣶⣤⣀⡄⢋⣀⣤⡄⠀⠀⠈⢷⣿⣦⢧⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⡀⠛⢿⣿⠿⠿⠿⠞⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠲⠶⢤⣠⠴⠒⠚⠉⠉⠉⠉⠉⠛⠛⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⣀⠤⠒⠒⠒⠤⣀⠔⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡠⠤⠤⢀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠑⠄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⢀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣈⡇⠀⢰⠃⣴⠦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⡷⠃⠀⠸⣼⣿⡿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⢷⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⠸⠀⠁⠀⠀⢢⡀⠀⢀⡰⠃⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢷⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⡰⠃⢤⠏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⢧⠀⠀⠀⢀⠎⢀⡇⠀⠀⠀⠀⠀⡔⠁⢠⠏⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠈⠳⣄⡔⠁⣠⠎⢻⠀⠀⠀⡠⠊⢀⡴⠋⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀
⠀⠀⠀⠰⠭⠴⣎⡁⠀⠈⣆⠀⠒⠒⠚⠉⡇⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢃⠀⠀⠀⠀⣷⡀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⡾⡇
⠀⠀⠀⣀⠤⣤⡀⣀⡠⠔⠋⠀⠀⠀⠀⠀⢀⡏⠹⡄⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠛
⠀⠀⠀⡇⣀⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠹⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢹⡗⠲⠶⠶⠶⠶⠶⠖⢾⠛⠋⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⢳⡙⠈⠃⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢹⡄⡀⡀⢸⡄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡼⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠙⠲⠦⠬⠤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠧⣼⢤⢾⡇⠐⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣇⣀⣸⣈⠀⠀⣣⣈⣥⡴⠋

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣠⢤⡤⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠈⢡⣀⣾⡿⠛⠋⠉⠀⠀⠀⠲⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠈⢀⣴⡿⠻⣿⠇
⠀⠀⠀⠀⢡⠀⠐⠀⠀⠁⢫⣠⣼⡏⠀⢠⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠨⠅⣲⡄⠀⣿⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡝⢀
⠀⠀⠀⣀⠊⠠⣐⣽⡁⢰⡿⣿⡇⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠈⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠐⣒⠂⠾⠛⢀⠞⠋⠸⠁⠀⠀⣠⣶⣿⣿⠟⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⣴⠟⡆
⠉⠉⠀⠀⠉⢱⡖⠀⠀⠀⠀⠀⢺⡿⣿⣿⣿⣿⣳⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡩⠀⠀⠀⠀⢠⡟⠀⣠
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠠⢀⢿⣿⣿⣯⠉⠁⠀⠀⠀⠁⠀⠨⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡼⠀⠀⡇
⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⡌⠀⠁⠀⠐⢶⣾⡀⠀⠀⠀⡼⠁⠀⠀⠅
⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⣿⠈⠀⠰⠁⠀⠀⠀⢀
⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡄⠀⠀⠀⠀⠈
⠀⣦⣊⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢹⠀⠀⠀⠀⠈⢦⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠘⠋⠀⢸⡀⡀⠀⠀⡄⠀⠂⠀⠑⢵⢀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠠⠃⠀⠀⠀⠀⠐⠀⠀⠐⠃⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⣛⣛⢛⣛⣒⠲⠶⢶⣤⣶⠶⠶⠶⣶⣦⣄⣤⣤⣤⣀⣀⣀
⠀⠀⠀⣶⣟⣉⠉⠀⣠⣾⣿⣿⣷⣤⣝⣿⡴⢚⡤⠈⠀⣀⠀⠀⢼⣿⣿⣿⣦⠈⠉⠛⠛⠻⢦⣀
⠀⠀⠰⣿⠉⠀⠴⣻⣽⣿⡟⠁⠈⠙⠟⣿⣿⣿⣡⡶⠋⠁⠀⠀⠀⠈⢻⣿⢻⣷⣾⣿⣿⠿⣿⠛⠛⠶⢦⣤⡀
⠀⠀⠀⠻⣾⣵⢞⣽⠟⣉⠀⠀⢀⡄⠘⣻⣿⡿⢿⣿⣀⣠⠤⠄⠀⠀⠚⠻⣦⢻⣿⡄⠙⠂⠀⠀⠀⠀⣐⣛⣿⣆
⠀⠀⠀⠀⠿⣷⡟⣡⠞⡁⠀⢠⣾⡷⢿⣿⣿⣯⣷⢹⣯⠖⠂⠐⠲⣶⣤⣾⣻⡎⣿⣟⠀⢤⣀⠀⠀⠀⠦⣽⠿⠛
⠀⠀⠀⠀⠀⠘⢿⣧⡾⠁⢰⣿⣿⣴⣋⡀⢻⣿⡏⢾⣧⣤⡶⠶⢶⡦⣬⣿⡟⣵⣿⡿⣿⣦⠙⣦⡈⠲⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣇⣠⣼⣿⣯⠗⠀⠀⠀⣿⠇⣾⣏⢤⠖⠒⠖⠶⣼⣽⢻⣿⣿⣿⣎⢻⣧⣌⣻⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣣⠖⠀⢰⡿⠠⣿⡷⠀⢚⠟⠛⢳⣿⡟⠸⣿⡟⣿⡹⣎⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣇⡄⢀⣾⠛⢳⣿⣤⢴⡟⠰⠶⢾⣿⢃⣖⣿⡇⣿⣧⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠀⠈⢉⣡⠞⠠⠴⠶⣦⣿⣾⣏⠘⠁⣿⣟⣛⣡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡙⠷⣾⣿⣧⢀⣀⣩⣍⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⢘⣧⠀⠤⢤⣤⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⢀⡞⣭⣿⠀⢄⣸⣿⡏⠀⢸⣿⣿⣿⣿⢟⣭⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢻⠰⡟⢠⣀⣾⣿⠃⡨⣿⣿⣿⣿⣡⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠄⢸⡇⡁⢤⣭⣿⠏⣄⣉⣭⣍⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠈⢻⣷⢾⣿⠉⠀⢦⣿⣿⡏⣿⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠠⣼⣿⢰⣿⢀⣿⣿⣿⡟⠀⣿⠻⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢽⣧⣾⡟⢀⣽⣿⡿⠀⠀⣿⡁⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠨⣽⣿⣿⡿⢺⣿⣿⠃⠀⠀⣿⠆⠒⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣾⣿⣿⠉⠀⠘⢻⣿⠀⠀⣸⣛⣤⢠⣄⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣇⣶⣦⣴⣿⠇⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⣀⣀⣤⣤⣾⣿⣷⣤⣴⣶⣶⣿⣯⣀⡀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⠀⠀⠀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣶⡿⠋
⠀⠀⠈⠙⠷⣦⣤⣀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠰⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⣀⡀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠉⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠈⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣶⣦⣤⣤⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⡁⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠉⠙⠛⠛⠛⢻⣿⡿⠛⠉⠉⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠈⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠒⠤⣄⣀⣀⣀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⣠⠔⠋⠉⠀⠀⠉⠉⠉⠁⠀⠈⠉⠙⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠙⠒⢦⡀⠙⢶⣤⡤⠤⠖⠛⠉⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠘⡆⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡆⠀⢰⠃⠀⢠⠀⡜⠀⠈⢧⠀⢸⠏⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡞⠀⠀⣸⡇⠀⠈⠀⠀⡧⠊⠀⠞⠓⢸⢀⣿⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⣸⣀⣠⡇⣶⣿⠟⠀⠐⠒⠢⠄⠀⠀⠀⠀⢀⡼⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣶⣿⣿⠀⠀⠉⠙⠒⠄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⣿⠀⠀⠐⠒⢦⠀⢀⡴⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣿⣿⣿⠑⠲⠤⠤⠀⣴⣿⡤⢤⣸⣿⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⣠⠴⠚⠉⠀⣠⠿⠋⢹⡐⠀⠀⠀⢠⣿⢿⡇⢸⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢸⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣾
⠀⠘⠓⠶⠶⠶⠒⠚⠉⠀⠀⠀⢸⠮⣙⣓⣀⣸⣟⡼⢀⣼⣿⣿⣿⣿⡛⢶⣤⣤⣦⣀⣠⣤⣄⡘⠘⣿⡞⠀⠀⠀⠀⠀⠀⠀⡎⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢅⣒⡚⢻⣶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡆⢈⠉⠉⠉⠉⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠤⠄⢸⡿⠀⢰⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠀⢸⠇⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠉⢹⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣠⣾⠿⠿⠿⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡓⠂⢠⡟⠀⠀⠀⢸⣿⡟⠉⠉⠉⠃⠀⠀⡸⠀⠀⠀⣠⣶⣾⣿⣷⣶⣿⡿⠋⠀⠀⠀⢠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠣⠉⣠⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠈⠘⡇
⠀⠀⠀⠀⠀⠀⢀⠔⠚⠉⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠇⢠⠂⠀⠀⠀⣸⡿⠋⠁⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢷⡆
⠀⠀⠀⠀⠀⠀⠘⠒⠶⠶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⢠⠃⠀⠀⠀⣠⡟⠁⠀⠀⠀⠸⡀⢻⣿⠀⠀⠀⠀⡀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠘⣿⢀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⡇⠸⣿⡇⠀⠀⠀⡇⠀⢰⡿⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⡆⠀⡤⠀⣿⣶⡄⠀⠀⠀⠀⠃⠀⣿⠇⠀⢀⠀⢻⠀⠀⢳⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⠒⠂⠀⢀⣇⠀⠀⠀⢼⣿⣿⠀⠀⠀⠀⠑⠚⢻⠀⠀⠤⠄⠈⢧⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⠀⠀⢸⢿⣷⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⢸⣄⣠⣤⣤⣄⣨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠿⠿⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠨⠉⠲⡀⡠⢒⣼⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⣀⣀⣀⡀⠉⠐⠢⣀⠤⠐⠒⠁⠀⠈⠀⠈⠐⠃⠤⡀⠀⣀⠠⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠄⠊⠉⠀⠀⠀⠀⠀⠉⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⠤⠄⠀⣀⡉⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠈⠑⢄⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠁⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⠀⠀⠀⠀⠴⢤⣀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠱⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢸⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⣄⠡⠀⠀⡜⣠⣄⢡⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣙⢋⠔⠀⠀⢣⣙⣋⠌⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡅⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⢃⠰⠥⠄⠐⠂⠈⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠉⠐⠤⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠃⠀⠀⠸⠤⠄⠀⠀⠤⠄⠐⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊⠁⠉⠑⣄⠀⠀⠀⠸⠉⠁⠒⠂⠤⠥⢀
⠀⠀⠀⠀⠀⠀⠰⠡⠪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠈⠑⡄⢠⠓⠀⠤⠤⠠⠄⠤⠌
⠀⠀⠀⠀⠀⠠⢡⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⡇
⠀⠀⠀⠀⠀⡄⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⢀⠠⣀⡴⣏⡞⣂
⠀⢀⡠⢤⣚⠜⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡀⠬⡀⣸⣻⣼⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣀⡀⣀⡀
⠒⣯⠔⠊⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣇⣀⡈⠙⡏⠹⠤⠃⠀⠀⠀⠀⠀⠀⠀⡐⠹⠫⡉⠉⠁⠈⠁⠉⠛
⠀⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⣀⠟⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠑⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠄⢀⣀⣀⡀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠶⠒⠈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⢡⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⠀⠀⠀⠀⠀⢀⠰⠀⢀⢱⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠡⢀⢤⠀⠔⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠅⠥⠀⡅⠥⠀⣥⠽⠃⠉⠁⠀⠸⠤⡩⣇⣀⣉⣇⣀⣉⠷⠖⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⡏⢹⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡷⢹⡀⠀⢰⠁⠈⡆⠀⢀⡠⡎⡟⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢓⢤⡀⠀⠀⡇⡄⢧⡀⡸⠀⠀⢇⡰⢉⠊⡜⠁⠀⢀⡤⡚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡑⢌⠓⢤⣧⣘⠤⢽⣇⣠⣄⣸⡧⠼⣀⣇⡤⠚⡡⢊⠞
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠙⣄⠑⢄⣈⠗⠊⠉⠀⠀⠀⠀⠉⠑⠺⣁⡠⠊⣠⠋⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢖⢍⠒⠒⢺⢦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡴⡟⣉⠭⠉⣙⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⣉⣇⡎⠀⠐⣋⣭⡛⢦⡀⢀⡴⢛⣭⣙⠂⠀⢱⣸⣠⠞⠉⠁
⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠒⠊⠉⣹⠀⠀⠸⢯⣿⠟⠀⡇⢸⠀⠿⣿⡿⠇⠀⠀⣏⠉⠑⠒⠒⠢⠤⢤⣀⣀⡀
⠀⠀⠀⠈⠉⠉⠓⠒⠢⠤⠤⢄⣀⣹⠀⠀⠀⠀⠀⠀⡰⠁⠈⢆⠀⠀⠀⠀⠀⠀⣏⣀⡠⠤⠤⠔⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⡏⢇⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⡸⢹⣉⡑⢢⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣫⣍⣀⣒⣉⣼⠞⢣⡀⠀⠀⠈⠩⠭⠭⠍⠁⠀⠀⢀⡔⠳⡧⠤⠤⣑⠵⢄⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⠊⡠⠊⢉⡶⢄⣀⠀⠀⠀⠀⣀⡠⢴⡉⠑⢄⠙⣄⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⢊⡤⠚⢹⠉⡖⢺⡏⠙⠋⢹⣗⠒⡍⢻⠓⢤⡑⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡬⠚⠁⠀⢀⡜⡠⣁⠎⢱⠀⠀⡎⠈⢳⠘⢸⠀⠀⠈⠓⢥⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⣼⡸⠊⠁⠀⠸⡀⢀⠇⠀⠈⣇⢾⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣇⡸⠀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣤⣤⣤⣤⣦⣤⣴⣶⣤⣠⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠙⢿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣼⣷⣤⣾⣿⣿⣿⣿⣾⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣤⣀⣀⣀⣀⣤⣤⡾⠟⢉⣉⣿⣿⢿⣗⣶⠞⠛⠛⠛⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣉⡀⠀⠈⠙⣿⣿⣿⣿⣿⣯⣴⣆⠀⡀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠄⢀⡀⢸⣿⣿⢯⣿⣿⡿⠋⠀⠉⡀⠀⠙⡄
⠀⠀⠀⠀⢀⣼⡟⠀⠀⢠⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⢸⣿⣾⠋⠀⠀⠘⠯⠠⡛⣿⣧⣶⣚⡀⡇⠀⠀⢹⡄
⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⣷⡅⠀⠀⠀⠀⠀⠀⢀⣾⠗⠀⠀⠀⢿⣿⣾⡇⠀⠀⠀⡇⣿⡿⢿⣿⣟⡃⢻⠀⠈⠉⠻⡄
⠀⠀⢀⣿⣿⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠰⣯⣝⢧⡀⠀⠸⡇⣿⣷⣄⠙⢿⡁⠩⢴⣂⠐⠋⢳⡀
⠀⠀⢸⣿⣿⡄⠀⠀⠀⣧⣿⡇⠀⠀⠀⠀⠀⢠⣿⢀⡔⡰⠃⠀⠀⠛⣻⣧⣻⣶⣀⢷⡹⣿⣿⣿⣿⣿⣆⠀⢡⠒⠊⠰⡇
⠀⠀⣾⣿⣿⢻⠀⠀⣸⣿⢻⣷⠀⠀⠀⠀⠀⣿⣿⢊⡪⠁⠀⠀⠀⢠⣿⣿⡿⣿⣾⣤⣁⡉⠉⠉⠙⠻⣿⣿⣛⢯⣀⣾⣷
⠀⣼⡟⢹⣿⡀⠀⠀⣿⣿⡞⣿⣧⣀⠀⠀⣸⣿⣿⠋⠀⠀⠀⢠⣾⣿⣿⣟⣴⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⣿⣿⣷⣭⣛⣟⡛⠒
⢸⡟⠀⠀⣿⣷⠀⠀⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣹⣿⣿⠟⠛⢛⠛⢤⣀⣀⣀⣀⡀⠀⢀⣿⢿⣿⣿⡟⠉⠉
⠘⣷⠀⠀⢻⣿⣇⣦⠀⢹⣿⡏⠙⠿⠿⠿⢟⣿⣧⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠋⠀⠼⡛⠉⠀⠀⠉⠢⣸⡏⣾⣿⠋
⠀⠘⢷⡀⢸⣿⣿⣿⣿⣯⣿⣵⣾⣿⣿⡿⠿⠟⣻⠣⠀⠀⢀⣾⣿⠃⠀⠀⢠⠀⠰⡄⠀⣷⣴⣶⡀⠀⠹⣿⣿⠇
⠀⠀⠘⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⠀⠀⠀⣼⣿⣿⡀⠀⠀⣸⡀⠀⣷⣀⢘⣿⡍⠉⡀⠀⢿⣿⡄
⠀⠀⢸⣿⠀⣿⣿⣿⣿⡏⣿⣿⣿⣿⠏⠀⠀⠀⣿⡄⠀⢀⣿⣿⣿⣿⣷⣾⣿⠇⠀⢿⣿⡞⠉⠙⠻⣿⣄⠘⢿⣷
⠀⠀⠘⠁⣼⣿⣿⣿⣿⢰⣿⣿⣿⡏⠀⠀⠀⠀⢻⡇⠀⣸⣿⣿⣿⣼⣿⡿⠛⣷⠀⠀⣿⠇⠀⠀⠀⠀⠙⠻⣦⡹⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡏⢿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣧⣹⣿⣿⣿⣿⣿⣿⣷⠀⣿⠀⢀⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⣹⣏⠛⠙⣇⢸⣿⣿⡿⢿⡄⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⡿⣿⡀⣿⡁⢸⣿⡅⠀⠀⠀⠀⠀⠈⢿⣿⠇
⠀⠀⠀⠀⣿⣯⣤⣀⣼⣟⠛⠻⠛⠛⠋⠀⠀⠀⣸⣿⣅⠀⢹⣿⡿⠿⠷⠟⠁⣿⣉⣸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠷⠿⠿⠟⠁⠀⠀⠀⠀⠈⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠒⠲⠂⠠⠤⠤⠴⠶⠶⠶⠖⠒⠒⠛⠛⠛⠛⠛⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠁⠀⠀⠀⠀⠀⣠⠶⣄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣏⠠⠼⢦⡠⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠠⢤⣤⣀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣠⣤⣀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠛⠦⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠠⠤⣤⡀⠀⠀⡄⢀⣀⣤⣼⢀⣠⣴⠞⠉⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⢰⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⣀⠉⠀⠀⠛⠋⢁⡄⣀⣀⡤⠞⠁⠀⣿⣠⣤⠴⠛⠓⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿
⢀⣤⡤⠴⠚⢁⢰⡇⣠⣤⠀⢀⡴⠋⠀⣠⠎⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿
⠻⠶⠶⠒⠋⠁⢸⡇⢀⣠⠖⠉⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡷⢿⣥⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⡟⣧
⠀⠀⠀⠀⠀⠀⠸⡇⠐⠒⠂⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣼⠃⠈⢧
⠀⠀⠀⠀⠀⠀⠀⣇⢚⠛⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡉⡉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⢀⡟⢀⣀⡀⢀⣀⣤⠤⣼⠃⠀⠀⠀⡾⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠁⠀⠘⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣸⠀⠀⠸⡆⠀⠀⠀⠀⣼⠁⠀⢦⠉⠉⠁⠶⣤⡏⠀⠀⠀⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢻⣀⠀⡀⠅⢱⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⡄⢸⡇⠀⠀⢸⠁⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠈⠉⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⣇⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⢸⡆⠀⠀⠀⢸⡇⠀⣸⠁⠀⠀⣿⠈⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⢰⠃⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⡄⠀⠀⠀⣷⠀⠀⠀⠀⠁⠠⣤⠤⡄⢰⡇⣸⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⠒⠒⠋⠀⢿⣶⣚⣦⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣧⣛⣳⣠⠤⠂⠀⠀⣾⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⣤⠶⣄⣠⡶⣺

⠀⠀⠀⠀⢷⡀⢣⠘⢷⡄⠀⠐⣄⠀⠀⠸⡇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣤⢀⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠀⢀⣤
⠀⠀⠀⠀⢀⠙⣆⠳⡌⢿⣦⡀⠈⡆⠀⠀⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⣰⣿⣷⠈⠂⠀⠀⢰⠏⠀⠀⠀⠀⠀⢠⠤⠀⡀⢀⣴⠏⢠⡿⠁⠀⠀⢀
⠀⡄⠀⠀⠈⢣⠘⠀⣿⠸⣿⣅⠆⠀⠀⠀⠹⣄⠀⠀⠀⢸⡟⠀⠀⠀⢹⢈⡟⢢⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣀⡰⠁⣾⠁⣠⠎⡄⠀⢀⣴⣿
⠀⠀⡀⠠⠀⠀⠑⣸⠋⢤⣟⠉⠺⣦⠀⠀⠀⠈⠃⠀⠀⠈⣷⠄⠀⠀⢨⢘⣿⡆⠐⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⠋⠀⢰⡏⠰⠈⠆⠀⣴⡿⠛⢡
⠀⠀⢀⣤⠀⠀⠀⠀⢇⠈⢹⣆⠐⠟⢷⣀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⢸⠸⣇⠴⢀⡾⢃⠀⠀⠀⠀⠀⠴⠁⡄⢠⡟⠀⣧⡘⠀⣸⠏⣀⣴⣿
⠀⠠⡀⠀⠈⠳⣌⣠⣿⡀⠀⠻⡄⣇⠈⢳⡄⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⡾⣰⠏⢸⣼⡧⠀⢠⠜⠀⡀⠐⠀⠀⣰⣿⠇⢀⣿⠁⢠⡏⣰⢋⣼⠇
⠀⠀⠈⠂⠐⠢⠤⢁⡍⢻⡄⠠⡘⡀⡆⠀⠗⠀⠀⠀⠀⠀⢹⣧⠠⠀⠀⡆⢹⠀⣧⣿⠁⣄⠄⠀⢰⣰⠃⠀⢠⣿⠏⠀⣼⠋⠠⢋⡴⣧⠟⠁
⠀⠀⠀⠠⡄⠀⡀⠀⠘⡄⣿⣄⡐⢰⡷⢄⠐⠀⠀⠀⠀⠀⣿⡁⠀⡄⢠⠃⣼⠀⢻⡅⠀⣇⠀⢀⡟⠀⣠⠀⢫⠇⣰⣟⣡⠎⢠⠋⠘⠁⠀⠔
⠢⣄⠀⠀⠘⣂⠈⢦⠀⠘⢬⡛⢿⡄⠳⣈⡇⠀⠀⢀⠀⠀⢈⣿⣶⠑⠈⢾⢃⣴⠿⢃⣼⠟⢀⡾⠃⢾⠁⡠⠋⣠⡷⠋⡸⢀⡄⠀⠀⠐⠂⣄⡴
⠀⠘⡃⠈⠀⠹⢆⡀⠂⣀⠀⠉⣿⠃⠀⠠⡉⢦⡀⠀⠀⠠⣿⣿⣇⡀⠐⢹⣿⡇⠀⣼⠁⢠⡿⢀⡶⠃⠈⢠⡾⠋⠀⠀⢠⡟⠁⡰⣂⣤⠞⡝⢣
⠀⠀⠈⠲⣐⠀⠀⠙⠂⠙⢦⡄⣿⣇⠀⠀⠈⠜⠽⣢⠐⠀⠈⠙⣿⣿⣦⠈⠹⣿⡀⣿⣴⡿⠁⡀⠁⢲⣶⠟⠃⠀⠀⣠⢞⣠⠀⣴⢋⡤⣞⡶⠆
⠀⠈⢢⣁⢨⣇⡀⠀⠐⢦⠘⣯⠈⠻⣷⣦⣄⣀⠠⣽⣀⠁⠀⠀⣼⣿⣿⡇⠀⣿⡇⢹⣿⠁⠰⣁⣠⣾⠃⠀⠀⢀⠞⣁⣾⡥⢾⣿⣩⡶⠋⡠⠖
⠀⠀⠈⣏⠉⠙⢿⣅⠀⠈⢣⠙⠲⣤⣀⠈⠻⢿⣷⡌⢻⣷⢇⣴⣿⣿⡿⢠⣾⣯⣎⣾⡿⠀⠀⣿⠉⡠⠀⠀⡀⢀⣴⣾⣏⣴⠾⠛⢁⡀⢈⣤⣾
⠀⠶⢤⣈⡛⠛⢆⠨⠳⣄⠘⠳⣄⠀⢸⡇⠀⠘⣿⡿⢸⡟⢻⣿⡟⣿⢡⣿⣿⣿⣿⣯⣤⣾⣤⡿⠀⠃⡠⢂⣤⡾⣻⡿⠏⠁⣤⠔⢃⣼⣾⠷⠉
⣄⡀⠀⠀⠙⠶⠾⣟⢿⣉⢓⣦⠸⣄⣀⣙⣶⣴⣿⠁⣾⣷⠙⣿⣇⢿⣿⣿⣿⣿⣿⣿⡟⣛⣉⣡⡾⠋⣰⣿⠍⣰⡟⠀⠴⣉⣤⣿⡿⢋⡁
⠀⡉⠑⠄⠀⠀⠀⠘⢦⣙⣿⣿⣷⣤⣄⠀⢹⣿⣿⣧⡘⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⢋⣭⣭⣥⣾⣯⣥⠾⠫⢤⣾⠿⠿⢛⡿⠛⠋⠁⠀⡠
⢦⣄⡀⣈⠁⢀⡀⣄⠀⠀⠀⠙⠛⠛⣿⣇⢿⣿⣿⣿⣿⣿⠟⠋⠩⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣟⣁⢠⣶⣶⣟⣡⡶⠾⠋⣀⣠⡔⣂⣻⣷
⣀⡀⡀⠀⠈⠁⠉⠛⠷⠶⠶⠾⢶⣄⡹⢿⣬⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣤⣼⡿⢿⣛⣿⣭⣭⠿
⣋⡉⠁⠂⠉⠛⠶⠶⠶⣦⣤⣤⠶⣿⣿⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣟⣿⣭⡿⣧⠿⠶⠟⣉⣉⡄⠐⠂
⠙⠾⠶⣿⣁⠴⠶⣤⣤⠴⢦⣄⣀⣬⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⢛⣉⣹⣧⣤⣴⡚⢛⣷⣾⣧⣄⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣏⠉⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⠟⣿⠟⣛⣛⠋⣻⣿⣟⢉⣉⠙⠿⠿⢛⣁
⠠⠀⠄⠤⣀⣀⣀⡀⣀⣽⠷⣦⣌⣛⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡟⠛⢿⣛⠛⡿⠿⢿⠿⠿⣟⣛⣛⣋⣩⣍
⢀⡤⠌⠀⠉⠛⠑⣉⠉⢡⣶⣄⠉⢉⣼⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⢻⣬⡟⠲⢦⣉⠛⠛⠳⠾⠓⠚⠛⠛⠓⠢⠀⠄
⣀⣀⣤⢶⠾⠟⠾⠛⠳⠿⡥⠈⠟⠿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣶⣤⣶⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣮⡛⠿⣦⣉⡉⠛⡢⣤⢀⣀⡀
⠋⠉⠀⠀⠀⠀⠀⠀⠐⠀⣁⢀⣶⠶⢿⢠⣼⡿⣿⡏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣌⠉⠻⣿⣿⣷⣌⡙⢻⣶⣤⣠⡀⠀⠈⠛⠿⠛⢣⣶
⠀⠀⠀⠐⠉⠁⠀⢀⡄⣴⠏⠉⣁⠔⣤⢶⣿⣴⣟⣸⡏⣿⣏⣿⠏⢘⣯⢿⣿⡟⢧⡻⣿⣿⣧⣀⠈⠙⠳⠦⡷⢶⡍⢻⣯⡉⠤⡀⠠⢀⡈⠀⠈
⠀⠀⠀⠀⣠⡤⠴⠏⠀⠀⠔⠉⠰⠞⣁⣼⡏⢁⣼⠏⢀⣾⣏⣿⠀⢻⣇⢨⣿⢃⠸⡋⣿⣯⡛⢻⣷⣄⡀⠀⠀⠁⠙⠦⠹⣿⣤⡈⠉⠠⠀⣀
⠀⣄⡲⠿⠋⠀⠀⠀⠀⣠⢴⠿⣋⣾⣿⠛⠐⡏⠁⠀⣿⢹⣿⠃⠀⠸⣯⠹⣷⡘⢆⠙⣋⢿⠿⣿⣿⣿⣿⣌⡲⣦⡀⠑⠢⣝⠻⡿⢶⣶⣄⡀
⠚⠁⠀⠀⠀⠀⠀⠀⢈⣡⣁⣼⣿⠏⠉⠂⡔⢁⠀⢀⣾⣦⣿⠀⠀⢰⣿⡇⠈⢻⡎⡆⠹⡈⠀⠈⣿⣿⡏⢿⣷⣜⢷⡄⠀⠻⣄⠘⠊⢻⣏⠻⣆
⠀⠀⠀⠀⠀⠀⣰⠟⠋⢉⡟⢻⡉⠠⠀⡠⠃⠀⠀⢸⣿⡟⠁⠀⠀⠀⣿⠇⣀⣾⡃⢨⡀⠁⠀⠀⢻⣎⡳⣤⣙⠿⢷⡍⠻⣦⠀⠙⣦⡈⠉⢷⡌
⠀⠀⠀⠀⡀⢨⣿⢀⣸⡏⢀⣭⠋⠀⣼⠀⠀⠀⠠⢾⣿⡅⠀⠀⠀⠈⢻⣤⡙⡯⣿⠘⣧⡀⠀⠘⠙⢈⠙⢦⠈⢇⠀⠰⡆⣹⢷⣄⡘⠷⣄⡀⠈
⠀⠀⢠⣤⣤⣿⠁⢾⣩⣾⠟⠁⢀⢾⡏⠀⢀⣦⣴⢾⣿⠟⠀⠀⠀⠀⠀⣿⠟⠁⣼⠃⠈⣿⣦⡀⠀⠈⠀⠈⠂⡀⠐⠄⠀⠘⠷⣄⡙⠳⡀⠹⣧
⠀⢀⣿⠁⠀⠀⢈⣾⠛⠋⠀⢀⡟⢸⡇⢠⢻⠉⠀⢀⣿⠀⠀⠀⠀⠀⠀⣹⣷⡄⡈⠃⠄⠈⠚⣿⡆⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢌⠻⣆⡡⠀⠻
⡰⠟⠋⠀⠀⢠⣞⠅⠀⡀⢠⠊⢠⡇⠀⠸⠀⣧⠀⢸⠇⠀⠀⢀⡠⠖⠈⢿⡟⢧⣁⠀⣴⡀⠐⠿⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠌⣻⢷⣄
⠁⠀⠀⠁⠀⠼⠃⠀⢠⡸⢀⡤⢿⠀⣠⣴⠾⠛⠀⡞⠀⠀⢀⡏⠀⠀⠀⣟⢧⡘⠏⠐⠨⣿⣄⠀⢦⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙
⠀⠈⠀⠀⠃⠀⠀⢤⠋⢠⢸⡴⠃⢸⡏⠀⠀⠀⠸⠇⠀⠠⠊⠁⣄⠀⠀⢹⠆⠣⠈⢠⡄⠀⢻⡆⡘⠌⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠈⠛
⢠⠄⠈⠀⡀⠀⠰⠃⠀⢸⣼⠃⠀⢼⡇⠀⠀⠠⠀⠀⠠⠀⠀⢠⡁⠀⠀⠹⢦⡀⢣⠈⠉⢦⢼⡇⣶⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠁⠀⠀⠀⠀⠀⠀⣠⠞⣱⠏⢀⠔⡘⠀⠀⢠⠀⠀⠀⣰⠀⠀⣸⡇⠀⠀⠀⠀⡅⠈⢄⠀⠸⡈⢿⠻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⡞⠁⡼⠃⠐⠁⠖⠁⠀⠀⠃⠀⠀⡀⢙⠂⢀⢳⠈⠇⠀⠀⠸⡃⠀⠀⢠⡀⢸⡇⢣⠀⡄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣜⠷⠈⢰⠀⢿⠀⠀⠀⠑⠀⠀⠀⠇⠸⢷⡠⡋⠡⡀⠁⠀⠀⠀⠀⠈⠋⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⠀⠙⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⣾⡄⠻⡀⠀⠀⠀⠀⠀⡃⠰⠒⠂⠈⠃

⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢾⣿⣿⣿⣿⣿⣷⣶⣶⣦
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣵⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣥⣶⣿⣀⣤⣀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⢁⣴⢿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠚⠃⠀⠪⡍⠀⠙⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠃
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣤⠏⣠⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⣋⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⢠⡶⣦⣄⡀⣀⣀⣠
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⡀⢀⣴⣤⣤⡀⠀⠀⠀⠀⠀⠀⢸⠃⣾⣿⣿⣿⣿⣿⣿⣷⡶⠖
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⢀⣠⣿⣉⣿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒⠂
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠹⠿⠟⠚⠛⠉⢠⣿⣿⡟⠉⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⡇⠀⠉⠈⢽⣿⡗
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠿⣏
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣿⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠁⠀⢀⣀⠀⡀⠘⣁
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⢈⣷⣾⣧⠂⡀
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⠀⠙⣿⣿⣿⣿⣴⠗⠂
⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⢠⠞⣸⣿⣿⣿⣿⣿⣦⠆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠞⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⠉⠓⠶⠔⠒⠉⠉⠉⠉⠛⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠂⠀⡰⠞⣶⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠃⠈⢁⡀⠀⢀⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣷⢠
⠀⠀⠀⠀⢣⡀⠈⢧⠀⠎⠀⣠⡿⠁⣠⣾⣿⣷⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⣿⢰
⠀⠀⠀⠀⠀⠙⢤⣤⣠⣄⡶⠤⠶⠾⠛⠛⠋⠉⢋⣯⡆⠀⠀⠀⠀⠀⠀⡠⣄⣀⣠⣤⣀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡻⣄⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⢠⡟⠘⠃⠽⠾⣻⣧⡀⠀⠀⠀⠀⢀⣼⣿⣿⡃⠀⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡇⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠈⠑⠀⠀⢀⡴⢿⣿⣿⣿⣆⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡟⠀⠄⠀⢸⡿⠀⠀⠀⠀⠀⠀⢀⠃⢀⡾⠉⠀⠀⠈⢖⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⢠⠀⠻⡅⠀⠀⠀⠀⠀⠠⠁⠀⣾⠁⠀⠀⠀⠀⠈⡀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⠀⠀⠐⠴⢴⡄⢰⠀⠀⠀⠀⢀⣤⠖⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⣠⣤⣤⣄⡀⡿⢟⣤⣤⣄⣀⣀⠀⠋⣀⣀⣄⣠⣘⣇⠀⢀⣀⣀⣠⣴⣀⣀⣘⣿⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠀⠀⠈⠈⠉⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠁⠉⠉⠉⠉⠉⠀⠀⠈⠁⠀⠀⠉⠉⠀⠉⠀⠀⠈⠈⠉⠁⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠠⠀⠀⠀⡄⢠⢿⣷⡀⠁⠀⠁⠀⠐⡀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣤⡀⠀⠂⠀⠀⠀⠿⠸⢿⣇⠀⠀⠀⠀⢀⡴⡫⣷⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠹⡌⢎⢳⣤⠐⠀⢀⢸⠁⠀⣆⢹⡀⠀⠀⣰⠞⢱⢣⡟⠀⠀⠀⠈⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⠀⠐⠀⠀⠀⠸⡇⠈⢄⠟⣷⡆⠀⠇⠀⠀⡇⣼⣷⠀⡴⠃⢀⣏⢎⡟⠀⠀⠀⠈⠀⣀⠈⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⢿⡳⣴⣄⣀⠀⠐⣇⠀⠘⣞⣰⣽⣿⠤⠤⠶⠻⠿⠿⡿⣅⢀⡞⡿⣜⡟⠀⢁⣠⠤⠚⣡⢾⡿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢮⠪⣝⣗⢶⣾⣀⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⠔⠋⠁⣠⢞⣵⡏⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠄⠐⠠⡀⠀⠘⢧⠀⠙⠪⣪⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣠⣞⢕⣿⡏⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠘⢧⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣀⡄⣠⡤⠤⠶⢦⣴⡶⠂
⠀⠀⠙⠻⣿⠯⣟⣻⢏⣓⠿⣖⣻⠿⠀⠀⢀⡤⢴⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣀⣀⠀⠀⠀⠹⡅⠀⠀⣀⠤⢒⣭⠾⠛
⠀⠀⠀⠠⠉⠓⢦⡉⠙⠛⠿⢶⡿⡀⠀⠀⠀⢀⣤⣤⣤⣤⣶⣟⢷⡀⠀⠀⢀⡴⠟⣥⣀⣀⣴⣉⣀⠀⠀⠀⠀⠸⣦⠛⣠⣴⠞⠋⠀⠄
⠀⠀⠤⠄⠀⡀⠀⠉⠳⢤⡀⣼⠁⠀⠀⠀⠀⠁⠀⣻⣿⣿⣇⣽⣿⣷⠀⠀⣼⠻⠓⠛⠹⣿⣿⡟⣨⡗⠠⠀⠀⠀⢻⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⣿⡄⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠠⠀⠸⡅⠉⠙⠓⠶⠆⣠⣀⠀⠁
⠀⣀⣠⣶⠶⠞⠋⠭⣭⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣧⣤⣤⣶⣶⣶⣶⣴⠿⠖
⠀⠉⠿⠏⠩⢉⣀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⣶⠖⠚⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠉⠑⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⢐⣰⢿⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⢀⠈⠲⢦⡀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⡴⣏⡬⠗⠋⠉⠙⡄⠈⠀⠀⠀⠀⠀⠀⠀⠲⠔⠓⠒⠦⠤⠚⠛⠛⠒⠒⠀⠂⠀⠀⠀⠀⠀⢠⣿⣷⣿⣟⣾⣥⣂⣽⣷⣄⠂
⠀⠀⠀⣠⣾⣗⣋⡥⢤⠤⠴⠖⠶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣄⣀⠋⣤⢊⠂⢀⠀⠀⠀⠀⢀⡴⠉⢻⡀⠁⠀⠉⡁⠉⠙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⠫⡫⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠠⠐⠀⠀⠀⢀⣴⢿⡢⡀⠀⠩⡄⠈⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⢀⠄⠊⠀⢀⣼⡋⣠⠞⠁⢀⣹⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⣀⡤⠞⢿⠷⣴⣝⢮⡲⢄⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⠞⢁⣠⢖⠋⠘⣯⢋⣻⠋⠛⢳⣶⣦⣤⣤⠤⠴⢶⣶⣿⠋⠄⠀⢸⡄⠌⠉⠻⠿⢦⣕⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠵⠞⡁⠀⠀⠀⢸⢇⢈⠇⠀⣰⠋⢸⡏⢿⠀⠀⠀⡜⠘⠿⣆⣌⠄⠈⣏⠂⠀⠀⠀⠀⠁⡉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⢀⠀⠀⢸⡏⡌⠀⡞⠀⠀⠈⣿⢸⠈⠀⢰⠁⠀⢠⠘⢿⡌⠄⢧⠀⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣾⡝⡰⠃⠀⠀⠀⠀⠘⣷⢠⢀⡇⠀⠀⠀⠀⠀⠹⣤⣬⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⡀⠀⠐⠀⠀⠀⠀⢻⣼⡘⠃⠀⠂⠀⠠⠈⡄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠂⠈⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠦⣤⠒⠊⠉⠉⠉⠉⠉⠙⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⠔⠊⠉⠉⠉⠉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⡠⠊⠁⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⡜⠀⠀⠀⠀⠀⠀⠀⢈⢀⠀⠀⢀⠤⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡇⠀⠀⠀⠀⠀⠀⠀⢁⣤⡇⠀⡎⣴⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢳⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠊⠀⠀⡀⠀⠀⢀⠎⠀⠀⠀⢠⡇
⠈⣆⠀⠀⠀⠀⢀⢾⠀⠀⠀⠀⠀⢀⠂⢠⠃⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⡾
⠀⠘⣆⠀⠀⡠⠃⣸⠀⠀⠀⠀⡠⠀⣠⠏⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠈⠢⠈⣠⠞⠉⡆⠀⢀⠀⣠⡴⠁⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⢀
⠀⠀⠀⠁⠉⠳⠤⠤⠾⡀⠉⠁⠀⣇⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢂⠀⠀⠀⢳⡀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣰⠇
⠀⠀⢀⠤⠤⣀⠠⠔⠋⠀⠀⠀⠀⢀⡏⠱⡄⠀⠀⠙⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘
⠀⠀⢸⢠⢰⡄⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠹⡄⠀⠀⢻⠀⠀⠀⠀⠀⢸⠉⠛⠛⠛⠛⠛⢹⠉⠁⡹⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠳⣄⣀⡐⠀⣀⡠⠴⠊⠁⠀⠀⠀⠀⢳⢠⠄⣸⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠸⢤⣤⠇⠀⠀⠀⠀⡀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢴⣤⣤⣶⡖⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠀⣰⣾⡟⠁⣤⣶⣿⣦⣴⡇⢴⠀⡀
⠀⡄⠀⠀⣠⣰⣿⣿⣿⠟⠀⠹⠿⠛⢿⣿⣿⣾⣿⣷⣇⡇⢰⡆
⣷⣷⢀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣟⠩⣑⣿⣠⠀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣽⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣯⣻⣤⡀⠀⣀⡰⠁⠀⠀⢰⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠉⠉⢄
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⣽⣿⣀⠀⣴⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣧⢇⠀⠈⠂⠀⠸⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣛⣯⣀⣊⣻⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⠀⠀⢲
⣿⣿⣿⣿⣿⢹⣿⣿⡏⠙⢿⣿⣿⣿⡿⠛⠉⠉⠙⠻⣿⣿⡟⠛⠛⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣧⣿⣯⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⡀⠀⠀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡠⠀⠠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠠⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠗⠀⢸⠇
⣿⢟⣡⣿⣿⣿⣿⡏⠉⠂⠀⠀⠀⠀⢧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡜⠂⢻⡂
⣿⠇⠈⢻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢣⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣧⣷⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣸⣿⣿⠃⣂⠠⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⢀⣷⠀⢀⠠⠀⣾⣿⣻⣿⣿⣿⡿⠯⡀⢨⣽⣿
⠀⢠⣤⡆⣿⣿⣿⠃⠀⣇⠈⢻⣷⣄⠀⠀⠀⠘⣿⡜⣼⡄⠀⣿⣿⣿⣿⣿⣿⣡⣬⣾⣿⠟
⡀⢨⡟⣷⣿⣿⡇⠀⠸⣿⠁⠀⣿⣿⣧⠀⠀⠀⢹⣯⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⢏⠁
⣷⣼⣷⣿⣿⣿⣷⢠⣦⣿⢐⣠⣿⣿⣿⡟⠀⠀⠈⣿⣿⣦⣠⣿⣿⣿⣿⣿⡿⣷⣿⣌⠀⠀⠀⡄
⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢠⠀⠀⠀⠙⣿⣿⣿⣿⣿⣼⣿⣿⣷⣿⣿⣷⡆⣀⡀⣁
⢋⣿⣟⣿⣿⣿⣿⠿⢟⠛⠿⠟⠻⠟⠛⠛⠶⣰⠰⣾⡟⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣁⣭⠤⠄
⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠞⠙⠃⠘⣿⣿⣿⣿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣤⡀⠀⠀⣄⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣦⠀⢹⣷⣄⠀⣿⣿⣿⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⡈⢻⣿⣿⣿⡆⣾⣿⣿⣴⣿⣿⡏⠀⢀⣾⡇⠀⠀⣠⣾⣿⠋⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⡿⠀⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢿⣶⣶⣾⣿⣶⣤⣀⠀⠹⣿⣿⣿⢿⣫⣽⣶⣶⣶⣾⣭⣟⠿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⢿⣿⣿⣷⣾⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿⡿⠟⠉⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⣿⣿⣏⣾⣿⣭⣥⣭⣝⣿⣿⡿⠿⠻⠿⣿⣧⢻⣿⣿⣷⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⠿⣿⣿⣿⢹⣿⣿⣿⣟⣧⣿⣿⣿⣾⣿⣿⣻⣾⣿⡟⣿⣿⣛⣉⣀⣀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣼⣿⣯⡉⠉⠙⠛⠛⠋
⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠉⢁⣴⣾⣿⣿⣯⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣾⡿⠟⠛⢋⣿⣿⣶⣽⣛⣿⠿⠿⣿⣛⣭⣾⣿⣿⣿⣿⡛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣠⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⢸⣿⣿⠏⣿⣿⣿⠏⢿⣿⡆⠀⠀⠻⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠸⣿⠃⠀⣿⣿⣿⡄⠀⠉⠛⠶⠄⠀⠀⠀⠀⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠀⠀⠹⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠒⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠋⠀⠀⠀⠀⠀⠓⠿⣿⣿⣿⣿⠋⠀⠀⣤⣤⡀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠀⠀⠀⠀⠈⠛⠲⢿⠀⠘⣧⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠘⠿⣿⢀⣶⣧⠀⠀⠀⠀⠘⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣷⠀⢴⡀
⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⣿⣿⣿⠟⠋⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⡿⠸⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣶⣤⣤⣶⠆⢀⣴
⠀⠀⠀⠀⠀⠀⡇⠀⢨⣿⣿⠏⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣃⣴⣾⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣇⠀⠀⢿⣿⠀⢀⡴⣿⣿⣿⡿⠉⠉⠉⠉⠙⣿⣿⣿⡏⠻⣶⡀
⠀⠀⠀⠀⠀⢺⣿⠀⠀⢸⣿⢀⡎⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠈⠁⠀⢀⣿⡇⠘⠀⠀⣸⡇⠀⠀⠀⠀⠀⢰⣦⠐⣾⣿⣿⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡄⠀⠀⠀⣿⣅⣀⣀⠀⠀⠀⠈⠻⡧⠋⠉⠁⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠂⠀⠐⠂⠒⠂⠒⠀⠀⠶⠶⠶⠶⠒⠒⠦⣄⢿⣄⠒⠄⡀
⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡸⣭⠍⠉⢷⡛⠦⢤⣀
⠀⠀⣴⠏⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠨⢸⠀⡠⠈⠉⠀⣵⣤⠰⢓⡗⡀
⢀⡾⠁⠀⠀⣾⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡇⣿⠃⠸⠀⠀⢰⢲⣿⡿⠂⠈⠉⡔
⣸⣤⠀⠀⡇⠹⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡿⠔⢙⠓⠉⢲⡆⠀⠀⢸⢰⡏⠀⠀⡠⡀⠀⠻⡀
⣿⠘⡆⠇⢣⡄⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠸⠁⠀⡘⠈⠻⣤⠀⠀⡿⠡⣄⠈⢘⠃⢀⡤⢆
⣯⠀⠹⡀⠈⠳⠌⠀⠀⠈⠂⠀⠀⠀⠀⡄⠀⠀⠀⡞⠀⠠⠖⠀⠀⠂⣸⠳⡗⣠⠇⠠⣄⢸⣧⠀⢚⣵⡌
⣻⡀⠀⢳⡀⠄⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠀⠐⢀⣷⠀⠀⠀⠀⠀⢼⠃⠀⠀⠂⠀⠀⠀⠀⣿⠇⡀⢻⡟
⢸⣗⠀⠀⠷⣄⠀⠀⠀⠠⠀⣬⡦⠴⠛⠚⠋⠉⠁⢸⡄⡆⠀⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠄⢘⢱
⠀⠀⠀⠀⠀⡌⠢⣀⡀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡧⠇⠚⢠⢶⠇⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣆⡞⠋
⠀⠀⠀⠀⠀⢸⠀⠿⡄⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣽
⠀⠀⠀⠀⠀⡾⠀⠀⢰⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣷⠹⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠉⡄⠀⠆⢱⡄⠀⠀⠀⠀⠀⠀⡀⠀⣻⡷⠏⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠫⣀⡀⢀⡼⠀⠀⠀⠀⠀⠸⢄⣈⢉⠨
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠿⣦⡢⡀
⠀⠀⠀⠀⠀⠀⣨⢣⡇
⠀⠀⠀⣀⡴⠊⢠⠞⠁⠀⢀⠴⠚⣉⠀⠁⠐⣄
⠀⠀⣴⠏⢠⡞⠁⠀⠀⠈⢰⣎⠀⣁⠀⠀⣀⣤⡅⠀⠀⠀⠠⡄⠀⣀⡀
⠀⠘⣿⠂⠈⣳⠚⠁⢀⠄⣄⢛⣀⣀⣠⠚⠛⠛⠀⠐⢄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠙⠿⣷⣤⣴⣆⣁⣴⣿⣟⡉⠉⢹⠀⠀⡀⠀⢢⣼⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢰⣄
⠀⠈⠐⠒⠿⠟⠒⢉⣟⣽⣋⠁⢈⣦⣼⠤⣷⣿⣿⠟⠋⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠉⠉⠉⠻⣿⣿⡟⣧⠀⠀⡀⠀⠀⠀⣿⡷⣠⡄⠀⠀⢀⣠⡞⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠑⣀⠁⢀⠀⠀⣿⣷⡟⠅⠀⠀⠚⣟⣶⣿⢣⡟⣿⠁⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⠊⠐⠿⢦⣞⣿⣿⣁⣀⠀⡤⣼⣿⣿⣿⣾⣿⡏⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢽⣿⡟⠂⠀⠠⠀⢻⡟⠿⢿⣯⣭⣶⣿⣿⣻⣿⢫⡟⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⡀⠀⠀⢨⡇⠀⠀⠀⠀⠈⠛⢿⡿⡟⡿⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⠋⠁⣿⠀⠀⠀⢀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡏⠀⠀⠀⢀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠰⠀⢸⣿⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣸⠇⠀⠀⠀⠀⢂⠀⢰⡇⠀⠀⠀⠀⢀⠿⠀⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢘⡆⠀⠀⡀⢀⢈⠀⠀⠱⠀⠀⠀⠀⠿⢠⣤⠾⠋⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢛⣛⡛⠓⠲⠦⣤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⣀⣠⣤⠴⠶⠶⢾⢟⣴⠾⠟⠛⠛⠿⣿⣇⠠⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠉⠉⠭⢽⡿⠟⠋⠁⠀⠀⠀⠀⡿⠋⣀⠀⠀⠀⠀⠀⠙⠿⠛⠓⠄⣐⠤⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡏⠀⢀⠀⠀⠀⠀⠀⠀⣆⠀⢶⣗⠿⢦⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡞⠁⢀⠀⠀⠀⡠⠀⠈⠳⣄⣨⠋⣄⠒⣻⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⣠⠜⠁⠀⠀⢠⣿⣿⣦⣘⣧⢸⣇
⠀⠀⠀⢀⣴⡿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⢿⣷⣾⣦⣇⣴⣿⣿⣿⣏⠙⣆⣿
⠀⠀⠀⣸⡟⠀⠀⠸⣷⣀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⡄⠀⠀⠀⠀⢈⣻⣿⠇⠙⠻⣿⣷⡌⠻⡀
⠀⠀⠀⢿⡇⠀⠀⠀⠻⣿⡷⠀⠀⠀⠘⣄⢧⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⡄⢠⡇⠀⠀⠲⣷⢇⡿⡿⠀⠀⠀⢨⣿⣿⡶⣌⡲⢄
⠀⠀⠀⣼⠀⠀⠀⠀⠀⢹⣿⣦⡀⠀⠀⠈⠿⣿⣿⣦⣀⣀⣀⣤⣤⣶⣿⣋⣽⣿⣿⣈⣿⠀⠀⠑⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⠙⠪⢿⣅⡛
⢀⣴⡟⠁⠀⠀⠀⠀⢰⣿⣿⡻⣅⠀⠀⠈⠳⣽⣿⣿⣿⣿⡿⠿⠟⠋⠉⠉⣿⣿⣿⣿⣿⣴⣀⠀⠈⠙⣶⡀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠁
⠺⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡂⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⡟⠻⢿⣧⣀⠀⠀⢙⡆⠀⠀⠀⠻⣿⢓⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢷⡄⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠘⣿⠁⠀⠀⠈⢻⡿⠀⠀⣧⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣀⢸⣦⣀⣾⣿⣿⣿⣧⣎⣿⣆⡀⠘⢷⣷⠠⣇⠀⢢⠀⢠⡄⣾⣿⣄⣀⣹⡆⢀⠠⠀⣼⠿⣂⡀⣹
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣷⣯⣷⣷⣾⣿⣷⡿⠍⣭⡍⠝⣷⣬⣼⣜⣷⣴⣛⣉⣽⣯⣷⣦⠄
⠀⠀⠀⠀⠉⠁⠀⠁⠙⠹⠟⠛⠝⠛⢻⠿⣴⣛⣹⡭⠿⠋⠁⠀⠉⠛⠁⠉⠁⠋⠁⠀⠉⠉⠛⠙⠛⠟⠿⠻⠛⠁⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣀⠀⠀⣸⣿⠀⠀⡀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢿⣤⡄⣿⣿⠀⢰⣇⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠈⢳⣔⣦⣿⣿⣦⣼⣿⣿⣿⣿⣦⣿⣿⣧⣿⡿⠁⢀⡄⠀⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⣻⣿⣿⡿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣇⣴⢟⡆⢀⣤⣶⡿⠟⠁
⠀⠀⠀⠠⣤⣤⣀⣀⡀⠀⠀⠐⢦⣔⡶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣦⣤⣀⡈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⣤⡶⠚⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣀⣤⣤⣤⣶⣶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣶⡶⠦
⠀⠠⠴⠶⠛⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣽⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠿⠿⢿⣿⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⢶⣤⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⢛⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣏⡉
⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠉⠀⠀⣨⡿⠛⢹⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣯⡉⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠮⠻⢦⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⢻⡟⠀⣿⣿⢿⣿⡟⠻⣿⣿⢿⣻⣆⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠚⠀⢠⣿⡟⠈⢻⡇⠀⢻⣿⠀⠁⠹⠄⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠃⠀⢸⣿⡆⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⢐⣀⣤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢴⣾⣿⣿⠫⠏⡿⢫⢳⡖⣶⢶⠞⡛⢿⣿⣿⣤⠄⠀⢀⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢠⣾⠋⠀⢸⣇⠀⣼⠿⠿⠶⠶⠿⠦⠾⢬⣿⣬⣧⡤⠿⠟⠋⢁⠀⣴⡿⢁⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣿⡇⠀⠁⣾⡇⠀⠀⣀⣀⠀⠒⢀⣤⣤⡄⠀⠀⡀⠀⠐⠶⠤⣤⡼⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠈⣼⡿⠀⢠⣾⠋⣸⡇⢠⣿⠏⠠⢇⣶⠀⢀⣴⠟⣹⠆⢠⣻⡇⢀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⠾⠋⠀⠀⣾⣿⠾⠛⠀⣼⣿⠀⢠⣿⢹⠀⣾⡟⠰⠋⢀⣾⣿⡾⠋⢠⣿⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠀⢀⡴⠒⣦⢹⣽⡄⠀⢠⡿⣿⣤⠟⠀⢿⣇⢻⣧⠀⣠⠞⣿⣿⠁⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡾⠁⣰⣿⠀⠙⠿⠶⠟⠀⢠⣄⠀⠀⣀⠙⠉⠛⠛⠁⠀⢹⣿⠀⠀⣿⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣾⠟⠁⣶⣶⣶⣄⠀⠀⣿⣿⣆⠀⢿⣇⢀⣾⣧⣴⣶⣌⠁⠀⡀⠘⢷⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⣷⠈⢻⣷⢸⣿⠉⣿⡆⠈⣿⣾⡟⢹⣷⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣿⡄⣼⡟⢸⣿⡶⢿⣿⡀⣼⡟⢀⠀⢿⣧⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢻⣿⠟⠀⠘⠛⢀⣤⠉⠘⠟⠀⢻⣧⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣤⣾⣿⠀⠀⠄⠀⠀⠈⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠈⣿⣿⢿⣻⣿⣶⠶⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⣿⠿⠻⣾⣿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠈⠿

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣴⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⢴⣾⡟⢿⡟⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣀⣰⠘⠀⠀⠀⠀⠀⠤⡄⠈⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣾⠿⣷⡿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠁⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡀⠀⣼⣷⣿⣿⣿⣷⣤⠀⠀⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣾⣁⢰⣿⣿⣿⣿⣿⠋⣀⣠⣴⣾⡇⢀⡀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣸⠋⠀⠋⠀⢹⣿⣿⠟⣻⣿⣿⣿⣿⡟⢸⣷⡟⣠⠇⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠔⢀⣯⠀⢸⣥⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣠⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⢸⣃⠠⡏⠀⠀⠀⠀⢸⣟⠈⢿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⣷⠀⠀⠀⠀⣼⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣻⠀⠀⠀⠀⢿⣿⣿⣷⠋⠻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⢻⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠙⢿⣿⣿⠸⣿⣿⠏⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⡁⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠘⣿⣿⣇⣿⡏⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⣿⡿⢸⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡷⠘⠇⠀⠀⠀⠘⣷⢹⡟⠆⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠃⠀⠀⠀⠀⣾⡷⢠⣶⠂⠀⠀⠀⠀⣽⡿⠧⠀⣰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠀⠀⠉⠀⠙⠂⠀⠒⠋⠉⠁⠉

⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠻⢿⣄⡀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠞⠉⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢦⠀⠀⠀⠀⠀⡤⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠰⣶⠀⠀⠀⣷
⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⢿⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢿⠲⢤⣀⣀⣀⣀⣀⣤⡶⠀⠀⢀⡇⠀⠀⠀⠀⠐⠛⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⠤⣀⣉⣉⣩⠵⠋⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠈⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⣟⡆
⠀⠀⠀⠀⢀⡤⠦⣏⣞⣹⠆
⠀⠀⠀⠀⢸⠀⠀⡼⠉
⠀⠀⠀⠀⠸⣤⠞
⠀⠀⠐⣟⡓⠦⢶⡆⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠈⡇⠀⢿⠞⠋⠀⠙⠳⣄⣀⣀⣀⣀⣀⣀⣠⡶⠋⠁⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣹
⠀⠀⠀⠀⣇⠀⢸⡀⠀⠀⢠⠖⠉⠉⠉⠉⠉⠉⡩⠋⠀⠀⠀⠀⠀⠈⢳⡶⠦⢤⣤⣀⠀⠀⣨⣷⠖⠋
⠀⠀⠀⠀⣿⠀⠀⢣⠀⢠⠃⡆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠈⠻⢞⣿⠏
⠀⠀⠀⢸⢻⡄⠀⠀⠳⢏⣀⣿⣀⠀⠀⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠸⡏
⠀⠀⠀⢸⡄⢇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠻⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⢧⣍⠓⡦⠤⠤⠤⠤⠒⠁⠀⠀⠀⣠⠖⢄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣤⠤⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⢰⡷⠶⠶⠶⠶⣶⠒⠚⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣾⡄⠀⡀⠀⠀⣼⠁⠀⠀⠀⠀⢹⣄⣆⣣⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠾⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⢇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠇⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠆⠀⢀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⡰⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⢰⢀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡾⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡞⠀⠈⢆⠀⠀⠀⠀⠀⡄⠀⠐⡀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⢰⠀⠀⠀⠀⡠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠆⠀⢠⠰⠊⠀⠀⠀⠀⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠆⠀⠀⠀⠆⠈⠀⠰⠀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢀⠁⠀⢸⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣠⠀⠀⡇⠀⠘⡄⣀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠇⠀⠀⣾⡀⠀⠀⢄⡀⡉⠁⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⡇⠳⣄⠀⠀⢹⣁⠀⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠀⢀⠃⠀⠈⠉⠁⠈⠇⠀⠀⢸⠀⠀⠀⠀⠀⡏⡀⠀⢀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡀⠀⠀⠀⢀⣘⠀⢸⠀⠀⠀⠀⢀⠐⢌⡖⠒⠃⠀⠀⠀⠀⠀⠏⠀⠱⠇⠸⠧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠄⢵⠁⠸⠥⠸⠃⠘⠀⠀⠓⠀⠐⠃⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⣤⢤⡖⣶⣦⡶⠦⠂⠀⠀⠀⠀⠀⠐⠦⢤⣤⣤⣀⣀⣀⡀⠂⠀⠀⠀⠀⣀⣀⣤⣄⣀⣤⣤⣠⡀⠀⣰⣏⣫⡀⠈⣡⣄⢠⣠⢀⣀⡂⠀⠀⠀⡀⢀⠄⠀⠀⠰
⡛⢙⣻⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⣷⣿⠖⢶⣤⠰⣿⣿⣾⣿⣯⣿⣿⣉⢻⠛⢛⣼⣿⣛⣿⣿⣟⢡⣮⡛⢿⠻⣿⣿⣻⣿⣾⡍⠁⠀⠀⢀
⡿⣿⡹⠿⢿⣟⢡⢦⡤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⠛⣛⣉⠼⣏⠉⣿⠏⠙⣹⣭⠿⣹⣆⣬⢙⣿⣟⣿⢭⣗⣾⣛⣶⣿⣟⡓⢟⡻⡿⠁⠀⠀⠀⠀⠈
⠶⠰⠦⠀⡎⠁⠀⠀⡀⠠⢈⡹⠷⠱⠖⠂⠀⠀⠀⠀⠀⠁⠁⠚⠃⠛⠐⠽⠿⠵⠦⠼⠿⠿⠿⣷⡏⣻⠻⣿⠼⠏⠀⢰⣿⠩⢭⣵⣿⣉⢿⠟⠀⠀⠂⠀⠀⠄⡀
⠀⠠⠖⠐⠂⠂⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢿⡐⠀⠀⡸⠦⠉⡷⠝⠓⠛⠣⠤⠄⠈⠀⠀⠀⠀⠘
⠁⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⢚⡀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠤⠊⣗⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠂⠀⠄⠘⠿⠖⠀⡐⠀⠀⠌
⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂⡐⠀⠄

⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠒⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⡀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠋⠉⠙⠓⠦⡀
⠀⠀⠀⠀⠀⡴⢋⣠⠤⠤⠤⣀⡀⠀⠀⠀⠀⠉⠓⡦⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠚⠉⠀⠀⠀⠀⣀⠤⠔⠒⠒⠤⣈⢦⡀
⠀⠀⠀⣠⢞⠔⠋⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠈⠳⣝⣆
⠀⢀⣴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠔⢉⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣈⠑⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣇⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣨⣿⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠑⠶⢤⣀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠙⣦⣄⡀⠀⠀⢻⡀⠀⠀⠀⠈⠀⠁⠀⣿⠂⠀⠀⣀⣴⡏⠙⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠉⠛⠒⠲⢧⠀⠀⠀⠀⠂⠀⠀⣿⠒⠚⠋⠁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⡇⠀⢀⠔⣚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡆⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⠹⢄⡀⠀⢸⣷⡴⢣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠘⡇⠀⠀⠀⠀⠀⠀⢰⠀⠙⢲⣤⣀⠁⠀⠀⠉⠉⣉⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠁⠈⠉⠙⠛⠛⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⠀⠀⠀⠀⠀⠀⢠⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⢸⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠢⢼⣀⡀⢀⠤⢄⠀⡀⣸⢰⡇⡀⢀⠤⢄⠀⡀⣸⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠾⣤⣸⣅⣀⣀⣭⣠⡼⠚⢧⣨⣅⣀⣀⣭⣠⡼⠖⠛

⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⡄⡀⡀⢀
⠀⠀⠀⠘⢲⢡⣤⣤⣤⣤⣮⣤⣴⠃⠀⠀⢀⡤⡄⡀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⡿⢏⣬⡆⣃⡃⡋⣚⢀
⠀⠀⠀⠘⠧⢨⣭⣭⠹⠋⣩⣭⡉⠀⠀⠀⠈⠳⣅⡄⣥⡥⠠⣄⡬⣼⠁⠀⠀⠀⠀⣯⢿⢼⠽⡵⣧⡧⢻⠄
⠀⠀⠀⢰⢱⢄⢠⠆⢲⠀⢿⣿⠇⠀⠀⠀⢙⣾⣭⡏⣉⣉⡀⣩⣍⠉⠀⠀⠀⠀⢋⣂⣃⣓⣛⣃⣛⣸⣚
⠀⠀⠀⢠⡞⠂⢰⣆⠐⣶⡆⢰⡖⠂⠀⠀⠙⡾⠢⣲⣠⢠⠄⠉⣬⡒⠀⠀⠀⠀⢪⣼⣼⣤⣦⣤⣵⣤⡧⠂
⠀⠀⠀⠈⠛⠃⠋⠛⠚⠃⠛⠚⠛⠃⠀⠀⠀⠁⠀⠉⠉⠉⠁⠈⠌⠉⠀⠀⠀⠀⠸⠿⠾⠧⠿⠤⠧⠼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⢰⡏⡽⠀⣰⣽⣷⣧⣆⠀⠀⠀⢀⡀⣀⠀⠀⣀⣀⠙⠛⢿⢷⠀⠀⠀⢺⡙⢀⣋⢉⡩⢙⣰⡀⡀
⠀⠀⠀⡀⠹⣦⣰⠗⣴⣳⠇⣞⠂⠀⢰⣇⣟⡼⣧⢘⣟⡛⣢⣸⣇⠀⠀⠀⠀⢦⠽⣿⣿⣟⣷⣟⡷⣿⠇
⠀⠀⠈⠳⣶⠋⣙⠚⣛⢙⢋⣘⠃⠀⠀⢸⡴⢃⠯⢺⢚⠞⠧⡟⢻⠂⠀⠀⠀⠘⢾⣇⣇⣮⣰⣌⡿⠹⠏
⠀⠀⠀⠈⠕⠶⢿⡁⡟⢹⢺⣙⠀⠀⠀⠘⠵⠿⡜⢹⢸⠩⢻⡉⢳⡅⠀⠀⠀⠦⠤⠷⠶⠴⢨⠸⠴⠸⠆
⠀⠀⠀⢸⡟⣶⠀⣿⡇⠘⢷⡞⠀⠀⠀⠀⢰⣻⣶⣷⡇⣇⣀⢳⠃⠀⠀⠀⠀⠀⣿⣿⢾⡷⣿⢬⣯⠄
⠀⠀⠀⠸⠿⠟⠲⠏⠿⠆⠾⠇⠀⠀⠀⠀⠀⠉⠈⠉⠁⠉⠁⠈
⠀⠀⢀⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡀⠀⣀⡀⣀⣀⣀⡀⡀⠀⠀⣠⣤⣤⢄⢀⣀⢀
⠀⠀⠾⣟⡋⠋⢀⣤⣤⡀⠀⢶⣶⡆⠀⢨⠆⠣⠂⠟⠃⠟⠘⠊⠇⠧⠀⠈⢣⣏⡤⡤⡤⡠⢥⣯⣄⡤⢰⡄
⠀⠀⠀⢯⣁⣀⣿⣻⣻⣿⣀⠄⡌⠀⠀⢰⣿⣟⢿⡟⢿⡟⡟⢟⢻⣿⠀⠀⠘⣬⡊⣫⣍⢛⣽⠈⠋⣫⣌⡃
⠀⠀⢬⠎⣭⣩⡍⢸⡅⢡⢩⡦⡅⠀⠀⢘⡛⡛⣛⢛⣛⢛⡛⢛⡛⡿⠀⠀⠸⣇⡜⣿⠀⣿⠂⢠⡴⢋⠛⠇
⠀⠀⠈⠈⠛⠛⠓⠋⠓⠚⠚⠛⠃⠀⠀⠙⡾⡷⡧⠿⢹⠜⡧⣯⠼⡇⠀⠀⢐⣷⢶⣰⢲⠚⡖⠠⠶⠾⠦
⠀⠀⠀⠀⠘⠀⠀⠧⠀⠐⠀⠁⠀⠀⠀⠒⠼⠧⠿⠼⠳⠧⠼⠌⠇⠔⠀⠀⠀⠈⠀⠴⠌⠤⠥⠭⠦⠅⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣤⠴⠚⠉⠙⠲⢄⣀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠴⠊⠉⠉⢙⡛⢿⣯⣤⣀⠀⠀⠀⠀⠈⠻⡙⢆
⠀⠠⠤⠖⠋⠉⠉⢉⠟⠁⠀⠀⠀⠀⠉⠋⣻⣿⣿⣿⡿⠂⡀⡄⠀⠀⠀⠀⠙⢢
⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠐⢻⠏⠉⠉⠘⠉⠙⠻⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢼
⠀⠀⠀⠀⠀⢼⡁⢀⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⡀⠀⠀⠀⠠⣤⣦⣀⣀⡀⠀⠀⠃⠠⢊⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠈⣧⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠀⢠⠀⠙⢿⣿⣿⣿⡤⠖⢊⠀⠁⠀⠀⠀⡐⡍
⠀⠀⠀⠀⠀⠺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣟⣻⣧⣌⣤⣄⣀⣀⣀⣠⣤⠖⠁⡄⠀⠀⠄⣈⠜
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣦⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⢿⣿⣿⠿⠛⠛⢻⣿⣷⣾⣻⡷⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡗⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠁⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣀⡀⠤⢤⣊⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠣⠀⠈⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⢠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢃⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⢠⠁⠀⠀⢸⣧⣿⡆⠀⠀⠀⢸⣿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠰⢆⡀⠠⠀⠀⠰⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠤⠀⠀⠠⡄⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⣀⢠⠐⠁⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠈⠀⠀⠀⠀⠀⢀⠔⠀⠀⠁⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠒⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡁⠀⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠅⠀⢀⠂
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢘⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⢀⢀⡀⣀
⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠉⠈⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠃⠀⠀⠀⠀⠀⠀⠘⠀⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣋⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡆⣾⣿⣴⣿⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⣿⣦⣿⣷⢸⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡹⠟⣼⣫⠟⠁⠀⠀⠈⠻⣿⣯⣽⣿⠟⠀⠀⠀⠈⢿⣝⣧⠻⢏⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢀⣠⣤⣤⣤⣭⣭⣤⣤⣤⣄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣄⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣾⣿⣿⠗⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠸⣿⣿⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣦⣌⣛⠿⢿⣿⣿⡿⠿⣛⣡⣴⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣚⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠒⠉⠙⠛⠿⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⢀⡀⠀⠀⡀⠀⢀⡀⣀⣤⣴⡄
⠀⠀⡀⡀⠀⡄⠀⡀⠄⢄⣦⡵⠊⠉⠉⠉⠁⠒⢄⠒⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⣀⠈⠰⣷⡅⢈⣁⣠⢀⡀⢀⠈⠀⠠⡀
⠀⠀⠃⣹⣾⠗⠀⠀⠀⣠⠟⣶⢖⡴⢿⡢⠐⠀⠀⠀⠐⠓⢀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣠⣿⣶⣲⣿⣏⠀⢀⠉⠚⠅⠛⠁⢠⠀⠉
⠀⠀⢰⡝⡏⠀⣀⢄⠘⠻⠉⢿⡀⠻⡾⠀⠉⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠟⠚⠁⢙⡵⠻⡏⢻⣁⡤⠀⠈⠀⠀⠀⠒⠠⡀
⠀⠀⠸⠉⠁⠀⠉⠆⠀⠀⢀⣿⡏⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⡟⠁⠀⣿⡭⢹⣋⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠘⠷⠗⠚⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠀⠀⠨⠁⠀⠀⡽⠓⠴⠋⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⣠⣦⡴⠀⠀⠘⠀⠀⠐⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠠⠄⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠞⠃⠐⠣⠈⠁⠀⠀⠀⠄⠀⠀⠄⠀⠀⠄⠀⠀⠀⣀⣠⣡⠀⠘⣆⠀⠀⠀⠀⠀⠁⠒⠀⢀⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠁⠀⠈⠟⡇⠈⠙⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠦⠔⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣎⠘⢻
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠔⠃⠀⠀⠀⠀⠠⣴⣤⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠰⡀⠀⠀⠁⠈⠁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣄⣠⣶⣶⣷⣶⣶⣦⡀⠀⠀⠙⠒⠀⠂⠁⠤⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⡿⠃⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠋⠀⠀⢿⠆⣤⢸⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣰⣿⣤⡄⠀⠀⠀⠀⠘⣿⣿⣷⣶⡀
⢠⡶⠂⠀⠀⠀⠀⠀⠻⠃⡠⠀⢀⢀⣤⣤⣀⠀⢠⣿⣿⣵⣶⣾⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣣⠀⠀⠀⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠉⠉⢰⣶⣶⣴⣶⣤⠀⣉⠋⠀⠀⠀⠀⠀⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⢿⣿⣿⣿⡦⡤⢤⣀⡀⠀⠀⠀⢀⣸⣿⣶⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠒⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠏⠉⠉⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠻⣿⣿⣇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣸⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠂⠀⠀⠀⠉⠁⠒⠂⠀⠀⠀⠀⠀⡀⠀⠀⣀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠖⠊⣡⡴⠂⠀⢀⠐⣠⡴⠛⠔⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠈⠁⠀⢀⠀⠴⠊⠀⠀⠀⠀⢀⡾⠃⡔⠂⢀⡠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠁⠀⠀⠄⠠⠆⠘⠁⠀⠀⠀⠀⠀⠀⣰⠏⠶⠃⢤⡶⣫⠾⠛⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⠀⠀⠀⠤⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⠀⠀⣰⠇⠊⣠⣴⠂⠉⠐⠢⠌⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡤⠖⠈⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⣄⠀⢠⠃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢹⡆⢸⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⣂⠀⠀⠀⢀⠀⢷⠘⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠂⢀⠄⠀⠀⠀⠀⠀⠀⡏⠀⠈⠄⠀⠀⠀⠃⠀⣠⠀⠀⠀⠀⢀⡙⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠤⠤⠤⣄⠀⠘⠁⠀⠀⠀⠸⠀⠀⢀⡠⠄⠀⠀⠐⢠⡏⠀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠈⠱⡄⠈⠀⠀⠀⢀⡀⠖⠁⠀⠀⠀⠀⠀⣼⠁⠙⢠⠤⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠠⠔⠚⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⢐⠉⠀⠀⠀⠀⠉⠉⠀⠘⠛⠑⠋⠀⠈⠀⠀⠀⠒⠂⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⣀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠠⢔⠎⢑⠋⠀⠀⣀⠄⢀⡠⢄⡀⠀⠀⠀⠀⠀⠉⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠠⠔⠁⢐⣨⢔⣪⡴⠞⣉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⢉⡠⠄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡨⠞⠋⠁⠔⠋⠡⠔⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣰⠂⠀⢤⡀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠄⠀⠒⠂⠁⣄⠀⠀⠀⢀⡖⠀⣡⠚⠤⠤⠀⠀⠙⠦⠀⣤⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣤⣩⣤⣀⡀⠀⣁⣤⠶⠋⠀⠀⠀⣸⠀⠀⢸⠐⡀⠀⠠⠆⠉⠉⠙⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⠾⠛⢋⡽⠀⠄⠂⠠⠀⢀⡽⣇⠀⠸⠀⠈⠂⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⡋⢀⡀⠀⡀⢀⡤⠀⠀⠈⠓⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠤⠞⠋⠀⠀⠀⠐⠂⠀⠉⠉⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠉⠁



⣿⣿⣿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠘⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠰⡄⠀⠀⠀⡟⠀⠀⣾⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢤⡀⠀⠀⠀⠀⣄⠀⠙⣄⠀⠀⠹⡄⢀⠀⡇⡀⢰⠇⡀⠀⡴⠁⠀⢀⡤⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⠳⢄⠈⢢⠐⢄⠱⠸⠄⡇⡇⡞⡜⢠⠎⡠⢀⡴⠋⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠠⡑⠄⠑⠌⠀⠁⠀⣇⠀⠐⡰⠃⢊⠔⠉⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣄⡀⠨⣑⠈⡀⠀⠠⢀⠠⠤⠤⠄⡈⠢⠀⡀⠔⣋⠤⠂⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠲⠶⠶⠤⢤⣄⣀⣀⡨⠁⠂⠁⢀⠋⡐⠁⠀⠀⠀⠀⠈⢢⠁⠀⠠⠀⠂⠉⣀⣀⣤⢄⣠⣤⣤⠖⠒⠶⠤⠶⠒⠲⠦
⠀⠀⠀⢀⣀⣀⣠⠤⠤⠤⠤⣀⡀⠀⠈⠉⠈⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⡖⠉⠉
⠐⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠓⠤⢄⡀⠀⠀⠀⢣⣀⣀⣀⣀⣀⠤⠚⠂⠉⠉⠉⣡⠏⢁⣠⠀⠀⠠⠤⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⡀⠄⠂⢀⡀⠀⠀⠀⠀⢀⠀⠉⠑⠒⣍⣁⣀⣀⣀⣀⣀⣀⣀⣠⠤⠴⠚⢁⣐⠊⢀⡀⠀⣠⠤⠒⠉⠉
⠀⠀⣀⡀⣀⡀⢀⠀⠀⡁⢈⣁⣐⢒⣤⣍⣀⣀⣈⣨⣽⣦⠄⠀⠀⠀⣀⡼⠁⠄⠐⣀⠀⠀⠀⠀⡩⠄⣲⠉⠲⡒⡢⣀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⡼⣃⡤⠷⣬⠶⠷⠬⣁⣀⣀⣐⣠⣅⣀⣄⣈⣉⣀⣠⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢖⡒⠒⢦⠶⠚⢛⡛⠉⠠⠤⠤⠤⠤⠤⠴⠀⠨⠉⠁⠀⠀⠈⠉⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠴⠚⠉⠉⠉⠉⠉⠉⠙⠯⢤⠀⠀⠀⠀⠤⠶⠮⠍⠤⠤⠥⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣄⠎⠈⠀⠈⡆
⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠋⠀⠀⠀⠠⢾
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠄⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⢸
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠄⠐⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢰⠀⠀⠀⠀⠆⢠⠀⡈⠀⠀⠀⠀⠇⡀⡄⠀⠀⠀⢸⠂⠁⢀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⣲⠀⢇⠸⡄⠀⢠⣲⠀⡏⠀⠀⠈⠃⢸⠈⡆⡎⠀⠀⢸⠚⠁⡎⠀⣐⡆⢘⠀⢷⠈⠆⠀⢸⠆⠀⠘⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⢄⡰⠀⠀⠀⠀⠀⠓⠀⠀⠀⠆⠈⠀⠃⠈⠁⠀⠈⠓⠁⠈⠁⠀⠀⡌⠁⠀⠸⠀⠀⢸⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣅⣀⣀⡀⠀⠀⠈⠀⠄⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠅⢀⠃⠠⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢲⢰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⡏⠇⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠘⠀⠀⠀⢰⠸⠀⠀⠀⠀⢨⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄
⠠⠀⠀⠀⠀⠐⠁⠀⠀⠀⠠⠀⠀⠀⠀⠐⠄⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠆
⠀⠀⢠⠀⠀⣀⠃⡈⠀⠀⡀⠤⢄⠀⢀⡀⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣆⡀
⠀⠀⠀⢀⡶⣄⡀⠀⣀⣴⣾⣿⡿⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠿⣿⣿⣦⣄⠀⠀⣀⡴⡆
⠀⠀⢙⣺⣷⣿⢿⣿⣿⣟⣉⣁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣉⣙⣿⣿⣿⢿⣷⣷⡊
⠀⠀⠀⠀⠈⠁⢾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠆⠉
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⣿⣿⣿⣿⣟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⠀⠀⠀⠀⠻⠿⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠀⠐⠒⠒⠒⠀⠀⠀⠀⣀⠔⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠱⠖⠉⠐⢄⢀⡤⠂⠉⢂
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢫⠀⠀⠀⠘
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⣀⢦⡄
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠘⠥⠇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠄⠀⢸⠒⠀⠀⠀⠀⡇⠀⠀⠐
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢀
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⣀⣀⠠⠴⠃⠀⠀⠈⡀⠀⠀⡚⠀⠀⠀⡸
⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣨⠒⢌⠠⡞⠀⠀⠀⣠⠃
⢰⢀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢊⠃⠀⠠⠓⠌⣂⠄⣚⠁
⠈⡸⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⢀⠚⠁⠀⠁⠀⠠⠁⠀⠀⠀⠀⠀⠁
⠀⣿⡅⠀⠀⠀⡇⠀⠀⠀⠀⢠⠄⠀⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠘⠀⠀⠰⠀⡴⠁
⢸⢿⡷⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⡀⠑⢥⡀
⠈⠙⠇⠀⠀⠀⡧⠂⠀⠄⠀⢀⣀⢀⣀⠄⠀⠀⠀⢰⠀⠀⠀⠀⠈⢀⡀⠀⢉⢢⣀⡤⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠂⠀⠀⠐⠒⠒⠀⠀⠒⠂⠀⠀⠀⠀⠀⣲⠤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢰⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⡀⢸⣀⣦⣠⡀
⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⡷⠆⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⢍⢂⠀⠀⠀⢰⢄⡀
⠀⠀⠀⠀⠀⢸⠁⢠⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠤⠤⠄⠀⠉⠀⠨⠱⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢦⡑⢄⠀⢨⠑⠺⠆
⠀⠀⠀⠀⠀⣼⠀⠘⢁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡌⠑⠽⠌
⠀⠀⠀⠀⢸⣿⢠⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡀
⠀⠀⠀⠀⠺⡿⠃⠀⢀⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠁⠱⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢇
⠀⠀⠀⠀⡰⠁⠀⠠⠃⠀⠐⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠐⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠄
⠀⠀⡠⠊⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⢡⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢢⠀⠘⠄
⠀⠀⠈⢆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢘⠀⠀⠀⠀⠘⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢢⡀
⠀⠀⠀⠀⠙⠻⠾⠀⠀⠀⢈⠀⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⣠⣬⡆⠀⠀⠀⠀⢄⠀⠀⣀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠈⠲⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠚⠛⠛⢀⠀⠘⠛⠛⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠲⠶⠖⠈⡇⠀⠳⠶⠃⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠓⠒⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣥⣀⣀⣀⣬⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⢷⡀⠀⠀⠈⠓⠦⣖⣒⠒⠶⣤⠶⠋⠀⠀⢀⡴⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⣀⠀⠙⠳⢤⣀⣠⡶⠤⠭⠇⠀⠀⠀⢀⣠⡴⠋⠀⠀⢀⣀⡈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣈⡉⠓⠲⠶⠶⠶⠒⢛⣉⣥⠴⠖⠚⠋⠉⠉⠉⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠓⠶⠶⠒⠒⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⠀⠀⢀⢀⣀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⠿⠿⠶⠶⠶⢤⣤⣤⣤⠤⠤⠔⠒⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣴⣿⣿⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠘⣿⡯⠄⠀⡖⢦⠈⠆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⡇⠀⠀⠀⠈⠛⢿⣦⡀⠀⣽⣿⣅⣠⣝⡏⠀⢠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣧⠀⠀⠀⠀⠀⠀⣻⣿⣴⣿⣿⣿⣿⣿⠁⠀⠈⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⡟⠻⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣧⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢹⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢿⣿⣷⡄⠀⡟⢻⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠇
⠀⠀⠀⠀⠀⢸⠁⢿⡀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠰⠈⣷⠀⠀⠀⠀⠀⢸⠏⠀⡜
⠀⠀⠀⠀⠀⢸⠀⢸⣷⡀⢀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢻⡄⠀⢸⡆⠀⠀⠀⠀⡞⠀⡘
⠀⠀⠀⠀⠀⠘⣤⣿⣿⣷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⢇⢠⠈⠇⠀⠀⠀⢰⠇⠐
⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⢸⡟⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠸⣿⡇⡿⠏⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡀⠀⢠⠃⠀⠀⡀⠀⠀⠸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠀⠻⠴⠄⠤⠾⠀⠤⠥⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠈⢿⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⠀⡅⡃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣀⣀⣤⠤⢄⡀⠀⠀⣾⠑⠄⠀⠀⠀⡠⠞⡠⠚⡠⠃⠀⠼⠋⠅⠀⠀⠀⠀⠀⣸⡏⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣨⣭⣈⠉⢢⡈⢆⠀⠉⠀⣄⠀⠀⠎⠁⠀⢀⣴⣁⠔⠂⣠⠔⠁⠀⠀⠀⠀⠀⣼⠃⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠳⠀⡇⢨⡀⠘⠀⠸⡖⠀⢀⠀⣀⣆⣻⠁⠀⢰⡟⡀⠠⢀⠀⠀⠀⠚⠁⣠⢆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠘⢷⣇⠀⣠⠴⣛⣋⡭⠭⠭⠭⣍⣛⠲⢦⣠⠈⠀⠀⠀⠀⠀⡉⡡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡾⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⢌⡳⣤⢨⠾⠭⣀⡀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠉⠱⣀⣀⠠⠁⣴⢋⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢳⡀⠀⣀⣠⠀⣁⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈⠙⠓⢸⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢳⡈⢉⠁
⠀⠀⠀⠀⠀⣠⣺⣍⣉⡉⠢⣄⣳⡀⢀⡇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⡗⠒⠠⠐⢄⠀⠀⠀⠀⢀⣤⠶⣤⡀
⠀⠀⠀⢀⡼⠛⣁⣤⣄⡈⠢⠈⠙⠭⢽⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠈⠂⠑⠤⠴⠶⠛⣡⡶⠋⠉
⠀⠘⢿⣯⣰⡾⠋⠀⠀⠈⠢⡀⢀⠀⢘⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡿⠚⢿⠳⠄⡑⠦⠤⠤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⢧⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⠈⢣⠀⠉⠓⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠤⠾⠂⠈⢧⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⡟⢀⠽⠓⢄⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠴⠆⠀⠠⠤⣀⣼⣳⣌⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠃⠈⠄⠄⠀⠈⠐⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠒⠛⠓⠀⠈⢱⢮⣙⠲⠤⢤⣄⣠⣤⠤⠖⣚⡩⠖⠛⣬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣡⠒⠉⣁⣀⠀⠀⡂⠀⢀⢈⠉⠙⢲⡶⠖⠒⢚⠋⠉⢄⠀⢀⠏⢧⠀⠆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⠟⠁⠀⠀⠀⠀⠀⡸⠃⢀⡠⢺⡇⠀⠀⠈⠀⠈⠙⠆⠈⠀⠘⡀⢆⠈⠛⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣿⠀⠀⠀⠀⠀⠀⡉⢀⠀⠀⢠⠉⡠⠀⡡⠊⠀⠀⠰⡀⢸⡆⠀⠙⠢⢟⣶⠶⠴⠦⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⠟⠀⠀⠀⠀⠀⠀⠓⠋⠀⠰⡃⡞⠀⣾⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣣⡀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣟⣻⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣛⣛⠓⠒⠶⣤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⣀⣀⣀⣤⡴⠶⠚⠛⡿⣣⠾⠟⠛⠛⠻⣿⣯⡠⠄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠰⢾⠿⠛⠉⠀⠀⠀⠀⢸⠟⣁⠀⠀⠀⠀⠀⠈⠻⠋⠙⠂⡠⣆⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡀⣀⠄⠀⠀⠀⠀⠀⢳⡀⠻⣯⡟⠶⢘⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣁⣀⠄⠀⠀⡴⠀⠀⠙⢦⣴⠁⣆⠉⣿
⠀⠀⠀⠀⢀⣤⣾⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣷⣤⣞⠁⡀⡠⠀⣿⣿⣷⡼⣧⠹⡇
⠀⠀⠀⣰⡿⠋⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠙⠿⠿⠷⣷⣾⡿⣿⣿⣧⡘⢧⡇
⠀⠀⠀⣿⠁⠀⠀⢹⣷⣦⠀⠀⠀⠀⡀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⠀⠀⢀⢀⣠⣼⣿⠃⠀⠉⢻⣿⣄⡓⢄
⠀⠀⠀⣿⠀⠀⠀⠀⠻⣿⡁⠀⠀⠀⠱⣜⣦⣧⡀⠀⠀⠀⠀⠀⣀⣠⡿⣿⣿⡀⣿⡄⠀⢈⣻⣧⣟⡿⠀⠀⠀⢸⣿⡿⣝⢦⣝⢢⣄
⠀⢀⡤⠏⠀⠀⠀⠀⣠⣿⣿⡧⠀⠀⠀⣌⢻⣿⣿⣶⣶⣶⣾⣿⡿⠿⠶⣿⣿⣷⠾⠇⠤⠀⠹⣿⣏⠀⠀⠀⠀⢼⣿⡇⠀⠁⠛⠶⠄
⣰⣿⠃⠀⠀⠀⠀⠀⣿⣿⣷⣕⠆⠀⠀⠈⣿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠸⣿⣿⣿⣶⠶⣶⣖⠀⠘⠛⠧⠀⠀⠀⠸⣿⣷⣄⡀
⠈⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠘⣿⡟⠀⠉⠛⢷⣖⡀⠘⣇⠀⠀⠀⠉⠻⠞⠉
⠀⠀⠀⠀⠀⢠⠀⢀⣿⣿⣿⣿⣈⢷⣄⠀⢺⣇⣄⠀⡄⠀⡀⡀⢀⠀⣾⡧⠀⠘⣇⠀⠀⡀⢘⣷⡄⠀⢸
⠀⠀⠀⢠⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠈⢿⣦⡷⣤⣌⣤⣾⣴⣿⢛⡛⢛⣿⣠⣃⡄⢿⣡⡶⠖⣺⡖⣄⢀
⠀⠀⠀⠈⠛⠋⠙⠛⠿⣿⠿⢿⠿⠿⣿⣁⠶⠶⣚⣿⠟⠛⠙⠛⠟⠛⠃⠨⠏⠁⠘⠛⠻⠷⠿⡿⢷⣿⠿⠋⠋⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠄⠀⠨⠀⠀⢀⠀⠀⠀⢀⠇⠀⠀⠀⠘⡆⡰⠁⡁⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠁⢄⢁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠁⠉⠀⠀⡠⣷
⠀⡀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠘⠀⠢⢀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⢸
⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠠⠀⣀⠀⠀⠀⠡⠀⠀⠈⠀⢀⠃⠀⠀⠀⠀⠀⠐⡇⠢⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠘⠀⠑⠨⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⣇⠠⠀⠀⠀⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⠈⡆⢀⡀⢠⠀⢠⠀⠀⠀⢀⡀⢸⡅⠀⠀⢰⡇⢸⠀⢄⢀⢤⠈⠀⢸⣠⠇⣠⠄⠀⣀⠈⡴⠀⡇⠠⡀⠀⠀⡇⠀⠀⠐⠉⢹
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣧⣰⠃⠧⢿⠘⠇⢸⠀⠀⠸⠝⡇⢸⠀⠀⠀⢸⠀⠸⠁⡜⠸⣀⠀⠀⢸⡉⡆⢯⡀⠪⠺⡀⣇⡀⠟⢠⠇⠀⢀⡏⠆⠀⠘⠤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠞⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠃⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠄⠀⠀⠘⠀⠀⢸⠆⠁⢀⡀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠤⡀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠲⣆⣀⣀⡀⠀⠀⠘⠀⠠⠇⠀⡯⠤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⢀⠸⠅⢀⠓⠠⡖⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠒⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠐⠁⠀⠠⠉⢢⣰⠁⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠆⠀⠘⡇⣗⠤⣀⠀⠈⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠁⠀⠀⠀⠄⠀⢀⠐⠀⠀⠈⠀⠀⠾⡀⠀⢠⢱⠸⡄⠀⠉⠁⠀⢸⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢸⠀⠀⢀⠀⠀⠀⠈⠂⠀⠀⡀⠀⡀
⣀⠀⠀⠀⠀⠀⡠⠃⠀⠈⠀⠀⠀⠀⡀⠀⠀⢃⢀⠂⢸⠀⣥⠀⠀⠀⠀⠚⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⠅⠈⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠁
⠈⠁⠂⠐⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⢸⠀⢸⡀⡀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⢰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠂⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⢀⠠⣅⣀⡠⠤⡑⠄⠀⢀⣥⢚⡗⠦⡀⠠⠂⠀⠀⠼⠀⢸⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠄⠀⠀⠀⠂⠠⠄⠀⠀⠀⠊
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣠⣀⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠠