Drunkenness Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⢀⣲⣦⡀
⠀⠀⠀⢀⣤⡄⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠹⢿⡇
⠀⠀⢀⣿⠉⠀⣀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣾⠃⠐⠛⠓⢺⡇
⠀⠀⢸⣷⠄⠀⠤⠴⢼⣿⡇⠀⣠⣤⣶⠂⠀⠀⠀⢢⣾⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠄⠰⠆⢀⣠⣤⣤⡉⠀⠀⣿⠋⠀⠀⠻⣿⣧
⠀⠀⢸⣿⠀⠀⢠⠀⢈⣿⡇⠀⣿⣋⠉⠀⠐⠒⠒⣾⣿⣿⣿⡟⠇⠀⣠⣤⠄⠀⢤⣤⡀⠈⢻⣏⠀⠀⠀⣀⣼⣿⣿⣿⠧⠀⠀⣿⠀⠀⠀⣠⣸⣿
⠀⠀⠘⣷⠀⠀⠀⠀⣼⣿⠃⠀⠈⠙⣶⠶⠴⠾⣷⣿⠟⠉⠀⠀⠀⢸⠇⠀⠤⢻⣎⠻⣿⠀⠀⠙⠿⡁⠠⣘⣻⠟⠙⠀⠐⠀⠀⢻⡆⠀⠀⢁⣿⡏
⠀⠀⠀⠈⠷⣄⣸⣦⡿⠁⠀⠀⠀⠀⠻⢤⣤⣦⡾⠟⠀⠀⠀⠀⠀⡿⠃⠦⣐⣢⣼⣿⣿⡆⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢲⣿⡟⠋
⠀⠀⠀⠀⠀⠸⣿⠇⠀⢀⡀⠀⠀⠀⠀⠘⢦⡿⠃⠀⠀⠀⠀⠀⠀⢳⡀⠺⠟⠿⣎⣽⡿⠃⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢀⣠⢀⣸⠀⢀⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⣠⠀⠀⠀⠀⠀⠀⠈⠉⠲⣿⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣼
⢀⢠⡷⠟⠋⠉⣻⠀⢨⠒⢟⡷⢶⡶⣄⠀⠀⡇⠀⢿⣁⠉⠄⠠⢤⣄⠀⠀⠀⣿⠀⠀⠀⡀⠒⢶⠠⠀⢰⠇⢰⣤⣿⠆⠀⠻⣾⣤⠆⠀⢹⠀⠀⠰⢦
⠻⠂⠁⠰⡖⠐⠙⠃⠈⢹⡿⠇⠈⢳⣿⠐⠈⢻⣶⣦⠀⠀⠀⠀⠀⣿⠂⣤⠐⠙⣦⣤⠐⡄⢀⡟⢠⣻⠚⢷⣦⡄⠀⠐⢊⣽⡧⣤⡄⠒⣹⣷⣶⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠈⠁⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢂⣴⠏⠀⠀⠈⠉⢀⡒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⣷⡋⠁⠀⠀⠀⠀⠀⠀⠙⣦⠛⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⢀⢈⣷⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⢀⣤⣴⣶⣚⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣤⣀⠐⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢿⡟⠛⣿⣿⠋⢹⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠧⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠉⠒⢎⣍⠀⢸⠀⣱⡶⢤⡀⢀⣤⣓⠓⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⡟⡏⠐⠋⠁⣰⣧⠀⠻⠏⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢻⣄⠀⠉⡁⠿⠀⠀⠄⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⡞⠙⠁⢤⠀⠀⠙⠀⣤⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⡟⢹⣿⣏⡶⠚⠀⠀⠈⠙⠀⡆⠘⡄⢹⢻⣷⠤⣄⠐⠇⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢿⡆⣀⢴⣯⡈⢟⡟⠻⣿⠃⠀⢿⡙⢷⣦⣤⣤⣤⡄⠀⣿⠀⠀⢸⣏⠁⠀⠀⠀⠀⡀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡖⠫⠀⠑⣜⡆⠀⡛⠀⠀⢸⣧⠀⠈⠻⣏⡜⠀⠀⢿⡀⠀⢸⢿⣿⣶⣦⡂⠀⢨⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠈⣿⠀⡁⠀⠀⠈⣿⠀⢀⣠⣯⣴⣦⡀⢸⡇⠠⣾⣄⡀⢠⣿⡅⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢸⡇⣿⣶⠀⠀⠛⠀⠉⢻⣿⣿⠃⠁⢸⡇⠀⠈⠿⢷⣾⣇⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣘⣷⢹⠋⠀⠀⠐⠀⠀⠀⣿⣿⣆⠀⢸⠀⠀⠀⢀⣀⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⡀⠀⠀⢇⠀⢰⣿⣿⣿⠀⡟⢀⣀⣤⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣾⣶⣾⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣱⣿⣿⣿⠅⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⡾⣧⣤⣤⣀⠀⢀⣦⣠⣄⠀⠀⡁⠹⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣼⣶⡷⣿⣽⢺⠸⢯⣯⢻⠡⠀⠂⡠⢼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢵⣿⡇⠀⢳⣥⡼⠗⠀⠀⠀⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣯⡾⡦⠀⠈⠓⢄⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠈⠀⠀⠀⠀⠂⢿⠖⠁⠀⠈⠊⠀⠀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣽⢛⣈⡀⢀⠀⠀⢀⢰⣷⡄⢀⣀⣠⣤⠄⢀⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⢹⣿⣿⣿⣿⡿⣼⣿⣿⡿⣯⠀⠋⠀⡼⢸⣿⣿⣿⣼⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⡀⠘⠛⠓⣿⠙⢿⡧⢿⡀⢀⡼⠃⢸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⠙⠒⣲⣶⣿⣼⡷⠦⣤⣥⡾⠶⡄⢸⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢽⣿⣿⣟⠁⢀⡏⠀⠀⠀⠹⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠠⣶⠒⠀⠀⠀⠀⠉⡀⠀⠠⠀⠀⠀⠀⠀⠀⣚⡅⠀⠀⢈⣱
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡿⢟⣀⡀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠀⠩⣀⣀⠀⣀⠰⠁⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢱⢿⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠑⠦⣀⡉⢙⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡖⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠀⠀⢆⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠊⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣼⣿⣿⡏⠙⠀⠀⠈⢻⡶⣄⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⢿⣹⣦⣶⣔⢀⠀⠀⣽⠛⢮⣧⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⠛⠻⢿⣿⢀⢰⠏⠀⠀⠉⢷⡀⠀⠀⣿⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⢻⡀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⢹⣶⣤⣀⠘⢇⣻⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠈⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣊⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸⣢⡀⣠⠀⠤⠘⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠨⡙⠻⣿⡇⠀⡄⠜⢢⣀⣊⠁⠀⠀⠀⠀⠐⡿⡒⠂⠀⠈⣿⡇⠀⠀⠀⢸⠀⢀⠠⠐⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠻⢀⠀⠈⠚⠀⠁⠀⠀⠗⠀⠀⠀⠀⠰⡀⠁⠀⠀⣿⡇⠀⠀⠀⠀⢐⠀⢱⡄⠘⢀⠠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣠⡏⠀⣄⡓⠒⠊⠀⠀⠀⠀⠀⠀⣀⠘⢧⡀⠀⠀⢹⡇⠀⠀⢀⡠⡘⠢⠌⠒⠉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⡄⠀⠈⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⢿⣧⠀⠀⣎⠀⢸⠀⠀⠀⠀⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣦⣄⣀⣀⣀⣀⠟⠛⣻⣿⠀⠀⠈⢳⠂⢺⡛⠛⠋⠉⠀⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣿⢻⣇⠀⠀⠸⢤⣼⣁⣀⣈⡀⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣍⡙⠷⠶⠦⠼⠦⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠉



⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣠⡄⠀⢀⣄
⠀⠀⢀⣼⠷⠛⠘⠺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠤⠄⠰⠦⢼⡇⣄⣨⣧
⠀⠀⠸⣿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠰⣀⣾⣿⠻⠯⡼⠴⣦⠤⠀⠀⠀⠹⣿⡀⠀⠀⣴⣾⠷⠀⢸⡿
⠀⠀⢀⡿⣷⠀⠀⢸⣿⡄⠀⠀⠀⠀⡟⠛⠿⡇⠀⢈⢶⠁⠀⠀⠀⠀⠀⢹⡏⠀⠘⠋⢿⠀⠀⢸⣇
⠀⠀⠘⠁⠋⠀⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠂⠀⠘⠙
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠰⢦⣼⣿⠼⠀⠀⠀⠀⢘⣿⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣻⣷⡖⠒⠀⣀⣀⡘⢾⣏
⠀⠀⠀⠀⢺⣇⠀⠀⠀⠀⠀⠸⣻⣇⠀⠀⠀⠀⠠⣾⣿⣿⠟⠀⠀⠀⠘⠁⠈⣿⡄⠀⠉⠉⠙⣿⠟
⠀⠀⠀⠀⣼⢻⡆⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠰⢦⣿⡂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⡿⢷⣤⡀⠀⠀⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⢉⣿⣻⣗⡀⠀⠀⠀⠀⣿⣧⣤⣴⣿⣇⣀⡇
⠀⠀⠀⠀⠀⢸⡇⠻⠀⠀⠀⠰⠏⣿⣿⡄⠀⠀⢀⡀⠬⠋⠙⠋⠁⠀⠀⠀⠈⠋⠉⢻⠍⠉⠉⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠠⠶⢿⣗⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠲⣿⠟⠁⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣠⠶⠖⠒⠓⠐⠀⢤⢶⣿⣽⣿⣄⡀⠀⠀⣤⡉⢢⡀⠀⠀⠀⠠⠰⣿⣿⣿⠇⣴⡄⠀⠀⠀⠀⠀⠀⣳⡀
⠀⠀⠀⠀⢀⣀⣲⠾⣽⠑⠂⣰⣷⢄⢠⣤⣴⣺⠛⠋⠁⠀⠀⠉⠲⣄⠈⢷⡀⠻⡀⢠⣤⡀⠑⠈⠁⠀⣀⣼⣯⠀⡄⠀⠀⠀⠀⣼⡇
⠀⠀⠀⣶⣏⠀⠣⢀⣼⡇⠈⣿⣿⣿⠸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠙⠦⡘⣮⣿⠷⡀⠀⠀⠀⠹⣿⣿⣷⠗⠀⠀⠀⢀⡃⡟
⠀⠀⠐⡇⠈⣤⣴⣶⣿⣝⣂⣻⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡙⠳⢶⣀⢠⣁⢀⡿⠃⠀⠙⠛⠛⣩⣦⣀⣙⣻⡇⠀⠀⢸⡏⢴⠇
⠀⠀⠀⠁⣠⣿⡿⠏⠻⢉⡍⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⢠⣶⣿⣿⣿⣿⣿⡿⢷⣤⣤⣿⢓⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣳⣄⣁⠈⢛⡼
⠀⠀⠀⠀⠀⠀⠂⠈⣀⣉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠒⠲⠤⠤⣿⢿⣷⠽⠿⣿⣿⣿⣿⣟⣻⠵⠋
⠀⠀⢀⣚⣣⣖⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⠻⣦⠄⠀⠛⠛⠉⠉
⠀⠀⢸⡿⠋⣩⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢄⡀⠀⠀⢀⠀⣀⠀⠠⣀⣼⣿⡷⠂
⠀⠀⢸⡷⠀⠾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠡⣶⢾⣛⣯⣭⣥⠚⠋⠀⠘⣛⣫⣽⣿⣆
⠀⠀⣸⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⣸⣣⣾⣿⣻⡿⠁⣠⣄⠀⠿⠛⠛⠉⣼⣿⣷⣄⡀
⠀⠀⣿⡀⠀⣾⣿⣿⣿⡇⠀⠀⢀⡴⠋⡁⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠁⢐⣿⢿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣦⣤⣄
⠀⠀⣿⠀⢀⣽⣿⣿⣿⢷⣤⡴⢏⣠⣾⣿⣾⣴⣿⣿⣿⣿⡿⢿⣿⠁⢠⣾⣷⠘⠀⠀⠀⢠⡿⠈⠘⠋⠛⠟⠿⡻⣿⣿⣇
⠀⠀⣿⠀⠀⣿⣿⣿⠏⣼⠃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣿⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠀⡄⠁⠘⠙⣿
⠀⠀⢿⣶⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⣷⣶⣿⣾⣷⣆⣦⠀⢸⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⠇⣸⣿⣿⣾⡃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿
⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⡅⣼⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠁⠚⠙⠳⢿⣿⣿⡿⡿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⣀⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣏⣿⣿⣶⣶⣿⣿⣿⣶⡶⢂⣀⣾⡄⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡇⠉⠉⠉⠉⢹⣿⣿⣿⠁⠉⠹⢖⣤⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢘⣭⡻⣇⣄⠀⠀⠀⣼⣿⣿⡇⠀⠀⣠⣾⣿⣷⣄⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠙⠃⠁⠀⢀⣠⣿⣿⣿⣁⣤⣾⣿⡷⠿⣿⣿⠇⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢻⣿⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣇⣤⣤⠤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣿⣷⣮⡉⠙⠛⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣍⣿⣿⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠙⢿⣿⣿⣷⡄⠀⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⡟⣺⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠙⠿⠋⢴⣶⣤⠀⠀⠻⣯⡻⣿⣿⡄⠀⠀⠀⠀⠉⠛⠛⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢧⠄⠀⠈⣛⣊⣻⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠈⠠⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡗⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠈⠣⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢸⠀⣠⢀⠀⡠⢀⢄⣀⠀⣀⣤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠛⠾⠖⠧⠘⠴⠛⠋⠛⠶⠛⠆⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣓⣒⠶⠤⣤⣤⣤⣤⡤⠄⢸
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠉⠹⣿⠁⠀⠀⠀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⢽⠠⠾⠳⢤⡀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢹⣧⠀⢀⣀⣀⣠⣤⣤⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢹⠀⠀⠀⡀⠳⡀⣰⣟⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⣼⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣭⣭⣿⣍⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢹⢠⡀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⡞⣿⡿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⢻⠿⠿⣴⠶⢶⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣧⣤⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣻⠀⠀⣾⣿⣿⣦⣼⣿⡇⢿⠿⠋⠉⠉⠉⠉⠉⠉⠁⠀⠈⠻⣿⣿⣿⣿⡿⠋
⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⡿⠿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⡀⡐⠀⡀⠀⠀⡔⢋⣲⣄⣀⣀⣴⠒⠀⠀⠀⠀⠀⠀⠀⠼⠆⠀⠀⢰⣤⣶⣦⣆
⠀⠀⡴⢾⢒⡆⡆⡀⡀⠀⠀⢀⣷⡾⣶⣇⠀⠀⠳⢬⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣠⡶⠉⠂⠀⠀⠀⣿⣿⣟⣿⣭
⠀⠀⡇⢸⢸⡇⡇⡇⡇⠀⠀⠸⣿⠇⢿⡿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢀⣴⣝⡟⠁⠀⠀⠀⠀⠀⣿⣿⡽⣿⣿
⠀⠀⠙⠺⣬⣇⣇⣇⡇⠀⠀⢠⡆⠀⠀⣥⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠣⡸⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⢰⣿⣟⡴⠢⡀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⢸⣤⣀⣼⠀⠀⠀⢸⢩⣭⣭⣩⣍⣭⢹
⠀⠀⢠⣀⣀⡄⣿⣿⡇⠀⠀⠀⢸⣭⣭⡗⠃⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠴⣿⣿⣿⣿⡿⠆⠀⢸⢩⣍⣭⣩⣍⣭⢹
⠀⠀⠀⠻⡟⠁⣿⠀⠀⠀⠀⠀⠸⣿⡿⠇⠀⠀⠀⠀⠉⢹⡏⠉⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢸⣩⣭⣭⣩⣍⣭⣹
⠀⠀⠀⠰⠇⠀⠿⠿⠇⠀⠀⠀⠀⠼⠤⠀⠀⠀⠀⠀⠠⠾⠷⠄⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠸⠉⠉⠉⠉⠉⠉⠹

⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⣄
⠀⠀⠛⣦⣼⣧⣤⣤⡄⠀⠀⢀⣀⡀⠀⣿⣇⠀⠀⠙⢻⣿⣿⡟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣳⡴⠴⠤⠦⢦⡞
⠀⠀⠀⠈⠙⠿⠿⠋⠁⠀⠀⢸⣿⡇⢸⣿⣿⡆⠀⠀⠈⢻⡟⠁⠀⠀⠀⠈⣿⣧⣿⣷⣄⠀⠘⢇⢸⡇⡆⡆⡆⡎⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⠀⣸⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠆⠀⠈⢻⡅⠇⠇⠇⠇⡇
⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠛⠀⠘⠛⠛⠁⠀⠀⠐⠛⠛⠂⠀⠀⠀⠀⠛⠉⠙⠛⠉⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⠖⡆⠰⢲⠀⠀⢰⣖⣒⣒⣲⡆⠀⠀⣰⢶⡖⠒⢶⢲⡀⠀⢀⣀⠀⠀⠀⢀⡀
⠀⣠⢠⡄⣤⢠⣀⠀⠀⠀⣞⠉⣳⠁⢱⡋⢈⡆⠀⣼⠛⠛⠛⠛⣧⠀⢠⡟⣿⠛⠛⠻⡟⢧⠀⢺⣗⢀⠀⣀⣸⡇⡇
⠀⣿⢸⡇⣿⢸⣿⣤⡀⠀⡁⠄⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡄⣧⠀⠀⢀⡇⣸⠀⢬⡧⠀⠀⠀⢸⡇⡇
⠀⠛⠘⠇⠿⠘⠋⠉⠁⠀⡉⠍⠉⠉⠉⠉⠍⡇⠀⢸⣿⣿⣿⢿⡇⠀⠀⢿⣹⣏⣉⣿⣻⠇⠀⠼⣗⠀⠀⠀⢸⠧⠃
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡶⠲⢀⣤⣶⡆⠀⠀⣶⣶⣆⠲⡀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⡿⢈⡑⣱⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣌⢸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⡿⠛⠋⠙⣿⣿⣤⡍⢼⣿⣿⣿⣽⣷⣶⣤⣿⠿⣿⣿⣿⣾⣹⡿⣛⠋⠉⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠸⢧⣶⣼⣿⣏⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣽⣿⣾⣽⣻⣟⡻⣿⣿⣶⡆⠀⠈⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⣀⢘⣣⣤⣾⣛⡛⢻⣯⣿⣿⣷⣿⢿⡋⠑⠀⠈⠀⠀⡉⠙⢿⣿⣿⣏⣷⣴⢿⣯⣤⣴⡟⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⡉⠜⠉⢡⡾⠋⢩⣿⣿⣿⣿⣿⣿⢿⠀⣿⣿⣷⡄⡆⢠⣶⣶⣶⡿⣿⣿⣿⣿⡿⣿⡊⠁⠙⠛⠛⠛⠁⢄⠁
⠀⠀⠀⠀⠀⡠⠾⠉⢙⡄⠀⠊⠀⠀⣠⣿⣷⣤⣴⣿⣿⢻⣿⣿⣿⢸⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⣧⠻⢹⣿⣿⣿⣷⣽⡦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⢗⣾⢛⣾⠛⠁⠀⢩⣿⠛⡾⠘⣿⣿⡟⢺⡆⢿⣿⣿⠇⠀⢘⣿⣿⣿⡇⠀⢘⣿⣿⡛⠙⠻⣆⢱⣤⣤⡤⡀⠀⠀⢀⣄⣤⣄
⠀⠀⠀⠀⠀⣠⠞⢠⠔⠀⠈⠳⠶⠋⣀⣤⣾⣿⣿⣦⠃⣰⣿⣿⣷⡼⠃⣼⣿⣿⣆⠀⢸⣿⣿⣿⣿⡀⣨⣿⣿⣣⠀⣸⣿⣿⣦⣀⠙⢿⣟⣢⡼⢿⣿⠟
⠀⠀⠀⠀⣾⡃⢀⠄⠀⣤⡶⠞⣾⣿⣿⣿⣿⣿⢿⢿⣷⣿⣿⣿⣿⠷⢺⣿⣿⠿⡿⣶⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣋⣰⣿⣟⣷⠏⠉
⠀⠀⠒⢠⣻⣤⣬⠁⠐⠛⠉⠘⣿⣿⡿⠓⠉⠀⠀⠀⠀⠀⠈⠃⠙⠈⠀⠁⠈⠀⠀⠀⠸⣇⠉⠉⠁⠀⠀⠺⠷⢬⣬⣙⡋⠉⠉⠙⠛⠿⢿⡽⠟⠻⠧
⠀⠀⠀⠈⣬⠯⣿⣤⣴⡶⠠⣶⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⣩⡉⣕⢦⡀⠸⠀⠀⠀⠲⣄⡀
⠀⠀⠀⠀⢻⣷⣶⣿⡾⢿⠿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⡀⠀⠀⣼⣿⡡⠚⠃⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢄⡀⠀⠀⠀⠘⢷⣆⢠
⠀⠀⠀⠀⢼⣿⢁⣤⣤⣈⣀⠩⠹⣿⡀⠀⠀⠀⠂⠠⠀⠀⣾⣻⣿⣾⠃⠀⠀⠉⠀⠀⠐⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⠠⠀⢸⡟⣿
⢰⠶⣾⣷⣿⣿⣿⣿⡛⣹⣿⡧⠀⣿⡇⠀⠀⡠⠠⠛⠛⢷⣿⣿⣋⡁⠀⠀⠀⠀⣆⢀⣤⠆⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠙
⠘⠓⠉⠆⣿⣹⣿⣿⣿⠿⢫⠁⣠⣿⣇⡄⠈⠂⡀⠀⢀⡜⢫⡴⠾⡏⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢀⣀⠀⠀⠀⠀⡀⠀⠈⠙⢿⠄⠀⢠⣤⣦⡀⠀⠐
⠀⠀⠀⠘⣷⣿⣿⣿⠧⢺⣽⣿⣿⠿⣿⡇⠀⠀⠉⠤⠆⡿⠿⣦⢾⡇⠀⠀⠈⠁⠀⠀⠀⠐⠀⠠⠆⢀⣿⠓⡶⠖⠀⣈⠀⠀⡀⠀⠀⣠⡏⣿⣟⣿
⠀⢠⣾⢾⣿⣿⡿⠁⣽⣿⣿⣟⣿⣷⣷⡄⠀⠀⠀⢸⡷⠀⠀⠈⠉⢁⠀⠀⢙⠢⡀⠀⠀⠀⠀⠀⣤⠏⢈⣤⣀⠒⠀⡈⠉⠀⠀⠀⠀⣀⣀⢠⣿⠉⠁
⠀⠀⢿⢿⣿⣿⡇⠀⣿⣿⣿⡟⠙⠿⣿⣷⣆⠀⠠⠀⠀⠀⠀⠀⢀⣜⡢⠄⡃⣸⣷⡄⠀⠷⠠⣌⠛⣾⣿⣿⣿⣷⣦⣀⡀⣀⡀⣀⠀⣀⠁⡹⣟⢾⡄
⠀⠀⠈⠀⢻⣿⠃⣾⣿⣿⣿⡫⣄⠠⠉⡿⢻⠀⠀⢀⣤⣦⡴⠶⠢⠮⠥⠌⠠⡉⠈⠁⠀⢀⣀⣒⡂⠸⣛⣻⣿⠛⠉⠛⠁⠁⠘⠁⠔⡥⠪⣚⠿⠁⠄
⠀⠀⠀⠀⢄⣿⣧⣿⣿⣿⡏⢈⣿⣳⣶⡷⣾⣤⠐⢾⡛⣯⡄⠀⠀⠂⢘⣂⣀⣘⣠⡴⠶⢼⣿⣿⣟⠋⠉⠉⠁⠀⢀⣤⣀⡨⠟⠓⠮⣦⠔⢡⠀⠄⢄⡀
⠀⠀⠀⠀⠀⠻⣿⡟⣿⣿⣟⡀⠰⢿⣿⣧⣿⡿⢳⣺⡇⣿⠃⠒⠛⠛⠋⠉⠉⠀⠀⣀⣀⡄⠈⢻⣿⡀⠀⠀⠀⢀⣿⣿⡿⠁⢠⣦⡄⣭⡴⣀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠹⣷⡼⢻⣶⣶⠞⣠⣾⣿⣿⣿⣿⣯⣙⠛⠂⠀⡀⠀⠀⠀⣤⣶⣿⣿⣿⣷⡄⠸⣿⣷⡆⠀⠀⠀⢀⣿⣇⣠⣾⣾⠖⠿⠆⢬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣿⣃⣾⣿⣿⣈⣛⣨⣿⡛⢾⣦⣶⠶⠾⠀⠀⠀⡈⣿⣿⣿⣿⠿⡏⠁⢹⡿⣧⠀⠀⠀⢾⣿⣿⡟⢛⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⣌⣍⠉⠁⠙⠿⣶⣽⣿⣶⣤⣴⡀⠀⠈⢹⣿⣿⣏⢴⣿⡀⣸⣿⠻⣆⣰⣿⣿⣿⣿⣤⣤⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣤⣤⠤⢤⡄⠉⠻⠿⠁⠈⠠⣤⡤⡞⢩⣿⣿⣷⣿⣩⣿⣿⣻⣾⣯⢿⡁⠉⠳⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠴⣷⠆⡠⠄⠠⠥⠉⠈⠉⣉⢸⡟⢹⣼⣿⣿⣿⣿⡿⠟⠛⠓
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣉⣬⣼⣿⣿⣿⣟⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣴⠾⣛⣫⣭⠭⠭⠭⠭⣭⣽⣛⡷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠊⣷⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢬⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠙⢿⣿⣦⣤⣀⣀⡀⠀⢠⣶⣄⡛⠀⠙⢶⡝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡟⣥⠀⢀⡄⠀⠀⠀⠀⠈⠙⠻⣿⡿⡿⢟⡊⠉⢛⠟⠀⠀⠀⠙⣮⢻⣆
⠀⠀⠀⠀⠀⠀⣰⡟⡼⢡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⢀⡾⡵⠖⣿⣦⡀⠀⠀⠀⠈⢧⢹⣆
⠀⠀⠀⠀⠀⢠⡿⣸⠃⠈⠀⠀⣀⣀⣀⡀⠀⠀⠀⢰⣿⣿⣭⣴⣶⣶⠿⣿⣿⣄⠀⠀⠀⠘⣇⢿⡄
⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣤⣾⡙⠿⡿⠟⠋⠁⠀⠈⠻⣿⣷⡄⠀⠀⢻⢸⡇
⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠸⣿⣷⣽⣿⣿⣿⣿⣷⡙⠀⡀⠀⠀⠀⠀⠀⠈⠫⣾⣇⠀⢸⢸⡇
⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⢿⣿⠉⠉⠛⢻⣿⣿⡇⠀⢳⠀⠀⢀⠀⠀⠀⠀⠈⠹⣷⣼⢸⡇
⠀⠀⠀⠀⠀⠘⣷⢹⡄⠀⠀⠀⠀⠸⣿⠀⠀⠀⢰⣿⣿⠃⠀⣸⡇⠀⠀⠀⣀⣤⣤⣤⣄⢃⡏⡊⠁
⠀⠀⠀⠀⠀⠀⠹⣧⢳⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠱⣶⣶⣆⢀⣶⣾⣿⣾⣹⣿⣿⢟⡜⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡻⣄⣤⣤⣾⠿⠿⠀⠀⠀⠀⠀⣈⣩⣿⡾⣿⡿⣟⣋⣜⠉⣠⢟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠿⣍⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣿⣷⣾⠿⣿⣿⣿⡟⣣⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⣛⢦⣄⣀⠀⠀⠀⢀⣿⡿⠿⣿⣿⣿⠘⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣭⣝⣛⣒⣒⣚⣛⣚⣩⣴⡦⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡛⢿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⡽⠃⠉⠙⠻⢷⠗
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⠃⠀⠀⠤⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⣠⠔⠃⠸⣄⠀⠀⠠⢄⠁⠀⠀⣤⣐⣐⡒⢢⡀
⠀⠀⢀⡠⠂⠀⢷⠀⠑⣄⠘⢿⣦⠤⠄⠀⠀⠀⣧⠀⠀⠀⢸⠽⡆
⢀⠞⠁⠀⠀⢄⠘⡆⠀⣈⠳⡘⢉⣧⠀⠀⠀⠀⢸⠀⠀⠀⠈⣯⡇
⣾⠀⠀⠀⠀⠈⢷⡙⠚⠁⠀⠁⠈⠐⢦⠀⠀⠀⠈⠓⢤⡤⠀⠑
⢻⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢠⠀⢳⡀⠀⠀⣰⢣⡑⡼⠁⠀⠀⠀⣀
⢸⢷⡄⠀⠀⠀⢀⣀⣈⢦⡀⠀⠀⢸⢀⣤⣛⣦⡠⠛⢄⠙⠣⠀⠀⠀⡀⠁⢀⣈⢣⠀⠀⠀⢀⣀⣀⣀⣀⣀
⢸⠇⠙⢦⡀⠀⠀⠉⠉⠁⠉⠑⠲⠼⠭⢀⣀⣞⡁⠀⠀⠩⠏⢀⡀⠀⡏⠉⠉⢁⡨⠖⠚⠉⠨⡅⠀⠀⠀⠈⠙
⣸⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠹⡆⠀⠀⠀⢐⣮⠀⠑⠂⠐⢅⠀⠈⠁⠢⠄⠀⠀⠀⠀⠠
⣏⠀⠀⠀⠀⠀⠉⠒⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣭⣶⣦⡤⠐⠀⠀⠀⠀⢀
⠈⢣⡰⣄⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠭⠭⠤⠤⠤⠤
⠀⠘⢿⣾⣷⢢⣤⣗⡒⢲⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠒⠒⢒⣒⣒⣀⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣲⠿⠿⠿⠿⠿⢽⣖⣢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠮⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⣿⠁⡈⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢧
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣴⠃⠀⣀⡈⠀⠀⠀⠀⠤⢶⣆⠀⠀⠀⠀⣤⣶⣤⡸⣿⡀
⠀⠀⢀⣔⣵⣿⣿⣾⣏⠋⠛⠩⠷⠶⡶⣦⢄⠀⣞⡞⠁⠀⡼⠗⠒⠁⠀⠀⠀⠀⠀⠹⠀⠀⠀⢸⣿⣹⣿⣿⣿⠃
⠀⠀⡼⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣷⣽⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⠒⠀⠀⠀⠀⢻⣿⣿⣵⣿⣿⠇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣧⠹⢙⢲⢢⠑⠤⣀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠟⡫⠭⠍⢳⣳
⠀⠀⢯⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣄⣀⣼⣿⡿⠟⠺⠼⠾⠷⢦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡪⣪⢞⠜
⠀⠀⠈⢮⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣺⠕⠁
⠀⠀⠀⠀⠈⢉⣽⣻⣶⣿⣿⣿⣿⣿⣿⣧⠀⢹⣽⢫⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⠿⠊⠁
⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢞⣟⠀⢳⡷⡄⠀⠀⠀⠀⠀⠀⣠⡴⡻⠕⠋
⠀⠀⠀⠀⠀⠹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⡆⢄⡀⠀⠀⡊⠻⡼⡄
⠀⠀⠀⠀⠀⠀⠈⠳⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⣰⠋⠉⢱⣿⣮⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠫⢿⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠢⠙⢦⣀⣸⠸⣿⣿⣟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⡿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⡟⠀⢻⣿⣿⣷⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣧⠀⠘⣧⣿⣿⣿⣟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡀⠀⢿⣿⣿⣿⣿⣎⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣧⠀⠀⣻⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢟⣻⠿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣛⠯⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠛⠓⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠿⠿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠦⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠳⠦⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣀⣠⣤⣤⣤⣀⠠⠤⢤⣝⠟⠃⠀⠀⠀⠀⠀⣸⠟⣋⡛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣷⣿⣿⣿⣵⣦⣶⣾⣶⣿⣿⡿⠿⠛⢭⠆⠀⠀⠀⠀⢀⠠⠁⠸⠁⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠏⢸⠿⠟⠛⠁⠀⠀⠀⣮⣀⠀⠀⠀⠀⠐⡐⣿⠗⠞⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣼⠐⠀⠈⠁⠀⠀⠀⠐⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠬⢿⣭⣄⣠⠀⠀⠀⠀⠀⠀⠹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠿⣗⣀⠀⠀⠀⠀⠀⠀⠀⠠⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠚⠁⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠊⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠘⣆
⠀⠀⢠⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠸⡄⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⢇⢀⠀⠣⠀⠀⠀⠐⠁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⢳⠀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣾⡿⡿⠁⠀⠀⠀⠀⠉⠘⠛⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠈⠷⠿⠿⠿⠷⠒⠚⠛⠋⠉⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⡄⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢻⣇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⢻⠟⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠿⠿⠋⣿⣿⣾⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠉⠀⠀⢀⢀⠀⠀⣏⠉⣿⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣾⣶⣾⣿⣷⣶⣿⠀⡿⠁⠀⠀⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠾⣻⣻⡧⠟⠀⠀⠀⠀⢀⠄⣂⠠⣄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⣉⡛⢿⣿⣿⣿⡿⠋⣠⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⡄⡰⠋⣰⠃⠀⠘⠟⢦⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢯⡙⣷⡘⢿⣿⣇⡐⠕⡴⠀⠀⠀⠀⠀⠰⣤⠟⠋⠔⢀⣴⣿⣫⠆⠀⠀⠀⢛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡉⠿⠅⠈⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢻⡓⠋⠉⠉⠉⡁⠀⢆⠀⠈⠓⠉⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠢⣄⢋⠀⢉⢿⣿⠀⠁⢤⣄⣀⠉⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠈⡆⠀⠠⢬⣼⣷⣤⣜⢫⣿⣷⡶⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⠻⣿⡏⢻⣦⣄⣀⣀⣀⠀⢀⣀⣠⡤⠄⠋⠀⠀⠀⠀⠈⠓⢦⣀⠀⠉⠙⠻⢎⢻⣿⣾⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠉⠀⣻⣇⠀⠀⠉⠛⠛⠓⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢵⣄⠀⠀⠀⠦⠼⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠹⣦⠀⠀⠨⣟⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⣒⡤⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠷⡀⠀⠈⠻⣄⡀⣹⣧⠀⠀⠀⠀⡼⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣽⠄⣀⣠⢷
⠀⠀⠀⠀⣠⠶⠛⠁⠀⠱⡄⠀⠀⠈⠙⠻⢿⣆⠀⠀⢸⠛⠢⡀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣼⠿⠚⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠙⢳⠏⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⠶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣤⣴⣶⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠋⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣤⣴⣶⠒⠤⠀⠠⠤⠄⠻⢿⡽⠥⢀⠀⢍⠉⠒⠤⡐⠒⠒⠒⠒⠒⠒⠞
⠀⠀⠀⠀⠠⠀⠀⠒⣀⣀⠀⠲⡿⡿⠛⢈⠒⢀⡀⠀⠀⠀⡜⢀⠀⢸⠀⠠⠁⠀⠀⠀⡠⡀⠀⠀⠀⢠
⡀⠀⢀⠠⠎⠉⠁⠠⠴⠀⣇⣠⠊⠇⢀⠸⠓⠢⠌⠱⠀⠾⢧⠔⢆⠸⠖⠁⠀⠠⠔⠊⣀⣜⡐⠀⠀⡈
⠈⠰⠜⠒⠢⢤⠤⠤⠤⠒⠊⠓⡀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⣀⣀⣽⡾⠻⠟⠛⢀⠄⠀⢒⡇
⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⣤⣶⣾⠀⠸⡁⠟⠛⠋⠀⢀⡠⠒⠉⣉⣉⡉⠁
⠀⠀⠘⠂⠀⠀⠀⠈⠑⠂⠠⠒⠒⠈⠉⢹⡇⠀⠀⡞⢿⣻⠛⠀⠰⠄⠁⠠⠤⣖⡇⣰⣿⠀⠀⠀⣤⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⢀⠞⠀⢠⠋⠀⠀⠀⢉⣢⣄⡀⠙⠷⣿⣿⠀⠀⠠⣿
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⡡⡑⢾⣇⣊⡀⣠⠇⠀⠀⢐⠒⠚⠥⠻⢽⠲⣄⡀⠉⡁⠠⡀
⠀⠀⢠⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢮⣢⠀⠙⠕⠛⠀⠀⠀⠀⠑⡤⠤⠂⡸⠀⠆⣧⡊⢠⠴⠁⠤
⡀⢠⣦⠐⣦⠀⠚⠀⠀⠀⠀⠀⡇⠀⠀⠑⠳⠼⠠⠤⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠤⠄⠊
⠀⠀⢀⣀⠀⠤⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⣶⣿⣷⠄
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⣿⣿⣧⡟⠛⠛
⠀⠀⠀⠀⢀⡾⠟⠛⣋⣉⣶⣾⣿⣿⠹⣷
⠀⠀⠀⣀⣤⣶⣴⣿⣿⣿⣿⣿⣿⣿⡇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⢠⡄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⠇⠀⡀⠒⢶⡶⠀⠀⠀⠀⢦⣾⣷⢛⣧⡔⠛⠁⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠉⠀⠀⠘⠛⠛⠗⠀⢐⠈⠀⢀⣘⣯⣿⣿⣿⡡⣾⠃
⠀⠀⠀⣿⣿⣿⣿⠟⣛⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⣤⣀⣤⣶⠟⢿⡿⠟⠁⢿⣁
⠀⠀⠀⢹⣿⣿⣿⡌⠉⢓⡈⠉⠋⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢀⣬⠟⠉⠙⠀⠘⠃⠁⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠈⢿⣿⣿⣿⣄⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⡂⠀⠀⠂⠀⠠⠤⢠⣄⣤⡶⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⠀⠙⠳⢤⣀⣀⣀⠀⠀⠀⠀⣠⣤⣴⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⠙⠛⠻⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠤⢄⣀⠤⠒⠚⠠⣀⣀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠣⢤⣀⣀⣀⡀⣀⣀⣀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠛⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣻⣿⣿⡅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⡄⠀⢒⢷⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠄⠀⠀⠚⣛⠣⠀⠀⠀⠀⠀⠰⢊⣡⣤⣬⣛⠲⣿⣿⡿⣃⡈⢆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠉⠉⠀⢠⡄⠀⠠⣤⣶⣿⡿⣿⣿⣧⣄⠉⠉⠉⠉⠙⠈
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⢟⣆⠉⠀⠀⠀⠀⠀⠘⡄⢲⠒⠉⠉⠀⠈⠑⠋⠉⠀⠀⠀⠠⠄⣤⠤⠄⠡
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⣍⣠⡀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠈⠻⠦⠤⢤⣤⡤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠱⣄⠀⠀⠀⠀⠀⢶⠀⠀⠲⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢄⠀⠈⠓⠤⠤⣀⣀⠈⡾⣷⠂⠀⠀⠈⠲⠒⠠⠄⠤⠤⠀⠀⠀⢀⠄⢾⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⠑⢄⡀⠀⠀⠀⣼⡻⣼⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⢠⡈⢦⡀⠀⠀⠀⣇
⠀⠀⠀⢀⠤⠚⡀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠏⠻⢮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⠲⠤⠤⢾
⠀⠀⡐⠁⠀⠀⠈⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠢⡀⠍⠑⢒⠒⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⣰⣷⣒⣓⣀⠀⣀⣀⠤⢀⣀⣉⡰⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⡎
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠒⢀⢀⣀⢐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⠪⠡⡀⠘⡄⠀⢉⠦⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣠⠃⡎⠀⠀⠱⡐⠆⡤⢒⠥⠊⠈⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠒⠀⠤⢤⠁⣀⠀⣉⣒⠂⠠⠔⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⠂⠤⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⣄⣀⠴⠷⠞⢹⡦⡱⡀⠀⠀⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠁⠈⠢⠀⠀⠀⢘⡇⠙⢌⠤⠊⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠖⢀⡉⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠤⠤⣀⣀⡠⠤⠄⠂⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⣀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⢀⡠⠔⠊⠀⠡⠉⠒⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠈⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠃⢀⡀⠘⢀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢃⠀⠀⠸⠀⠀⠀⠀⠈⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠡⠀⠀⠀⠀⢀⡐⠋⠀⢀⣀⣀⣀⠑⢄⠀⠀⠀⡌⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡀⠀⠀⠀⠡⠑⠄⠂⠁⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠀⠄⠤⣀⢁⢀⠈⠀⠀⠀⠀⡀⠀⠀⢨⢱⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⠀⠀⠀⠀⢠⠂⠀⣄⠀⠉⠛⠆⠀⠀⠀⠀⠠⠀⠀⣈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠃⠀⠔⠀⠈⠂⠀⢃⠀⠀⠀⠀⠀⠀⠀⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡇⠀⠀⠀⢋⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢸⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⠀⠀⠀⠈⠂⠄⡀⠀⢂⠊⠀⠀⠀⠀⠀⠀⠀⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠦⣉⠒⠤⠤⠄⢀⣀⠀⠤⠤⠒⢊⣡⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠑⠒⠂⠤⠤⠤⠤⠔⠒⠊⠉⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢄⣀⣀⣀⣀⣀⡠⠤⠒⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣽⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠟⠛⠛⣛⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⢿⣷⣄
⠀⠀⠀⠀⠐⣻⠁⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⢀⣀⣄⣠⣭⣷⡄
⠀⠀⠀⠐⠿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⢿⣿⣿⣿⢀⣺⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⢀⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠁⢩⣀⣉⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢠⠞⣵⡟⠁⠌⠀⠀⠀⡀⠀⠀⡤⠈⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⣛⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⢸⡋⡀⢞⡥⠤⠆⠱⣦⣈⡇⠀⠀⠀⠀⠀⠀⠀⠻⢇⣐⠋⢙⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⣻⣿⡿⠀⣆⠰⢺⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢰⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠈⠙⠛⠀⠸⠁⠈⢲⡮⠄⠀⠀⠀⠀⠀⠀⠀⠐⣲⠇⢰⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢈⠙⠀⠀⠀⠀⠀⠀⣠⠇⠀⢠⡋⠈⠁⠀⠀⠀⠀⠀⠄⢄⣴⠃⠀⠘⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣀⣠⠞⠀⠱⣀⠀⢐⣤⠤⠴⠒⠈⠀⠀⠀⠈⠫⠦⢴⣴⣿⣯⣬⡽⠾⠟⠁⠀⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠙⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠢⢄⣀⣤⣀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⡸⠀⠁⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⢈⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣣⠞⠑⣀⡀⠴⠒⠛⠉⠀⠀⠀⠀⣠⠞⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃⡼⠀⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⢀⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢠⣴⣴⢰⣴⡄⠀⠀⠀⠀⠉⠀⠀⠠⢿⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⣀⠀⠠⣤⣀
⠀⠀⠀⠀⠀⠘⠐⠉⠄⢿⡇⠀⠀⠀⠀⠰⠈⠂⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠿⠀⠀⠀⠀⢠⡀⠀⠀⠀⠒⢶⡄
⠀⠀⠀⠀⠀⢀⠀⠈⠰⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠰⠄⠢⠤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⠐⢠⡟⠀⠀⠀⠀⠀⠰⡀⠀⣠⡾⠀⠀⠀⠀⣦⠀⠠⣴⠀⠀⠀⠀⠀⢀⠀⢀⣤⠃⠀⠀⠀⠀⠸⣆⡀⠀⠀⢠⣴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⡀⠀⠀⡀⠀⠤⠄⠀⣀⡀⠀⠀⠀⣀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢺⡇⠀⠐⢻⣥⠃⠀⠀⠀⢨⠀⠀⠀⠁⠀⡇⠀⠀⠡⡀⠀⠀⢀⡞⠁⠀⠀⡏⠀⠒⠒⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⡀⠀⠐⠁⠀⠀⠀⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠐⡀⠀⠊⠀⠀⠀⠀⠈⠂⢀⠀⡀⠀⠀⠀⠀⠸⠐⠀⠀⠸⢷⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡶⠎
⠀⠀⠀⠀⠀⣄⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡔⠚⠁⢀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠀⠀⢰⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣴⠆⠀⠀⣀⣐⣦⠀⠀⠀⠀⣤⣠⣴⣧⣤⡀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⡖⠊⠉⢭⣶⠀⠀⠀⠀⡤⠀⠀⢐⢤⣤⡀
⠀⠀⠀⠀⢹⠀⠆⠠⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢁⠀⠀⢸⡏⠀⠀⠀⠀⡛⣠⢿⣼⡧⢸⠃
⠀⠀⠀⠀⠀⣆⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⡗⠐⡘⢁⠟⢸
⠀⠀⠀⠀⠀⢸⡀⠀⢀⡌⠀⠀⠀⠀⠀⢠⡀⠀⣀⡇⠀⠀⠀⠀⡤⠀⠀⣠⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⠀⠀⠀⠀⣄⠀⠈⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⡾⠿⠛⠛⠿⢿⣿⣷⣄⠈⠙⣿⡅⠀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠜⣬⣜⣩⣤⣤⣤⣦⣴⣶⡾⠿⠿⢷⣦⠸⡇⡼⠋⠉⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢂⣶⣦⠲⣶⣶⣶⣶⣖⣤⣠⣤⣤⣤⣦⣴⣶⢐⡒⠒⠒⢶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⣼⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣆⠙⢷⣶⣄⣘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠀⠠⠿⠿⠿⠿⠿⠆⠻⠿⠿⠿⠿⠿⠿⠿⠱⠿⠿⠿⠆⠈⠿⠿⠿⠿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⣴⣿⣿⣿⣿⣿⣿⣆⠸⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣷⡄⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡀⠙⣛⣛⠃⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠙⠛⠁⠘⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣵⣤⣤⣦⣤⣴⣤⣤⣦⣤⣴⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠙⢛⡋⠉⠛⠙⡛⠛⠛⠛⠋⠙⠉⠙⠋⠉⠙⠛⡉⠛⠛⠛⢉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⢰⡿⣿⡄⠀⢸⣷⠀⠀⣿⡇⠀⢠⡿⠀⠀⣸⡿⣷⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⣾⡇⠀⠀⣿⣁⣹⣧⠀⠀⣿⡄⢰⡿⣿⠀⣼⠇⠀⢠⣿⣀⣻⣇⠀⢸⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⣸⡟⠛⠛⣿⡆⠀⢸⣧⣾⠁⢻⣦⡟⠀⠀⣾⠛⠛⠛⣿⡄⢸⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠀⠉⢀⣀⣀⣈⣉⣀⣀⣉⣉⣀⣈⣉⣁⣀⣈⣉⣀⣀⠀⠉⠁⠈⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⠀⢰⠆⠀⣠⠤⣄⠀⣤⠀⢴⠀⢸⡟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⢿⠀⣾⠀⢸⡇⠀⢸⠇⣿⠒⠛⡇⢸⠏⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠛⠉⠀⠙⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠂⡀⠀⠈⠀⣀⣠⡤⠶⠶⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠐⠄⠈⣠⠴⣛⢽⣲⠥⠬⢯⡤⠭⢴⣒⢭⣓⢦⣀⠀⠐⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢠⣞⡯⠂⠞⠭⠒⠩⠥⠤⠦⠍⠑⠂⢅⠨⠳⣝⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⣀⣶⣿⡄⢠⣶⡏⠀⠀⢠⣾⡿⢟⡂⠀⣿⣦⠀⢠⣶⠊⠃⢉⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⡿⣿⣧⢸⣿⡇⠀⢠⣿⡏⠀⠀⢿⡄⣼⣿⠀⣻⣿⠀⣠⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣀⣸⣿⢸⣿⡇⠀⢸⣿⠀⠀⠀⢸⡇⣿⣿⠀⣿⣿⢀⣿⡟⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⢻⣿⠈⣿⡇⠀⢸⣿⠀⠀⠀⣼⡇⣿⡟⠻⣿⡟⢸⣿⣇⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣸⣿⠀⣿⡇⠀⠈⣿⣧⣀⣰⡿⣸⣿⠃⢰⣿⠇⣿⣿⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠻⢿⡄⣿⣷⣶⣿⣎⠻⠿⠟⢁⣛⣛⣀⣈⣛⡀⠛⠛⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣀⣁⠉⠉⣉⣁⣤⣶⠾⠿⠟⠛⠛⠛⠻⠿⣿⣿⡶⢤⢀⡉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣉⠛⠛⠛⠛⠛⣋⣉⣥⣤⠶⠞⢛⣛⣉⣉⡛⠒⠄⣙⠫⣍⣿⣽⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠟⣛⣉⡴⠶⠟⢛⣛⣛⣋⠛⠛⠶⢬⡑⠈⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠛⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣤⣼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⠻⢿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣾⣿⣿⣿⣦⣶⣯⣶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢈⣻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⡹⠿⢿⣿⣿⠟⠋⠑⠳⡄⠀⠀⠀⠀⠀⠀⠐⣥⣀⡀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢲⣤⣀⠀⠈⠛⣛⢓⣄⡑⠙⠦⣄⠀⢰⡀⠀⠀⡿⣥⡅⠀⠀⢻⣿⣿⣶⣶⣾⣭⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣼⡁⠀⠉⠉⠉⠉⠀⠉⠉⠙⠲⢤⣧⣴⠛⠃⠀⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠆⠀⠀⠀⠀⠀⠐⠖⠀⠟⣛⡻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣙⣿⣿⣿⠟⠋
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⡶⣄⠥⠴⠛⠛⢿⢿⠟⠁
⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢈⢰⢦
⠀⠀⡈⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡀⠀⠀⠀⠀⢀⡼⠃⠀⢱
⠀⠀⠀⠀⠀⠀⣀⠴⠒⠚⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠐⠒⢞⡌⠇⢀⡤⠐⠚⠁⠀⢀⡠⠋⠑⢄
⠀⠀⡀⠀⠀⠊⠠⢂⣠⡤⠊⠀⠈⠉⠉⠉⠐⠒⠒⠊⠁⠀⠀⠀⠉⠈⣏⠀⣩⡼⠀⠀⡔⠀⠀⠀⠀⠀⠀⠐⠢⢤⣀
⠀⠀⠐⠦⣀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⣄⣀⠀⡜⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣿⣿⣿
⣶⣶⢶⢶⠶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹
⠀⠀⠀⠀⠀⢀⣀⣀⣄⣸⡀
⢠⠔⠈⠀⠀⣀⢀⠀⣀⡀⡀⢀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡴⢛⠆⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠱⣤⡀⠀⠉⠈⠁⠉⠉⠉⠈⠈⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⣷⠀⢸⢁⡞⠀⣀⣀⣼⢏⡀⠀⣀⣄⠀⠀⠀⢠⠏
⠀⠀⠈⠉⠛⠛⠛⠛⡏⡏⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣰⠇⠀⣹⡞⠀⣞⣩⠇⡟⠉⣟⢰⣁⣼⣀⡀⠀⠈
⠀⠀⠀⡖⠒⢀⠀⢈⢉⠉⢉⡁⣀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠙⠦⠞⠁⠓⠚⠁⠉⠁⠈⠁⠀⠁⠀⠈⠀⠉
⠀⠀⠀⡇⠀⠈⠀⠛⠘⠃⠘⠈⠋⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠞⠀⠃
⠀⠀⠀⠙⠛⠋⠉⠛⡏⡏⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⢠⠠⠀⠀⡀⢀⠀⡔⠀⠤⡄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡎⢸⠈⢰⠀⠀⠈⢱⠁⠀⡀⢠⢠⢻⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣀⠰⠘⢀⠌⠈⠐⠁⠒⠰⠄⠤⠂⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠶⠁

⠀⠀⡠⠤⠄⢀⡀⠀⢀⣀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⡀⠀⢀⣄⠀⠀⢀
⠀⢸⠀⢄⠠⡏⠙⠄⡇⢨⠆⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⡇⠀⢠⢳⠀⡜⠀⠀⢰⢼
⠀⠸⠤⠎⠀⠣⠚⠀⠉⠉⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⣄⠇⠀⠣⠀⠘⠈⠀⠳⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⠖⠂⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠀⠖
⠀⠀⠀⡀⠀⠀⡆⠀⡦⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⠀⡗⠀⢰⠒
⠀⠀⠀⠓⠂⠀⠁⠀⠁⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠁⠀⠈⠓⠂

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⢿⠇⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⣯⠏⠀⢀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣴⣳⣄⡠⠞⠣⡤⠴⣯⠟⢩⡟⢳⡠⣯⠽⢤⠤⠆⠀⠀⠀⠀⠀⠀⠀⡏⢸⣀⣾⣽⣀⣴⣠⢦⡴⢶⣹⣇⣼⣤⠾⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣟⣛⣿⣿⣿⣾⣿⣷
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⠀⠉
⠀⠀⠀⣠⣿⣿⣿⣾⣷⣿⣿⣿⣧⠀⠻⠘
⠀⠀⢰⣟⢿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠲⣶⠘
⠀⠀⢸⣿⣿⣶⣶⣶⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⡀⠀⠀⣀⠀⡀
⠀⠀⠈⢿⣿⣿⣿⡟⠭⣝⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠂⢘⠋⠀⠀⠀⠀⠀⠒⠓⠀⠀⠀⠀⠀⠸⠀⠰⣜⠓⠘⣇⡀
⠀⠀⠀⠈⢿⣿⣿⣇⠀⢈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡤⠤⠄⢀⠀⣶⡆⠀⠀⠀⠀⠀⡠⠲⠘⠛⣷⣾⣿⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⠯⣥⣸⣿⣿⣿⣷⡁⢠⠟⠛⠿⢋⡿⠂⠐
⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢬⡙⠛⠛⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠘⠛⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆⠲⡖⠒⠒⠒⠋⠙⠲
⠀⠀⠀⠀⠀⠀⣰⠚⠁⠈⠂⠀⠀⠀⠀⠀⠠⠛⢀⡇
⠀⠀⠀⢀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣀⠀⠀⠀⠀⠀⡇⠹⣦⡀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠈⠑⠦⣀⠀⠀⠸⡀⢷⣝⢦⣀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠈⠑⠚⢦⡳⡈⠻⡷⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠶⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢷⣤⡀⠀⢸⣿⠀⠀⠀⠀⠀⠘⠦⠖⠋⡇⠉⣙⠆⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⢀⡀⠀⠈⠻⣿⣄⢸⣿⠀⠀⣠⣤⣶⣶⡤⠀⠀⠈⠉⠁⠀⠠⣄⡒⠐⠀⠀⠀⠠⡀
⠀⠀⠀⠈⠙⣛⣛⣶⣾⣿⣮⣿⣴⣿⣟⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠍⠶⡀⠄⠀⠀⠸⢦
⠀⠀⡴⠾⡿⠿⠿⠿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠄⠀⠂⠒⠻⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠈⠛⢿⡄⠀⡀⠀⠀⠁⠀⠎⠩⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⡜⣿⢀⡆⠀⠀⠀⢠⣟⠜⠀⠀⠀⠀⠀⠀⢠⠖⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⢄⣸⣸⡷⣻⠀⣾⢳⣀⡿⢋⠀⠀⣀⣀⡄⠀⢠⣯⡀⠀⠀⢠⡆
⠀⠀⠀⣀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠃⣿⠀⡇⢸⣇⠝⢸⢟⡟⣠⢾⡯⡟⠀⠀⢸⣝⣿⣤⢐⡠⠖
⠀⠀⠀⡁⠘⠢⡀⠉⠀⠀⠻⠴⠋⠀⠋⠀⠑⠀⠀⠀⠋⠘⠟⠁⠀⠀⠁⠀⠀⠈⠶⢀⣀⡰⠔
⠀⠀⠀⡇⠐⡀⠘⢧⡀⠀⠀⠀⠰⣄⠀⣠⣤⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⣀⠀⡀
⠀⠀⠀⢸⠀⠐⡀⠈⢳⡄⠀⢀⣠⢼⣦⣁⠀⠀⠀⠀⡸⠛⠺⠛⡟⣯⠿⠿⠛⠻⠿⣷⣾⣿⣿⣔
⠀⠀⠀⠀⢇⠀⠀⠀⠀⢻⡄⠁⠀⠂⡀⠉⠉⠁⠐⠂⠵⠤⠤⣄⣋⣠⣄⣀⣀⡠⠐⠁⠁⠈⠉⠀⣿⠄
⠀⠀⠀⠀⠈⠇⢀⠀⠀⠤⢷⠀⠀⠐⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠃⠀⠉⠉⠉⠛⠙⠛⠛⠿⠷⠒⠊⠂
⠀⠀⠀⠀⠀⠈⢃⣀⠐⢐⢺⡄⠀⠀⠀⠀⠀⠸⠐⢢⡖⠏⠟⣦⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠡⠅⠤⠁⠤⠥⠀⠉⠉⠀⠀⠚⠙⢒⠝⠦⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⠟⠀⣹⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡿⠀⠀⢀⡟⠀⣠⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⡼⠃⠀⠀⣼⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡇⢠⣯⠞⠁⢠⣄⣀⣿⣞⠁⠀⢠⡶⣶⠀⣠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⠀⣾⡏⠀⢠⣿⢹⡆⣿⢻⡇⠀⣿⣴⡏⢠⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⣻⠀⢀⡏⠙⠚⠀⠁⢸⡇⣸⠁⠸⣇⡞⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡾⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣦⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄
⣽⣧⠀⠀⠀⢼⡟⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⣿⣿⣷⣆⣠⣼⣷⣧⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⣿⣿⣿⣿⡟⠙⣻⡿⣿
⣿⣿⣭⣿⣷⣛⣿⣿⢻⢿⣿⣿⠿⠛⠛⠛⠳⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣴⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⢠⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠄⢀⣀⣀⣀
⠀⠀⠀⡾⢠⡀⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢿⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠀⠛⠀⠈⠃
⠀⠀⠀⣺⣂⣹⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⢀
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉
⠀⠀⠀⠀⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏
⠀⠀⠀⡀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠋⠁⡀
⠀⠀⠀⠠⢴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠘⡇⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⢋⣭⠐⡇⢠⣀⢀⡄
⠀⠀⠀⠀⠂⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡦⠖⡇⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⡤⠀⡇⢐⠛⠓⠁
⠀⠀⠀⡀⠲⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⡇⢠⣀⣀⡄⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⡇⢰⠤⢼
⠀⠀⠀⠙⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠘⠋⠛⠃⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠈⠚⠛
⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹
⠀⠀⠀⢠⣞⡛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣉⣉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡄
⠀⠀⠀⣿⣽⠿⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⣞⣷⣶⣿⣦⢀⠀⠀⠀⠀⡀
⠀⠀⠀⢹⣵⣤⠴⣿⠀⢸⣦⣥⣴⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢰⣶⠶⣶⡆⠀⠀⠀⠀⠀⠸⡯⠭⠭⠭⡿⠈⠻⢿⠿⠞⠁
⠀⠀⠀⠀⣷⣶⣶⡆⠀⠀⣭⣸⡍⠀⠀⠀⠀⠀⠘⣟⠋⠙⡇⠸⣿⡟⣿⠇⠀⠀⠀⠀⠀⠀⢷⣶⣦⣴⠇⠀⠀⠠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢰⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠇⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠀⠀⠀⢰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢻⡇⠀⠀⢀⠀⠀⢸⠀⠀⡜⠀⠀⠀⠀⠀⢸⢀⠄⠺⡆⠀⢠⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠘⣷⠐⠊⠁⠀⠀⢸⠀⠰⠀⠀⢠⠄⠐⣦⢸⡏⠀⠀⣇⠀⠸⣦⡠⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⣟⠂⠀⡸⠈⡇⠀⠀⠙⠂
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢷⡀⠀⠀⠘⣧⠀⠀⠀⠻⠦
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠁
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠁
⢿⡄⠀⠀⠀⠀⠀⠀⢀⠊
⠈⠷⣄⡀⠀⢀⡀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⡀⠠⡶⠂⠀⠀⠀⠀⠰⡦
⠀⠀⣀⠀⢀⣀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠸⠁⠀⢸⠃⠀⠱⣤⣒⣀⣤⣰⡶⢁⠀⠀⣀
⠀⢠⡏⠉⢹⢽⠀⢸⡿⠓⠲⠒⢳⠀⠀⠀⡄⠀⣼⠀⠀⠀⠘⢧⡄⢀⠝⠐⠉⠁⠈⠙⢇
⠀⠈⡇⠀⠀⣼⠀⣿⠶⠤⣴⠀⢸⡄⠀⠀⡗⢳⣿⠀⠀⠀⠀⠀⠑⠊⠀⠃⠀⠀⠀⠀⢸
⠀⠀⠹⢦⣴⠃⠀⡏⠀⠀⠸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⢠⣤⣼
⠀⠀⠀⠁⠁⠀⠀⢡⠀⠀⠀⢤⣼⠀⣴⣬⣍⢈⠀⢠⡄⠀⠀⡀⠠⣦⠄⡈⠙⢛⡛⠛⢁⡄⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢼⡇⢠⣏⠀⠀⠀⠀⠀⣾⠄⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠐⡗⠀⠀⠐⠒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡟⠛⠻⠿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡷⣶⣶⣶⣾⡇
⠀⠀⢀⡄⣄⣀⠀⠀⡇⠀⠀⣿⠀⢸⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠜⠿⠿⠓⠀⡇⣿⠁⢿⢿
⠀⠀⠈⠁⠁⠈⠁⠀⣿⣒⡛⢿⠀⢸⠀⠀⠀⢀⡇⢸⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⣸⣧⣤⣤⣾⣧⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣀⣼⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠼⢏⣑⣾⣏⡩⠯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢁⡠⢄⠁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⣴⢶⡄⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⣉⠰⡏⠤⢦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⡇⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⡄⠙⠶⡛⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⢰⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣼⠁⠀⠀⡆⢰⣿⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⡏⢠⡏⠀⠀⠀⠀⢸⣿⡇⠀⠈⠠⠄⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⣤⠶⠤⡀⠀⢸⣿⣇⡾⠀⡀⢠⣀⠀⢸⣿⡇⠀⠀⡀⠐⠂⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⢸⣿⡟⠁⣼⡇⢿⡉⡆⣸⣿⡇⢠⢿⣿⠀⢀⣾⠏⠀⠈⠃⠀⣀⣀⠀⠊
⠀⠀⠀⠀⠀⠀⠠⠅⢸⣿⠀⠀⢨⣇⣀⣼⣿⡇⠀⣿⡇⠀⠉⡏⢹⣿⣅⡏⢸⣿⠀⢸⡏⠀⠀⣰⠀⠁⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠻⢦⠴⠋⠀⠀⠘⣿⡇⠀⠘⢧⣠⠞⠁⢸⣿⣿⠀⠸⣏⣀⠼⣷⣤⠔⠻⣧⣀⣀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠂⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠌⠣⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠁⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⡴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢰⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⡄⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⣧⠀⢸⣿⠀⠀⣠⣾⠟⠓⠆⠀⢠⡟⠀⠀⣿⡀⠀⣿⠇⠀⠀⡀⠀⠀⠀⢠⠀⠀⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢸⣿⠀⢸⣿⠀⢀⣿⡇⠀⠀⡄⠀⣿⡇⠀⠀⠘⣧⠀⣿⠀⣰⡿⠋⠂⢀⠀⣿⠁⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠒⢻⣿⠉⠉⣿⡇⠀⣰⡇⢰⣿⠇⠀⠀⠀⠘⢷⣿⢰⣿⠁⠀⢀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢸⣿⠀⠸⡟⠀⠀⠘⠿⠿⠋⠓⢾⣿⠀⠀⠀⠀⠀⢸⡟⠻⣿⡀⣀⠺⣀⡤⠙⠷⠈⠿⡤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⣿⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⡾⠀⠀⠈⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡟⢀⠁⠴⠀⠂⠀⠀⠀⠀⠀⠀⢻⡀⢠⣆⠀⡰⠁⡀⠀⠀⠁⠊⠁
⠀⠀⠀⠀⠀⠁⠀⠘⣦⣤⣾⡿⠁⢤⣴⡎⢀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⢀⠁⣠⠞⠁⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⠈⢁⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⣴⠋⣰⠋⠀⣰⠏⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠓⢀⠀⠁⡼⠁⠂⣼⠃⢠⡿⠀⢠⣿⠀⢀⡼⠁⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣴⣃⣀⡼⠃⠀⣰⠏⢀⣾⠇⠀⣼⡏⣠⣞⣡⠴⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠙⢿⠈⠛⣷⠀⠚⢷⡖⠚⠻⣥⡁⠈⠑⠲⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⢇⠀⠈⢷⡀⠀⠙⣦⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⣄⠀⠈⠙⠶⣄⣀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣵⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⣙⣻⣿⣿⣆⢀⣤⣶⣶⣦⡀⠀⠀⠁⢀⠤⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⢿⣷⠀⠀⢰⠁⠀⠈⢆⠀⠀⠀⡠⣚⣦⣤⣀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠉⣠⣾⣿⣿⣿⠻⣿⣿⣦⣤⡁⠀⠀⠇⡐⠀⠀⠈⡆⢀⡼⠉⠉⢹⡯⠿⣿⣷⡄⣠⣶⣾⣿⣦⣄
⠀⠀⠀⠄⠀⠐⠀⠀⣀⢀⣾⣿⡿⠇⢹⡟⠀⠟⢻⣿⣿⡜⣆⢸⠀⠀⠀⠀⠀⢡⡜⠀⠄⠀⣤⣿⣶⣶⣿⣿⣿⣟⠿⠿⣿⣿⣆
⠀⠀⠀⠀⡀⠀⠀⣼⣟⢸⣿⣿⣷⠀⢸⡇⠀⠀⢸⠈⠿⣷⠈⢿⠀⠀⠀⠀⠀⡜⠀⠀⠀⣰⣿⢿⣾⡿⡟⣿⠙⣿⣿⣦⡀⠈⠙⠄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢻⣥⣾⡿⣿⡄⠀⢸⡇⠀⠀⡇⠀⠀⠉⠀⠈⡇⠀⠀⠀⠀⡇⠀⢀⠀⠸⠋⣸⣿⠁⠀⣿⠀⠀⣿⣿⣧⠀⢀⣀⣀⣀⡀
⢀⣠⣶⣶⣶⣶⣤⣌⣿⣿⣦⣤⣷⣄⢸⣇⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢨⠁⠀⠀⢠⠀⠀⡟⣇⣴⣶⣿⣶⣜⣿⣏⣿⣾⣿⣿⣿⣿⡟
⣾⣿⠻⠟⣻⣿⣿⣿⣿⣿⣍⠛⠿⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⡀⠀⡸⠀⠟⠛⢹⣏⣿⣿⣿⣿⣿⣿⣉⡉⠙⠀⠉
⠁⠁⠀⣼⣿⣿⣿⣿⣿⡇⠻⣦⡀⠀⠁⢿⡄⠀⢃⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⡀⠀⠀⠀⢠⠃⠀⠀⢀⣿⠟⢉⡿⢻⣿⣿⢿⣿⣿⣧⡀
⠀⠀⠀⢿⡿⠏⢹⣿⡳⠀⠀⠘⣷⡀⠀⢸⣇⠐⠘⡀⠀⠀⡂⠀⠄⠃⠈⠁⠀⠁⠈⠀⠐⠃⡀⠆⢀⣾⠃⢠⡿⠁⠈⣿⣿⡆⠈⠘⡿⣧
⠀⠀⠀⠈⠀⠀⠘⣿⣄⠀⠠⠀⠈⣷⠌⠀⠉⢉⠀⠁⢀⣰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠢⠾⡁⢠⣿⠁⠀⠀⠸⣿⡇⠀⠀⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠀⠀⢀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠉⠃⠀⠠⠀⠀⣻⠇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠰⠀⠀⡀⠀⠀⠐⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⢂⣤⢀⡾⣀⠀⣼⢡⡄⣴⢲⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⡏⣾⢱⣏⢼⠟⠸⠟⠧⠺⠖⠁⣠⠁⢸⡇⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⢈⡋⠈⠁⠀⠀⢀⠀⠀⣤⣄⣤⣤⡄⢠⡯⢠⣿⠀⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⠃⣼⡇⣰⡟⣿⡇⣾⢧⡷⢰⣿⢃⣿⢁⣿⡇⣾⡇⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣴⡟⢠⣿⣡⣿⡤⣿⠼⠿⠚⠗⠁⠙⠋⠉⠁⠉⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠇⠀⠉⠁
⣦⣴⣤⣶⣴⣤⣦⣦⣶⣴⣤⣶⣶⣤⣿⣦⣤⣤⣤⣤⣤⣴⣤⣤⣴⣴⣦⣶⣴⣦⣶⣴⣤⣦⣴⣤⣤⣴⣶⣤⣦⣴⣤⣦⣦⣴⣴⣤⣶⣴⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⠀⠀⠀⠀⢠⠂⠁⠀⠀⠀⠀⠀⠀⢠⢏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣾⠀⠀⠀⢠⢇⡴⠁⢀⣀⡀⠀⠀⠀⣾⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢠⡇⠀⠀⣀⡿⠋⠀⢀⣤⣤⣭⠳⣤⠾⢁⣤⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣡⡤⠴⠖⣺⠋⠉⠉⢹⠃⠀⠀⢸⣿⣿⣿⠇⢀⡶⠋⠰⣧⠔⠧⢾⣋⡔
⠀⠀⠀⠀⡴⠀⠀⠈⢉⡝⠁⠀⠀⠀⠀⡏⠀⠀⠀⠸⠴⠞⠉⠳⢬⣛⠅⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣼⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠻⣤⡤⠞⠁

⠀⠀⠀⢰⡆⠀⠀⣾⡇⠀⠀⢶⠄⠀⠀⢤⡄⠀⠀⢲⡆⠀⠀⣶⡄⠀⠀⣶⠀⠀⢰⡆⠀⠀⣴⠀⠀⠀⣶
⠀⠀⠀⢸⡇⠀⠀⠛⠃⠀⠀⢸⠀⠀⠀⠘⠃⠀⠀⣸⡃⠀⠀⠉⠀⠀⢀⣿⡄⠀⠀⠁⠀⠀⣾⠀⠀⢀⣿⡄
⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⢰⣿⣷⠄⠀⣤⠀⠀⣾⣿⣿⠀⠀⠀⠀⣾⣿⣿⠀⢈⣿⡁
⠀⠀⢸⠿⠿⡇⠀⣠⡄⠀⢿⣿⠿⡅⠀⡄⠀⠀⢸⠿⢿⠀⠒⣒⠒⠀⢻⣭⣿⠀⢸⡇⠀⣷⣶⣶⠀⣿⣿⣿
⠀⠀⢀⣀⣀⡀⠐⠾⠖⠀⣏⣡⣶⠁⢠⣀⣠⠀⢸⣤⣴⠀⠤⠭⠤⠀⢸⣿⡏⠀⢸⡇⠀⣿⣿⣿⡀⣉⣩⣩
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡄⠘⠛⠛⠁⢸⣿⣿⠆⠀⠀⠀⠀⣼⣿⣧⠀⠈⠁⠀⢿⣿⣿⠀⣿⣿⣿⠄


⠀⠀⠀⢰⣶⠀⡀⣀⡀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⡀⢀⢠⣤⠀⢰⢰⣶⡆
⠀⠀⠀⣾⣿⠀⠻⡿⠃⢀⣀⠀⢀⠀⢘⠃⠀⢿⠟⠀⠻⢿⠟⠁⠀⢴⣶⠆⢈⣳⣄⣑⠈⢻⠏⠀⢸⣸⣿⡇
⠀⠀⠀⢿⡯⠀⠀⠁⠀⠐⠿⡿⠛⠀⠀⠀⠀⢨⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠈⠙⠟⠉⠀⢀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠈⠉⠀⠀⠘⠃⠐⠛⠃⠀⠀⠚⠂⠀⠀⠐⠓⠀⠀⠐⠓⠀⠀⠚⠂⠀⠀⠚⠓

⠀⠀⠀⢸⡇⠀⠀⣠⡄⠀⠀⠰⣿⠀⠀⠀⣾⡆⠀⠀⣠⡄⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⢸⡇
⠀⠀⠀⢨⣅⠀⠀⠿⠇⠀⠀⢐⣿⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀⠀⠀⣼⡇
⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⡆⢰⡶⣶⠀⠀⣿⣇⠀⢠⡴⠦⣤⠀⠀⣸⣿⡀⠀⠀⣠⢧⡀⠀⣿⣿
⠀⠀⢸⣏⢹⡇⠀⣦⡆⠀⣿⠙⠋⠙⡇⢸⡤⣼⠀⣾⣿⣾⣦⢸⣶⣶⣿⢠⣾⢿⣿⣿⣷⡀⣸⣩⡇⠸⠟⠿
⠀⠀⠸⠽⠭⠇⠀⠈⠁⠀⣿⠀⠁⢀⡇⠘⠛⠛⠀⣿⣷⣾⣏⠀⠀⠀⠀⢸⣿⢻⣿⣧⣿⠇⣸⣿⡇⠐⠒⠒
⠀⠀⠸⠶⠶⠆⠈⠉⠉⠁⠻⠿⠿⠿⠇⠀⠀⠀⠀⠷⠶⠶⠟⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠀⠈⠈⠁⠰⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣾⢠⡾⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣷⣿⣿⣯⡾⠿⡿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣯⣶⠾⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣽⣿⣿⠟⣿⣿⣿⣿⣷⣆⠁⠈⠈⠛⢧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⢰⣿⣿⢻⣿⢿⣿⣷⣾⣿⣿⣾⣿⣷⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣧⣶⣶⡆⢸⣿⡏⠀⣿⡌⢹⠏⢀⣭⣿⣿⣿⣯⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣯⡉⠉⠋⢻⠇⠀⣿⣷⠀⠀⡾⢻⡿⣿⡿⠈⢻⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⣿⡿⡟⠳⠀⠀⢠⣿⣶⣿⣿⡆⠀⢠⣿⡇⣛⠁⠀⠠⣵⣦⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠟⡠⣔⣤⣼⡏⠉⢋⣭⡓⢀⣿⠿⠹⢿⢇⣀⠀⣠⣿⣿⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⢠⣾⣿⣿⣿⡏⢁⣴⡿⢻⠇⠘⣡⡟⠀⣴⣿⠟⢈⡽⠑⠏⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠿⠛⠛⣿⣿⣿⣿⣿⡟⣰⣿⡯⠞⢡⣤⣤⡸⢷⣾⡿⣡⣴⡜⠃⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⣰⣿⡿⢉⣿⡟⢹⣿⠏⢀⣄⡿⠛⣿⡇⣼⣿⠟⣿⣿⢇⣾⡿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⢆⣼⣿⠟⠀⣸⣿⠁⣾⣟⢀⣸⠋⢁⣼⠟⢰⣿⠏⢸⣿⠏⣾⡏⢀⣿⡟⣠⣤⣤⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⣠⣾⡿⠋⠀⠀⠹⠿⠀⠻⠿⠋⠙⠿⠛⠁⠀⢿⡏⠀⢺⣿⢀⣽⠛⠋⠹⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣾⣿⠟⢡⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⢤⣤⣄⣀⣀⣀⠀⠙⠛⠚⠛⠁⣀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⣸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠭⣼⣭⣭⣝⣛⣛⣿⣿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⣷⣄⢀⣠⣤⣄⠀⠀⠂⢀⢀
⠀⠀⠀⠀⠀⠀⣰⠾⡿⣿⣿⣿⣿⣿⡿⠿⡇⠀⠠⠁⠀⢣⠀⠀⣠⣶⣤⣤⣀
⠀⠀⠀⠀⡀⠀⠁⠀⣴⣿⠻⣿⠙⣿⣿⣶⢄⠀⠆⠀⠀⠀⠇⡐⠁⠀⢸⣛⣻⣷⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⡦⣼⣿⣯⠀⣿⠀⠁⡟⣿⡏⢲⠀⠀⠀⠀⡼⠀⠀⢰⣿⣿⣿⣿⡿⣿⣯⡉⠻⠧
⠀⠀⠀⠀⠀⢸⣧⣿⢿⡅⠀⣿⠀⠀⠀⠀⠃⠀⠇⠀⠀⠀⡇⠀⠀⠻⢃⣿⠁⢸⡇⠈⣿⣷⠀⣀⣀⣀⡀
⣠⣶⣿⣷⣶⣦⣿⡷⣶⣷⣄⣿⠀⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣮⣿⣼⣿⣿⣿⡿⡟
⠛⠋⢩⣾⣿⣿⣿⡷⣄⠉⠛⢻⡄⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⢀⠃⠀⢀⣿⠾⣿⣿⣿⣷⣶⣤
⠀⠀⢸⡿⠛⣿⡯⠀⠘⣧⠀⠘⣇⠀⠃⠀⠀⠀⠀⠂⠀⠀⠁⠀⠂⠎⠠⠀⣼⠁⣼⠃⢹⣿⡎⠙⢿⣧
⠀⠀⠀⠀⠀⢻⣇⠀⠂⠈⠧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⣸⠃⠀⠀⢻⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢈⠀⡈⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠡⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡶⣰⢣⢤⡿⣶⣼⣹⣠⠀⠄⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠻⠘⠓⠛⠉⠈⠁⡁⣈⣈⡁⣼⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⣾⢠⡖⣾⣰⣧⡆⣽⣏⣿⣸⡏⣼⣃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⡿⠰⡿⠺⠗⠟⠛⠋⠋⠈⠉⠈⠀⠀⠈⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⢰⠚⠹⠏⢀⠀⠀⠀⠀⠐⠀⢸⠁⢀⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡰⠊⠁⠀⠀⠀⠀⡀⠸⣉⠀⠀⠀⠀⠀⠉⠁⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⠀⠀⠀⢸⠄⠀⠲⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢂⠒⠀⠐⠇⠄⠀⠀⣀⣇⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠈⠀⠈⠂⠄⠀⠰⠩⠭⠀⠀⠀⠨⠥⠤⠀⢱
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡇⠀⠤⠀⠀⠀⠀⠀⠈⠀⢠⠤⠠⠒⠀⠀⠀⠀⡀⠠⢸
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠂⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡄⠀⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠂⣻⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠀⠀⠀⠀⠆⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⣉⠉⠉⣹⡄⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠄⠀⠊⠃⠂⠐⡂⠁⠀⠀⢀⡄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡄⡇
⠀⠀⠀⠀⠀⢠⡃⠀⠀⢠⠃⠀⠈⠀⢣⠀⡟⠒⠀⠉⠁⠀⠀⢸⠐⣄⡀⠀⠀⠀⢀⡠⠀⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠔⠁⠀⠀⠘⠄⠀⠤⠃⠀⠀⠀⠀⠀⠀⠈⠦⣀⡀⠉⠉⠉⢁⣀⠝
⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠒⡄⠀⠀⢸⣿⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⢸⣿⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠈⣿⣿⣠⡇⠀⠀⠀⠀⠀⣠⠆⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⢀⡶⣿⣶⣄⢻⣿⣿⠁⠀⣼⣷⠻⢿⡁⠀⣿⣿⡇⣀⣀⠀⠀⠀⢀⣴⣮⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣾⠁⣿⣿⣿⠘⣿⣿⠀⠀⣿⣿⠀⢸⡇⠀⣿⣿⣾⢿⣿⡇⠀⠀⣾⣿⢇⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢸⡏⠀⢻⣿⣿⠀⣿⣿⣇⢀⡿⣿⣄⣸⣿⠀⣿⣿⡏⣼⣿⡇⠀⢰⣿⣿⣾⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣿⠃⠀⢸⣿⣿⢠⡿⠙⠛⠾⠁⠙⠻⠛⠃⠀⠘⠛⠁⢿⣿⡇⢠⡏⢿⣿⠇⠸⣿⡇⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠀⠀⠈⣿⣿⣼⠇⡄⠀⢤⠀⢸⢧⠘⡆⠀⠀⠀⡆⠸⣿⣧⣾⠁⢰⡄⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⡇⠀⢸⡀⣾⠘⡇⢣⠀⣶⣰⡿⠧⣝⠛⠃⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠔⠚⡇⢿⠊⠻⠘⡴⠀⠻⠛⠂⠘⠇⠀⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⡷⣠⣆⠠⠔⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣒⠀⠀⠘⠻⣿⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡭⠶⣷⢀⡘⠓⣀⠘⠁⠈⢠⠰⠘⠀⢠⡀
⠀⠀⠀⠀⠀⢙⠀⣿⠀⠀⠀⣸⣿⡆⠡⠅⣎⠀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠚⢀⡈⠡⡄⠉⠶⡀⠴⠦⠰⢆⢁⡀⠖⣈⠠⠌⣁⠈
⠀⠀⠀⠀⠒⡰⣴⣿⣧⣤⣴⣿⣿⡞⠈⠁⠀⠀⠀⠉⠒⠀⠀⠠⠄⢤⡤⠶⢀⡐⢃⡀⠛⠄⡤⠘⠀⠀⠀⠙⠳⠴⠮⠰⠦⠁
⠀⠈⠁⠀⡰⠉⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠘⠓⢠⠐⢢⠀⠅⢀⠐⡦⡀
⠀⠀⠐⠈⠀⠀⠀⠀⠹⣿⠿⢿⣻⠅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠠⣌⣀⢚⡀⠈⣀⠘⠠⡆
⠀⠀⠀⠀⠀⠀⠠⠅⠀⡜⠀⡀⣶⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣾⣶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠅⣁⠀⠠⠀⠀⠘⠀⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⢀⠒⠠⠟⠀⠁⠒⠩⢀⡀⠀⠒⠉⢈⡁⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣶⠉⡀⢤⣄⡓⢠⡅⠨⠒⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣄⠀⣾⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⡄⢿⣄⣿⣿⣠⣿⢠⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⣿⣆⣽⣸⣿⣿⣿⣿⣇⣿⣰⣿⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣜⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣃⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠵⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠮⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⠿⣿⣿⣿⣿⣿⡟⠁⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠇⡄⢸⣿⣿⣿⡿⠀⣱⣿⣿⠟⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⢻⣿⠀⢇⣿⡟⠉⢻⠇⠀⡁⢹⡟⢰⡟⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠁⢸⡇⢠⣾⡟⣰⠄⣠⠀⣼⡇⠊⡄⠈⢁⣤⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⣾⠇⠘⠟⣤⣈⣴⣿⣴⣿⣷⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣴⣾⣷⣾⣿⣿⣿⣿⡿⣛⣭⣭⣤⣤⣤⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠋

⡾⠛⢻⠷⠷⠿⠶⠷⣞⠾⠶⠿⡾⠷⠿⢿⣷⣾⣿⣿⣿⣶⣾⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣷⣾⣿⣿⣷⣿⠾⣿⣷⣾⣷⠾⠿⠾⠷⢾

⠀⠴⢀⣀⣤⣤⣤⣤⣶⡶⠶⠀⠀⠀⣤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⢈⣶⠀⢠⠀⡤⠄⠀⠀⠀⠀⠀⢀⣀⡀⢠⡶
⠀⢰⠿⠿⠿⠿⠇⠈⠉⠉⡀⠀⠀⢺⡑⢖⣿⠂⠀⠀⠀⣠⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡿⣿⣟⠛⠃
⠀⠀⠀⠖⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡉⠉⠁⠀⠀⠀⠈⠁⠨⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⠈⣉⣀⣀⣀⣀⣀⣂⣀⣀⠀⠀⠀⠾⠋⠀⡀⠙⠃
⠀⠀⠀⠻⠽⠀⠀⠻⠽⠃⠚⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⢰⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡦⠄⠀⢤⣤⣤⣤⣤⢠⣤⣤⣤
⠀⠻⣿⠇⠀⠀⠀⠀⣀⠀⢴⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⢊⠃⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣧⠀⣤
⠀⠈⠀⡁⠀⠀⠀⠀⠉⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠐⠀⢵⠀⡴⣿⢾⢁⡞⢦⡼⢀⠀⡠⢤⡀⠀⠀⠀⠀⠙⠦⣿⠾⠁
⠀⠀⠒⠁⢀⣤⣄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⢁⠞⠀⡟⠀⠘⠄⠀⠛⠀⠺⡁⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣿
⠀⢀⠰⢶⡁⢿⢧⠝⣟⠂⣀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠠⢋⣀⡵⢂⡒⢀⡆⠹⠄⠀⠲⠌⠁⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣦⡀⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛
⠀⠀⢨⢗⡰⣧⠌⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡧⣿⣿⡿⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⣤⣤⡀
⠀⠀⢟⡠⢤⡁⣈⠥⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣷⡾⣷⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠋⠁⠀⠀⢸⡆⢐⣇
⠀⠀⠉⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣯⣽⣻⣭⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠙⠂
⠀⠀⠀⣀⣤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⣼⣿⡶⠄
⠀⠀⡀⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⠠⠀⣍⠁
⠀⠈⢩⡟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⣿⡿⣻⣽⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣍⣿⢿⣬⢢⡀
⠀⠐⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⡞⣸⢿⣿⢻⢥⡟⢷⡑⠄
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡷⠘⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠃⠸⠃⠀⠀⡖⠀⠃⠈
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂
⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠆⠀⢀
⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠐⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⠀⠉
⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠛⠻⠟⠋⠑⠁⠀⠀⠀⠀⠓⠁⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⢀⡄⠛⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠠⠄⠀⠀⠀⠀⠠⣤⠀⠀⠀⠤⠶⣶⠶⣶⡶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠶⠖⠂⠀⠀⢹⣷⣦⡄
⠀⠀⠀⠀⠀⠀⣀⣤⠂⢀⡾⠖⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣤⡄⢀⠀⠀⠰⠀⠘⠛⢁⣄⡀⠀⠀⠈⠒⠀⠀⢄⣾⡿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠨⠀⠀⡄⠀⣀⠀⡀⠈⠀⠀⠀⠀⠐⠃⢀⣾⣿⣿⣧⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠀⠀⠀⠀⢰⡞⢱⣦⠀⠈⠉
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠈⠁⠘⠛