Weasel Emojis & Symbols

⣴⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⠶⣄⠀⠀⢠⣴⣦⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣷⣷
⠛⠂⠘⢿⣿⣷⣶⣤⣤⣴⣦⣤⣶⡾⠿⠟⠋⢁⣠⣤⣤⡀⢸⡇⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠸⢿⣷⣄⡀⠀⠀⠀⠠⣿⣿⣿⣷⡇⠘
⠀⠀⠀⠈⠃⠉⠉⠉⠉⠉⠙⠛⠗⠶⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⣧⣿⣦⣶⣦⠀⠀⠀⢹⡿⣿⣶⣶⡄⠀⢹⣿⣿⣟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣦⠀⠀⢻⠿⠿⠀⠀⠻⠆⠀⠀⠀⠀⠈⣿⢻⣿⣿⡇⠀⠀⠀⠀⠀⠿⠿⣿⣀⠀⠙⠛⢻⣿
⠀⠀⣴⣶⣶⣤⣀⣰⣿⣿⣦⣄⣴⠄⡟⠀⠀⠸⣷⣤⣤⣾⣷⠀⣀⣴⣄⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⢀⣠⣤⡀⠹⢿⣷⣆⠀⠉⠁
⠀⣀⡙⠿⠏⠙⠛⢿⣿⢿⠟⣿⣿⡂⠀⠀⠀⠀⠈⠛⠛⠛⠁⢰⠃⡌⠉⠀⠀⢰⣿⡟⠁⢀⣀⣤⣴⣿⡟⠉⠁⠀⠀⢹⠟⠀⠀⠀⡼
⠘⢉⡇⠀⠀⠀⠀⣄⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⣶⣦⡀⠈⠟⠀⠀⣾⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⣼⣇⣤⡀⠀⡼⢻⡛⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣦⠀⠀⠉⠁⠀⠛⠛⠻⠧⠀⠀⠀⠀⢻⣿⡧⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢹⣏
⢐⡽⣿⣿⣧⡀⠈⠈⢹⣿⣶⣶⣶⣾⣛⠛⠛⠋⠽⠃⠀⠀⠀⠀⠈⠐⣶⣦⡤⠤⠤⠀⠀⢈⣧⠀⠀⢰⢃⡍⠁⠀⢠⣶⣄⠀⢿⣿⠂
⠀⢠⣴⣾⡿⠁⠀⠐⠛⠁⠸⠀⠩⠟⠉⠻⠀⠀⣠⣄⠀⠀⠀⣤⣶⣿⣿⠟⠀⠀⠀⢠⣤⣾⡟⠀⠀⠘⢸⣧⣄⠀⠀⠀⢌⠳⢾⡏
⠀⢻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠇⠀⢸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠞⢻⣿⣷⠀⠀⠘⠃⠼⠁
⠀⢀⠉⠀⢀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣿⡀⠀⠈⠛⠀⠰⠾⣷⡄⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠸⠿⢿⡄
⠲⠛⣛⠿⣿⠻⠿⢿⣿⣿⣿⣶⣄⣀⣠⠀⠀⠀⣻⣿⣷⣦⣤⠀⠀⠀⠀⣿⣷⣶⡿⣿⣷⡆⠀⣨⣿⡟⠀⠀⢀⣼⣿⡄⠀⠀⢠⣶⣄
⠀⠀⠃⠐⠋⠀⠀⠀⠛⠁⠛⠈⠛⠛⠉⠀⠀⠈⠉⠉⠛⠛⠻⠧⠀⠀⠀⡼⠛⠀⠈⣿⡿⠟⠛⠛⠉⠀⠀⣰⣿⣿⠟⠀⠀⠀⣾⠇⠁
⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣤⣴⡦⠀⢀⣉⣭⣿⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⢀⣼⢿⡏
⠐⠛⢿⣷⣤⣤⣶⣾⢿⡿⢿⡿⠿⠿⠿⠛⠉⢀⣴⣿⣿⠿⠛⠁⢀⣀⡀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡆⠃
⠀⡶⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠲⢿⣿⣛⠛⢳⣿⡿⠟⢻⣷⠞⠛⠿⠆⠀⢠⣾⠟⣻⣷⣦⣿⣿⣇

⠀⢀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣰⠏⣡⡶⠀⠉⠉⠉⠉⠉⠀⠰⣌⠙⣦
⣿⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⡀
⣿⠀⠀⢠⣶⠆⠀⠀⠀⠀⢶⡆⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠋⠉⠉⠛⠛⠷⠶⣦⣤⣀
⢻⡀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⣰⣿⣿⣇⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠘⠀⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄
⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆
⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠘⢿⡄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣦⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⣰⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⣰⠏⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⣧⠀⠀⠀⢠⣿⣿⣧⢠⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣆⢀⣾⣿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠉⠉⠉⠉⠛⠛⠛⠛⠿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⣰⡏⠀⠀⠀⠀⣿⡿⠋⠁⠀⠀⠀⠀⢙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢠⡾⠛⠋⠉⠀⣀⣴⣿⡤⠆⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠐⢿⣴⣬⣽⣷⠶⠶⠶⠀⠀⠀⣀⣴⣿⡿⠛⠁⣀⣉⣙⣻⣿⡿⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠈⠻⠶⠶⠶⠟⠻⣿⠁⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣤⣴⣶⣿⡿⠛⣽⠞⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠳⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠈⠀⠒

⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾⣿⡶⡤⠆⠐⠒⠂⠠⠠⠶⣶⣦⡀
⠀⠀⠀⠀⠀⣼⢡⡆⢸⢃⢤⢀⡤⣤⠀⣤⢀⣤⣀⡟⠀⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠷⠞⠶⠋⠼⠮⠾⠔⠧⠾⠿⠼⠮⠼⠇⠀⠀⠀⠀⠞⠁⠀⢀⣤⣶⠀⠀⢀⣧⣴⢀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⢿⣿⣿⠈⣀⣀⡈⠸⣿⣿⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠮⣿⡷⠀⢹⠿⣥⡾⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠉⠀⠈⠙⠀⠀⠉⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⡀⠀⠀⠀⠀⣠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢰⠀⠀⢀⢀⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣤⣿⣴⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⠛⠁⠀⠀⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⢋⣠⣶⣿⣿⠹⠿⣿⡀⠀⠀⠀⠟⠁⠀⡆
⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣠⣿⣿⣿⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣄⢀⠀⣉⣙⣦⣼⣄⣰⣠⣽⣤⣤⣤⣠⣤
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⠱⠋⠀⢀⡀⠀⠀⠀⠉⣣⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⡄⢠⡿⢷⣶⠔⠢⠓⢹⣧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠶⠑⣾⣦⠞⣻⣿⡀⠀⠀⠙⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠈⠀⠐⠒⣀⣀⠀⠹⡤⠖⢦⠍⠙⠘⠩⡿⠁⠀⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⢣⡀⢃⣐⠁⠀⣀⣸⣀⠄⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣳⣿⡏⠀⠀⠀⠀⠀⠀⢶⡌⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠉⠀⠉⠁⠀⠀⠸⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠋⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣦⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣠⠤⠤⠄⠀⠠⠤⠤⢶⣿⣿⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢶⣄⣠⡀⠀⠀⢀⣀⣼⣿⡀⠀⠄⠴⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠠⠽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠾⠏⠛⣻⢧⣄⠀⠀⠀⠐⠂⠀⠀⢠⣠⡄⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠐⠂⢠⣶⡖⠖⠈⠀⠀⠙⢾⣧⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠈⢻⣇⠺⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⢻⠀⡀⣉⢹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠀⠉⠲⣤⣄⠀⠀⠀⠀⠘⠉⠙⠛⠛⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠚⠷⡿⠿⠏

⣶⣶⡶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣤⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠹⣮⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠈⠁⠉⠻⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣦⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠟⢻⣿⣿⣿⡿⠛⠉⠀⢀⣀⣀⣠⣤⣤⣄⣀⡀⠈⠻⣿⣿⣿⣿⣿⠛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣾⣿⣿⡏⠤⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠓⠀⠸⣿⣿⣿⡟⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠴⠾⠿⠟⣿⡗⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠋

⠀⠀⠀⠰⠊⠟⠦
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣷⣄⠀⠀⠀⡀
⠀⠀⠀⠀⢉⣾⣰⣾⣿⣿⣿⣿⣷⣄⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣠⣤⣐⢦⡀⠂
⠀⠀⢀⢠⣤⡝⠜⠁⠘⠋⢸⣿⣿⣿⣿⣿⣶⣦⠀⢀⡴⢄⣀⣄⣤⣰⣾⣴⣶⡤⣀⠀⣉⡁⣶⣟⡉⣉⣉⣉⣘⣀⡆
⠀⠀⠋⣿⣿⣯⣀⡀⢼⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠞⠃⠀⠐⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠛⢛⣿⣿⣿⡇
⠀⠀⢾⣿⣿⣁⡈⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠉⠩⣄⣻⣿⣮⡻⡅
⠀⠀⣺⣏⣿⠉⠀⠀⠀⢤⡈⠻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡆
⠀⠀⢻⡿⣃⠀⠀⢀⠀⠘⠇⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⡈⣿⣿⣿⣿⣿⣿⣛⣩⣽⡇
⠀⠠⠸⢄⣹⠀⢘⣿⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⣤⣿⣗⣽⣿⣿⣿⣧⣧⣾⣿⣿⠃
⠀⠐⠄⠉⠙⠛⠛⠉⣼⣿⣿⣦⣀⠀⠀⠀⠀⢀⣀⣀⣤⡾⠿⠿⠶⣄⠀⠀⠀⠀⢹⣿⡋⠉⠛⠿⠿⣿⣿⣿⣿⡻
⠀⢀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣙⣿⣣⡀⠀⢠⣿⠟⠋⠁⠀⠀⠒⠤⠤⠤⣴⣾⣿⣿⣿⣿⣿⠶⣶⣶⣿⡿⣿⡿⢟⠁
⠀⠀⠀⠀⢀⣤⣼⠟⠛⠛⢻⡟⠉⢁⠤⠞⠋⠀⣀⣀⠀⠀⠀⠀⠀⣈⣴⣿⣿⡿⠿⠻⠏⠁⠀⢠⠹⡿⣟⡏⢙⠛⠂
⠀⠀⠀⠔⢺⣿⡳⠗⡄⠀⡡⢦⣭⣴⣴⠂⠑⠀⠏⠄⠀⠀⠃⠀⠀⠋⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋
⠀⢀⣶⡖⣲⡦⣿⣦⣅⢀⡛⣷⣵⡿⠏⢀⢘⠁⢄⣀⢀⠀⠀⣠⡄⠀⢤⣤⠓⠀⢤⡀⠀⠂
⠀⠈⣧⡾⣿⣿⣷⣿⣝⠈⢻⣿⡟⡠⢠⣾⣯⣓⣶⠈⠀⠀⢀⡔⠘⠶⠀⠀⠐⠀⡀⠀⠀⠀⠀⠴⢦⠴⣶⣶⣆⠐
⠀⠀⠀⠠⣾⢿⣿⣿⣿⣿⠷⠄⠀⠀⠆⠷⠈⠺⠋⠁⠒⠓⠽⠿⠿⠳⠆⠄⠀⠰⠥⠤⠵⠤⠄⠠⠜⠂⠈⠁⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡏⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⠏
⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⡞⠿⣿⣿⣿⣿⡿⠿⠿⢻⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⣦⣤⣀⠍⠲⠤⣄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣷⡦⢨⣿⣿⡿⠷⠒⠒⠛⠋⠛⠑⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⢿⣿⣷⣦⣍⢓⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡙⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣧⣽⣿⣿⣶⣶⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⡄⠈⢍⣭⣿⣻⠟⠲⣖⠒⠒⢒⣿⣀⣀⣰⣈⣠⣔⣆⣄⣠⣤⣼⣿⣿⣿⣟⠯⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣧⣴⣭⣤⣈⣼⣿⣤⣤⣤⡬⠧⠌⠉⠉⠉⠙⠛⠻⠿⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⡿⠿⠿⠿⠿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⣈⠢⠄⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠈⠉⢀⡀⠉⠉⠉⠈⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠞⠀⠀⠀⠀⠈⠀⢠⠆⠀⠀⠀⠀⠻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣤⠀⠀⡀⠀⠀⠀⡿⣶⡕⡄⠀⠀⠀⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠚⠀⠀⠀⠀⠹⠿⠵⠁⠀⠀⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠒⠀⠀⠢⢄⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣀⣈⠂⡀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠘⠀⠀⠀⠈⠁⠐⠂⠤⠄⣀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⡄⠀⠀⢀⠴⠋
⠀⠀⠀⣠⠎⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢰⠤⠔⠂⠁⠒
⠀⢀⠔⠁⠀⡠⢧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈
⢠⠃⠀⠀⢰⠀⠀⠉⠢⠄⢠⡀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠰⠀⢀⠀⢀⢂⠀⠀⠀⠠⠀⠁⢀⠀⠀⠀⠀⠐⢦⡀
⡏⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠉⠉⠒⠑⣊⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠈⠀⠀⠀⠀⠠⠀⠠⠆⠜⠁
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠢⢄⠀⠘⠄⣀⣄⣈⠆
⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⣀⣀⣈⣉⣓⣒⣒⣤⣤⣤⣤⣄⣒⣒⣒⣒⣚⣛⣋⣉⣉⣉⣉⣉⣉⣉⣋⣒⣒⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⢋⣩⡿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⡀⠀⠈⠉⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠙⣇⠑⡄⠀⠀⢀⣠⡤⠄⠀⠀⢸⠁⠀⠈⠳⣄⠀⠀⠀⠲⢶⣶⠦⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢿⠀⠀⢀⣈⡭⠴⠶⣄⠀⢀⡾⠀⠀⣠⠔⠋⠀⠀⠀⠀⡀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⣠⠖⠋⠁⠀⠀⢠⣿⠴⠋⠁⠀⣸⠷⠀⣀⡀⠀⠠⣤⣝⣯⡝⠛⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣄⣰⠞⠁⠀⠀⠀⠀⢠⡟⠁⠀⠀⣠⢾⡥⠶⠒⠛⠉⠉⠓⠾⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠿⠾⣿⠃⣬⠇⠀⠀⢀⡴⠋⠀⠀⢀⣾⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠠⠔⢒⡶⠀⢸⣤⠤⠤⠴⠶⣯⠀⠀⠀⢀⣾⠾⣛⣉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢀⡀⠀⢀⠀⡀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠚⠛⠋⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⣤⡤⠴⢶⡞⠋⠁⠀⠀⠀⠀⠀⣀⣬⡷⠦⣄⠀⠀⠀⠀⣰⠋⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⣲⢤⡴⠋⠀⠀⠀⢤⠖⠲⡟⠋⢯⠀⠳⣄⡼⠧⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡓⠻⣾⠁⠀⠀⠀⠀⠸⡆⠀⢹⡄⢈⣧⠴⠋⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡈⣳⠞⠛⣦⠀⠀⢻⣄⡤⠗⠋⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⡿⠃⠀⠀⢸⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⠀⢡⠀⠀⠀⢸⠛⢦⡀⠀⠀⠀⠀⠀⠀⣰⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠻⠏⠀⠀⣀⣙⡟⠀⠀⠀⢸⡀⠀⠙⠶⣄⣀⣀⢀⡜⢻⠀⢸⡆
⠀⠀⠀⠀⠀⠀⣴⠛⠉⠁⠈⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⠻⡄⠀⣠⠾⡏⢉⡿⢦⣸⡄⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⡀⠀⢸⡀⢻⡔⢋⡴⢧⣼⣀⣀⣯⣤⣶⣾⠓
⠀⠀⠀⠀⠀⠀⣼⠁⠈⠳⣤⡀⠀⠀⠀⠀⠀⢨⣿⣿⡟⠛⠁⠀⠀⡾⠀⣿⣩⡤⢬⣙⣣⣻⠿⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⣸⠁⣼⠀⠀⠀⠀⢀⣿⠖⠁⠧⠤⠴⠾⢿⣜⣇⢳
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡇⠀⠛⠒⠒⠒⠒⠚⠛⠀⣼⠛⠓⢶⣤⡴⣋⣁⣸⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⢉⡟⠉⠉⠛⠶⣬⡽⣟⣉⣉⡿⠁⣈⣡⡤⠶⠖⠲⣦⠢⡀⠈⢦
⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⣀⣀⣠⣤⣤⣼⣧⣀⣉⡿⠛⠉⠁⠀⠀⠀⠀⠀⢹⠀⢱⠀⠜
⠀⠀⠀⢀⣠⠴⠻⡘⢆⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣡⣤⡴⣁⠞⠁⠀⠀⠀⠀⢸⠀⠋
⠀⠀⠀⠸⡇⠀⠀⠑⠌⠁⠀⠀⠒⠚⠉⠁⢹⠀⠀⠀⠀⠙⣯⠉⣉⣠⣤⠴⠾⠁⠀⠈⢹⠇⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢨⠟⣹⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⣴⠋⢠⡇⠀⠀⠀⠀⠀⠀⠀⠷⠶⠒⠛⣏⠈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣯⠿⢷⣖⠛⠉⠀⠀⠀⠀⠀⠀⠘⣇⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠋⠉⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⢦⣤⣠⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠛⠛⠛⠶⣶⣿⣿⣿⡿⠟⠛⠛⠛⢷⣦⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠻⢿⣿⣿⣿⣿⠋⠀⢠⠶⣤⠀⢸⣿⣿⣿⣷⣶⣄⣉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣤⣀⡀⠀⠀⠀⠸⢿⣿⣿⣿⢿⣮⣽⣛⡶⣦⣌⣉⠛⠿⢿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢶⣤⣀⡀⠈⠉⠁⠀⠈⠉⠛⠿⢶⣭⣝⣛⠶⢦⣌⣉⡙⠛⠛⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣤⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣬⣽⡿⠛⠷⢶⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠙⠛⢦⣤⡤⠚⠋⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣦⣄⡈⠻⠿⣿⣿⣿⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠉⠁⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠉⠉⠛⠳⠶⣤⣤⣠⡞⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⣿⡁⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠋⣿⣦⣤⣤⣤⣤⡀⠀⠀⠀⠉⠀⠀⠀⣿⣿⠷⣦⣤⣤⣤⡶⠛⠁
⠀⠀⠀⠀⣰⡟⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣠⣿⠿⠗⠲⠶⠤⣤⣄⡀⠀⣿
⠀⠀⠀⣰⠟⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢀⠀⠈⠙⢶⣿
⠀⠀⣰⡏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠀⣻
⠀⢠⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣶⠏
⠀⠸⣧⠘⢷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⡾⠋⠀⠉⠛⠉⠙⣇⠀⠀⢀⣤⣠⠾⠋⡀
⠀⢠⡿⢧⣄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⣦
⠀⢸⡇⠀⠙⠳⢶⣤⣀⡴⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⣾⠿⣤⡀⠀⠀⠀⢹⡇⠀⢀⠿⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠉⢻⣦⣤⣤⣤⣤⣤⣠⣤⣠⣿⡀⣀⣀⣀⣀⣀⣀⡀
⢸⡏⠀⠈⠛⠳⠶⣤⣼⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢸⣧⣤⣤⣤⣤⡤⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠙⣿
⣾⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⢶⣤⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠻⣦⡀
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠈⢻
⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⣿⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⣿⣋⠀⠀⠀⠓⠠⠄⣀⡀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠞⠛⠉⠁⠀⠀⠀⢈⣿⣿⣷⣦⣤⣀⡀⠀⠀⠙⠒⠠⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡶⠶⢿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠸⠷⢶⣶⠶⠟⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠐⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣤⣀⡀⠀⠈⠐⠢⠤⣀⡀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠈⠁⣲⡾⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠶⠂⠀⠀⠲⠶⠆⣀⣀⣈⣳⠆⠠⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⠛⠋⠁⠀⠀⠀⠀⠀⠉⠉⠛⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⢀⡠⠄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⣀⠐⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣤⠞⠚⡋⠀⠈⠄⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠿⣆⣨⣄⣀⣧⣀⠠⣶⠦⠾⠟⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⢀⠖⠈⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⡘⠃⢀⡤⠋⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠜⠋⢱⡄
⣄⠈⠳⠆⠉⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠳⠖⠲⠶⠂⠉⠉⠁⠀⠀⠀⠀⣤
⠉⠓⠀⠀⠀⠀⠀⢀⡄⠚⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⠈⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⣷
⠀⠀⠀⠀⠀⣾⠀⢀⡴⠋⠀⠀⢣⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠖⠉⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠛⠓⠈⠀⠀⠀⠀⠈⢳⡄⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒⠂⠈⠀⡤⠊⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠰⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠙⢦⡀⠀⠠⠤⠀⠉⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⣴
⠀⠀⠀⠰⣦⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠉
⠀⠀⢰⡀⢹⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶
⠀⠀⢸⡇⠈⠇⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉
⠀⠀⠘⢃⠀⣧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌
⠀⠀⠀⠘⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠠⠊⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠋⠙⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣇⣠⣀⣀⣠⣤⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⠈⠁⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠶⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⢀⣴⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠓⠗⣦⢶⡿⠟⠀⠀⠀⠀⡠
⠀⠀⠀⠸⡇⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡎⠀⠀⡶⠋⠙
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⠀⠀⠀⠀⡀⠀⠰⡀⠀⠀⠳⡀⠰⣅
⠀⠀⠀⠀⠀⠀⠀⣯⣦⣀⠀⠀⠀⣀⡤⠐⣲⠖⠻⠀⣰⡆⢠⣿⣷⢄⣠⡀⠀⠀⠀⠀⠙⠍⣓⢤
⠀⠀⠀⠀⠀⠀⠀⠉⠿⠻⡿⣾⠞⠁⡠⠐⡁⠀⡠⣴⣿⠀⠈⠙⢿⣦⡙⢻⣿⣶⣦⣤⣀⣤⠟⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠈⣴⠋⠀⣿⣿⠀⠀⠀⠀⠙⢿⣦⠈⠓⠦⣤⣅⣠⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢿⣤⣤⣟⡋⠁⠢⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠘⡀⠀⠀⠀⠀⣽⡟⣠⠄⢠⠀⠀⠠⠀⠈⣿⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣄⠤⣤⣤⣾⡫⠘⠁⠀⡀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠀⠰⠋⠀⠀⠀⠀⢀⠀⠀⠈⠛⠻⠋⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠔⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡭⠉⠉⣩⣍⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠄⠐⠀⠀⠀⠄⠐⠁
⠀⠀⠀⠀⠄⡝⠀⠀⢠⠀⡀⠂
⠀⠀⠄⠀⠀⠐⠢⠀⠀⠂
⣄⠐⠀⠀⠀⢎⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⣶⣶⣶⣶⣶⣶⣤⣤⣄⡀
⡇⠀⠠⢀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣾⣷⠲⢶⡶⣶⣶⣿⣿⣿⢿⡟⡀⠙⠿⠋⠉⣉⣩⣭⣤⣬⣭⣿⣶⣤⣄⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠉⠁⠀⠀⡰⠿⠁⠐⠊⠤⣄⣠⣼⠀⠠⠔⠀⠀⠂⠐⡛⠉⠋⢭⠿⠟⠿⠟⠿⢿⣿⣿⣿⣿⣿⡖
⡇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢋⠀⠀⠀⠈⠀⠀⠀⠐⠢⠄⡠⠤⣄⣀⠀⠀⠀⠠⠤⠀⠀⠹⣦⡤⠀⠀⡀⠀⠈⣶⠀⠀⣽⡿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⢀⡜⣛⠉⠛⠁⠀⠀⠀⠀⠒⠀⠉⠒⠀⠀⠤⠤⠤⠤⢀⣀⣀⣀⠀⠀⠀⢄⡸⠃⠂⢤⡤⡄⢢⣶⡵⠖
⠀⠀⠀⠀⠀⡠⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠛⢿⣶⡖⠞⢿⣷⣦⣷⡾⠛⠙⣿
⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⠈⠁⠀⠀⠀⠀⠓
⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⠤⢤⣴⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⣀⣀⣀⡤⠤⢺⢉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡨⠖⠁⠈⠉⠁⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠒⠒⠒⠚⢛⣻⡡⠯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⠉⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠒⠒⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⣶⣶⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠟⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠉⠻⠿⠉⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣷⠀⠀⠀⠈⠉⠉⢻⡇
⠀⠀⠀⢀⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⣰⣦⣤⣿⣦⡄⠀⠿⠆⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠂⠀⠀⣀⣤⡀
⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠘⠿⠛⠉⠀⠀⠀⠀⣠⠾⠿⠟⠃⠸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣾⡿⣻⠟⠉⠑⢢⡄
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⢿⣿⣷⠀⠀⠠⣿⣇⢫⠀⠀⠀⢀⡟
⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣀⣀⠀⠙⠿⣷⣷⣶⣖⣋⡀
⠀⠀⠸⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠠⠤⠀⠀⠀⠀⣿⡛⠛⠻⢷⣦⣄⠀⠀⠉⠉
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣶⣶⣶⡇⠀⠀⠀⠀⠀⠀⢀⡠⠒⢹⡈⠟⠁⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠈⣿⣷⠂
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠹⣇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠳⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠀⠀⠀⠀⠀⢀⠀⠀⠀⢐⣼⣿⣿⡴⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢷⣶⡾⣿⣿⣿⣷⣤⣤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠲⠤⠔⢋⣰⣠⠶⠎⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠈⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣄⠤⠤⠒⠒⠲⠚⠀⠠⠀⣴⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠘⠃⠀⠀⡼⠤⠤⣌⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠠⠀⠉⢀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡰⠊⠀⠀⠰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢐⣀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠎⠑⢄⡀⠀⠀⢇⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⡠⠊⠈⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⣄⠀⠜⠉⠑⢄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠈⠙⢆⣀⣀⠜⠑⢶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢼⡄⠀⠀⠀⠸⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⡸⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⠀⠀⠀⠀⠀⢂⠀⠀⠀⠿⢤⣀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃⠀⣠⢤⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠃⢠⠃⠀⠀⠀⠀⠀⠈⡆⠀⠀⢣⠀⠈⠙⠲⢤⣀⠀⢀⡜⠃⠐⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠌⠀⢠⠎
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠎⠀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠙⠄⣀⠸⠆⢤⠀⠀⠀⠈⠉⠚⢇⣀⢀⡔⠀⠀⠁⠒⠠⢄⡀⠀⡀⠀⠀⠀⢠⠎⢀⢠⡆⢀⠠⠇⢄
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠠⠁⠠⠾⢤⣤⣤⣤⣤⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠈⠀⠀⠈⡆⠠⡴⠁⡐⠁⠀⠀⠈⣇⡠⠞
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠱⠦⠤⠤⠤⠄⠤⠄⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⠠⠾⡄⣰⠀⠀⢣⡀⠀⠐⠀⠉⠄⣠
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠒⠊⠉⣠⠤⠄⡀⠐⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠒⠂⣿⠈⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⢀⡀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡇
⡜⠉⠀⠉⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠑⠦⠚⠁⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠶⣽⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠄⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠋⠀⠀⠀⡅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠒⠚⠠⠤⠤⠄⠀⠀⠀⢀⡀⠀⠀⠀⠤⠤⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠐⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢤⠀⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠁⢠⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠸⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⢠⡀⣠⡀⢸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⠐⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠿⠀⠀⠿⠽⠆⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⡿⠛⡁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣟⣿⣿⡟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠴⠃
⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣠⡏
⠀⠀⠀⠙⢿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⠛⠛⠛⠛⣿⢿⣿⣿⣿⣿⣿⣏⣠⣿⣯⠀⡀
⠀⠀⠀⠀⠀⠈⠉⣭⠛⢋⣿⣿⣿⣿⣿⠿⠟⠉⠀⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠻⢿⡏⠙⠁⠀⠙⣿⣿⣯⠴
⠀⠀⠠⠤⠤⣤⣤⣬⡂⠆⢀⠉⠹⣿⡵⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢶⣭⣭⣉⣙⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠛⠁⠈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢘⠶⠲⡄⠀⢀⡡⠤⣄⡀⠀⠀⠀⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⠀⣰⠋⠀⠀⢷⠀⡾⠀⠀⠀⠙⣦⢀⡖⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠞⢀⡀⠀⠈⠑⢦⠀⠘⡇⣇⠀⠀⠀⠀⠈⣿⠀⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠷⠋⢣⡤⢦⣤⣘⢧⠀⠹⣿⡀⣀⠀⠀⠀⠸⡷⠿⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⢧⠀⠙⢷⡉⠀⠀⠀⢀⡇⠀⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⣄⣸⣽⠀⠀⠈⠳⣤⣀⣀⡜⠉⠉⠛⠛⠦⠤⠤⠤⠴⠶⠒⠒⠒⠋⠉⠉⠉⠉⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠷⠦⠙⠋⠀⠀⠀⠀⠐⠛⠉⠀⠀⠐⢶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⢛⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣄⣀⡀⠀⠀⠀⠀⢀⡀⢄⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣺⠖⠋⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⢲⡶⠴⠖⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡡⠚⠁⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠞⢡⠞⠀⠀⠀⠀⠀⢀⡴⠋⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢉⢇⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⣰⠛⠶⠤⢤⣀⣀⡴⢯⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢴⣃⠴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⡏⡔⠉⣉⣽⠂⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡰⢬⣥⠖⡋⡧
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠹⠃⡐⢦⡼⣂⡴⡋⢸⣀⣀⣠⣤⡤⠴⡖⠊⢉⣠⠟⠀⣈⡭⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠙⢦⡀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠚⠉⠒⠋⠁⠀⡼⣺⡅⠀⢠⠜⠳⣄⣏⡏⠉⠀⣠⠞⠁
⡔⠀⢀⡀⢀⡞⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡴⠃⠀⠀⠈⢻⡇⡠⠞⠁
⠇⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠉⠳⣤⣀⣀⣀⣤⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⡼⠳⠤⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀⣀⣠⠼⠁
⠀⠀⠀⠀⠀⠀⠙⠲⡦⠤⠤⠤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⢀⡧⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠇⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⢀⣀⡤⠖⠚⠉⠀⣳⠦⣤⠎⠠
⠀⠀⠀⠀⠀⠀⠀⠙⢗⣒⡶⣯⡉⠀⠀⠀⠀⠀⠀⡟⠹⡇⠠⠃⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠀⠀⠀⠀⠀⠀⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⡆⠀⠀⡀⠀⠀⡏⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠃⢀⣞⠹⡄⠘⠃⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⠀⠀⠀⠸⡖⠈⠑⢄⠀⣼⢄⡀⡇⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠄⢀⠀⠀⢿⠁⣀⡈⢳⡇⣾⡇⡇⠀⠀⠀⠀⠁⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⡘⢿⢦⢳⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⣽⠇⣈⣀⣉⣓⠒⠲⠦⠤⠤⢤⣀⣀⣀⣀⣀⡀⠀⡰⢁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠯⠁⢀⡚⠥⠷⠾⠞⠃⠀⠀⠀⠀⠀⣀⣠⠤⠤⠞⠛⠋⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠋⢋⠀⠃⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠃⡠⡞⠀⢀⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠻⠊⠀⣇⡠⠛⡇⢠⠞⣧⠞⣦⠴⠛⠉⠙⢣⢀⣹⠭⠭⠭⣝⡒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⡀⠈⠁⣀⡔⢲⣴⠾⠛⠁⠀⠀⠀⠀⠈⠳⣜⢆
⠀⠀⠀⠀⠀⠀⠀⢠⢋⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢚⡟⠑⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡃⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡸
⠀⠀⠀⠀⠀⠀⡎⠘⠀⠀⠀⠀⡰⠄⠀⠀⠀⠀⠀⠀⢀⣞⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⡴⠋⣀⡴⠁
⠀⠀⠀⢠⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⢴⠛⠀⣸⠋
⠀⠀⠀⡇⠀⠛⠉⠓⢲⡶⠤⠤⠖⠒⠏⠉⠀⣀⡴⠋⠿⣄⡀
⠀⠀⠀⠈⠢⢏⣂⡀⠀⠈⢁⣀⣀⣦⠶⠖⠋⠁⠓⠒⢲⡤⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣆⠀⠀⣈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢼⡾⢿⣿⣿⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣴⣋⠙⢷⣴⣸⣷⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣁⣤⡙⢛⠛⢻⣶⣶⣮⡙⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢶⣀⣶⣤⣦⣴⣿⢿⣿⠉⠿⢿⣶⣤⣈⣋⣛⣿⣶⣬⡛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣤⣶⠿⠿⠛⢋⣋⣉⡉⣩⣿⣿⣿⣧⣄⢨⡿⠻⠟⡛⢻⣿⣿⣛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡶⠟⠉⣁⣤⣤⣶⣾⣿⣿⡟⣿⣿⣿⡿⠗⢞⣹⣻⣷⣾⣿⣷⣵⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷⠾⢛⣤⣴⠿⠿⣿⣿⣿⢯⣿⣟⢹⣿⣿⣿⣿⣿⣿⣸⣧⣿⣿⠋⢻⠟⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡾⣉⣴⣿⣿⣿⡛⢿⣼⢫⣾⣷⡼⠿⣦⣻⣿⡏⠛⣭⣿⣿⣿⣿⣟⡀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⣶⣿⣿⣿⣿⣿⢾⣣⣽⣿⣷⣿⢢⣀⡿⢾⣿⣿⣛⣿⡿⣿⢽⣶⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⢹⣾⣿⣿⣿⣿⣿⣿⣿⡃⣸⣿⣿⣇⣻⢿⣿⣟⠊⣱⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣻⠿⠟⠛⢣⣿⣗⠀⠻⢿⣾⣶⣦⣤⣤⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣾⢶⡷⣿⣿⣯⠤⣴⣶⣦⣿⠿⠖⠑⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣼⣇⢼⣿⣿⣏⣘⣷⣿⣿⣿⣿⢿⡽⣽⢿⠿⣿⠛⣛⣿⣭⣟⣻⡿⠻⢊⠝⠇⠴⠇⠐⣢⠀⠈⠂⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⣿⡿⣏⣼⣿⣿⠀⣾⣿⡿⠁⢈⣹⣿⢻⣿⣿⡿⠿⣦⣶⣾⠛⠟⠛⠋⠁⠶⠿⠀⠂⠐⠀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣨⣽⣿⣿⣿⣿⡁⣘⢿⣯⠄⣠⣜⢻⡭⡜⡥⠘⢉⠀⠃⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢘⣿⡿⢠⣿⣿⡟⢱⣿⣿⣿⣷⡛⡝⠁⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⠀⣰⢾⣿⣯⣿⣿⣿⣆⣿⣿⣿⠷⠛⠁⠌⢀⣀⢠⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⢻⣿⣿⣯⠍⠘⠖⠊⠁⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠒⠂⠐
⠀⠀⠻⢷⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠉⠻⠿⢿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠛⠉⠉⠉⠉⠉⠙⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠙⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠂⠁⠄⠳⢤⣤⣐⢷⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠉⠀⠀⢰⡄⠀⠀⢀⠋⣸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠀⠀⠀⠀⠀⠀⢑⡎⢰⢧⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡄⠄⠀⡏⠈⠀⠀⢠⡀⣱⠀⠈⠲⢤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠉⠉⠙⠒⠦⣄⠀⡳⣄⡀⠀⠀⢄⣠⡜⠀⠐⠈⠊⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⢀⡴⠁⠀⠠⡀⢀⠄⠀⢢⡀⠥⠐⠒⠒⠢⣄⠀⠈⠁⠁⢀⠹⠛⠛⡄⠣⠇
⠀⠀⠁⠀⠀⠀⠀⠙⢧⡀⠀⡘⠀⠀⠀⠀⠀⠀⡜⠀⠀⠁⠀⠀⠀⢣⠀⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡏⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡀⠀⢀⠀⢣⡀⠈
⠀⡄⠀⠈⠂⠂⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠈⡾⣄⠘⠃⠀⡄
⠀⠈⢢⡀⠀⠑⡀⠀⠀⠀⠠⡶⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠃⠀⠘⠌⠢⢄⣀⠇
⠀⠀⠀⠙⢄⠀⠈⠀⠰⠊⠈⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠑⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⠜⠋⠁⠀⠈⠁⠐⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⡀⢀⣀⣀⣀⡀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠉⡟⠀⠀⠀⠉⠙⣇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠠⠤⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣡⠀⣤⣶⣶⣴⣦⡈⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣶⢤⡀⠀⠙⠉⢁⠀⢈⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠞⢿⠿⠀⠘⠓⡀⢘⣂⣀⡰⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⡀⢴⡶⢦⣶⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣲⣷⡄⠑⠚⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠶⣙⣃⣀⡙⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⢁⣀⡁⠘⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡠⣦⣤⣿⣤⠐⢀⡧⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⢾⡟⠆⠉⠀⠀⢹⠇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠈⣡⡔⢁⠀⠠⣿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⠹⣿⣿⡀⠀⠈⢷⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠛⠃⣬⡻⣿⣦⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠧⠉⠩⣤⡈⠙⢷⣤⣀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠲⠖⠋⠉⠻⠀⠐⡿⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⣀⣀⣬⡄⠀⠁⢠⣿⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⠀⠀⠘⠁⠀⠀⠀⠀⣿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡈⣰⣆⠀⣀⠀⠀⠀⠀⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⡉⠁⠀⠘⠃⠀⠆⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠡⠚⡀⠒⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⢁⣀⡀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠉⠉⠋⠀⣴⠀⠀⡄⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢗⣶⣴⠿⠿⠟⠛⠂⠀⣷⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠈⠙⠂⠀⠚⢀⡄⠀⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠉⣷⠀⠀⠀⠀⠁⡄⢠⡿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣿⣄⠁⠄⡼⠃⠁⣼⢇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢯⠀⣨⣽⠿⠀⣠⠂⠀⣼⡟⣸
⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠏⣿⡷⣠⡄⢀⣼⡟⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⣸⠏⣰⣿⡈⣁⣠⣾⣟⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣼⠏⠀⣿⣟⠛⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡷⠒⠤⠤⢴⡶⡞⢃⣾⠾⠁⠀⠀⠸⣟⠃⣿⣿⡆⢀
⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠻⣤⠘⣟⠷⣴⡓⠦⣀⣀⣀⣀⣀⡀
⢆⡘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠀⠠⢤⣤⣿⣷⠙⠖⠺⠿⠶⣶⣤⣾⠿⠿⠭⠉
⡁⢀⠀⠈⠦⠀⠀⠀⠀⣀⣤⣄⣠⣤⣤⣤⣤⣭⣍⡉⠉⠁⠀⠀⠀⠒⠲⠒⠒⢶⣿⣷⣀⠓⠚⣶⣬⣿⡷⠖⠂
⡱⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠿⠶⠶⠤⠀⠉⢛⣋⣉⡉⣉⣛⣻⣟⣟⣋⡉⠈⠉⠙⠓⠚⠋⠉
⠰⠊⠠⠆⢠⠀⠀⠈⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣯⣭⣭⡉⠉⠉⢉⣭⣭⣭⠛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⣤⣽⣷⣶⣶⣾⣷⣦⣤⣄⡈⡇
⠀⠀⠀⠀⢀⠤⠤⡀⢀⠀⣄⠠⠄⠀⠀⢸⣿⣿⠞⣡⡀⢹⣿⣿⣿⠁⣠⡈⣯⣿⣿⠀⠀⢠⠄⣀⠀⠄⢀⠤⠤⢄
⠐⠒⠒⢲⠃⠀⠀⠀⠀⠀⠘⠒⠚⠒⠒⠚⠛⠛⠒⠛⠓⠚⠛⠛⠛⠒⠛⠓⠛⠛⠛⠒⠒⠒⠒⡇⠀⠀⠈⠀⢀⠈⠖⠒⠒
⠀⠀⠀⠘⣆⢗⠀⣼⢠⣄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⡄⣠⠀⡸⣤⠂
⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣬⠾⠿⢿⣿⣷⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠁⠀⠀⢀⠄⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣿⣿⣯⣁⣀⣀⣀⣀⡀⠀⠀⢉⣛⣿⣿⣷⠀⠀⠀⠀⠀⠞⠂⠐⢉⣁⡍⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡿⣿⠟⠛⠻⠛⠛⢷⣶⣄⣿⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠱⠯⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣯⠤⠏⠐⠠⠶⣤⠀⠀⠈⢹⡑⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠋⠀⠀⠀⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢿⠋⢈⠿⣷⣤⣄⡀⡀
⠀⠀⠀⠀⠐⠀⠆⢠⡀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡄⠀⠀⠀⢰⠋⠉⠉⠛⠛⠃
⠀⠀⠷⠀⡀⠀⣠⠏⡿⡂⠁⠀⢀⡤⢦⣤⣤⠤⡤⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣤⣤⣾⠛⢀⣟⠕⠀⠠⠋⠀⠉⣿⣿⣤⣴⣿⣵⣴⣾⣿⣗⠀⠀⠀⠀⣀⠀⠀⢀⠀⣠⣤⣄⣐⣶⣤⡼⠟⡐⠁
⣠⣄⡀⠁⠠⠄⠸⠟⠁⠀⠀⠀⢰⠇⣤⣶⣿⡿⠿⠿⠿⠿⢿⣿⣿⣧⣶⣖⣴⣿⣷⣦⣿⣷⣿⣿⣷⣿⣿⣿⣷⣄
⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣬⣴⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠛⢿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⢻⡿⡂⢀⣤⣴⣀⡀⢀⣼⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠉⠉⠀⠛⠁⠀⠀⣿⣿⣿⡛⣿⣧⡃
⠀⠀⠈⡇⢩⠉⡟⢻⢟⠓⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⡀⠀⣶⣿⣿⣿⣇⣸⣿⣇
⠀⠀⠀⢹⠀⠂⠐⠂⠈⠀⣿⡇⠀⠀⠀⠲⢾⣿⣶⣾⣾⣾⣿⣿⣷⣾⡦⠀⠀⣴⣦⣤⣴⣿⣿⣦⣉⢻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠳⡘⠄⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣟⡿⣿⠿⢿⣿⣧⣤⣤⡻⣿⣿⣿⣿⣿⣿⡟⠛⠋⣺⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠱⣆⣻⣶⣾⣿⣧⣄⣀⣀⣠⣼⣿⡯⠚⣿⢛⠉⣴⣿⣿⣿⣻⡿⢃⣼⣿⣿⣿⣿⣿⣅⣠⣴⣿⡿⠛⠄⠠
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠿⣿⣿⡻⠿⠿⢃⣾⣿⣿⡏⠙⢗⠒⢉⢀⠀⠀⣈⣿⣿⣿⣿⣿⣯⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣠⣤⣤⣤⣭⣿⣿⣦⣴⣿⣿⣾⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣶⣂⠀⠄⠀⠀⣰⠟⠉⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣋⠍⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⢿⣿⣷⣐⡂⠀⠉⠀⠀⠀⠀⠀⠀⠈⠙⠭⣍⣯⣭⡄⠀⠀⠀⡻⠷⡶⢴⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⢳⣠⣤⠀⠀⠠⠋⡀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⢠⠎⠀⠘⡆⢀⡾⠁⠈⠛⢦⡀⠀⡠⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡈⠈⠀⠀⠁⢄⠀⠀⢻⢸⡇⠀⠀⠀⠀⠱⡎⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣀⠐⠀⠀⠀⠀⢳⡀⠈⣎⠇⠀⠀⠀⠀⠀⢡⢀⡦⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠘⠙⠢⣷⡀⠈⠿⡀⠂⠀⠀⠀⢨⡄⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢻⠆⠀⠀⠙⣄⠀⠀⠀⡼⠲⠤⢴⣞⣁⣀⣀⣀⣀⣀⣀⣤⠤⠀⠀⠀⠀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⣤⣍⡑⢯⠃⠀⠀⠀⠀⠙⠶⠞⠁⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⢤⣤⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣏⣠⠾⠟⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣀⣀⡀⣀⣀⡠⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⡵⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢋⡴⠋⠀⠀⠀⠀⠀⣠⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⢠⣎⡀⠀⠀⠀⠀⢀⠜⠁⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣠⣾⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⢀⠏⠀⠉⠉⠁⢒⠖⡁⠃⠀⢀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠉⠹⠚⡉⠧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⢤⠁⢀⠐⢂⠀⣀⠄⢹⠀⠀⠀⠀⠀⠀⡀⠠⠔⠒⡄⠈⠊⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⡹⣄⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⣀⣠⠤⣹⡧⠞⠁⣄⡿⠒⠚⠛⣲⣄⢉⠄⡤⠐
⠀⡀⠀⠀⠀⠀⡼⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠞⠁⣠⠞⠁⠘⢾⣼⠀⠀⡠⠊
⢘⠁⠀⡔⠀⢸⠁⠀⠀⠀⠈⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⠀⠀⠀⣀⣸⠔⠊
⠀⠀⠀⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠷⠶⠖⠚⠛⠉⠉⠉⠙⠲⣄⠀⠀⠀⠀⢰⠃⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣲⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠙⠛⠀⠛⠛⠀⠒⠒⠒⠒⣤⡀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⣀⣤⠐⠪⣍⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣧⣀⣀⣀⡤⠴⠒⠋⠁⠀⠀⢀⣯⣹⡏⢀⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠼⣍⢓⡄⠀⠀⠀⠀⠀⠸⣇⣸⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠐⠂⠀⠀⠀⠂⠀⠂⠂⠀⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠁⠘⠀⠃⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣀⡀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣹⣿⣿⡿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣶⠈⠙⠛⠛⣿⡆⠀⠀⠀⢠⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⣠⣿⠿⢾⣦⠀⠘⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣶⣾⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠉⠀⠀⠀⡀⠈⠉⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠸⣷⣀⣾⣏⣀⣀⣀⣈⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣤⣤⣴⣶⣿⡿⠿⣿⣟⠿⠟⣿⡟⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⢿⣍⣛⣁⣿⠃⠀⠈⠻⠿⠿⢟⡁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⢈⣝⣛⡛⠁⠀⠀⣀⣠⣴⣾⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡈⢿⣿⡛⢿⡟⠛⣟⠉⢻⣰⣿⣣⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡙⢿⣾⣧⣤⣿⣴⣿⣿⣵⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣾⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⠍⠉⢩⣭⠍⠁
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠈⠸⡀⠀⠐⠄
⡀⠠⠀⠀⢀⢄⠔⠁
⡇⠀⠀⠰⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠠⠠⠀⠂⠀⠄⡀⠀⠄
⡇⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡀⠄⠙⢻⡇⣤⣿⢃⢈⣜⡉⢻⢎⠂⢄⣰⡄
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠀⠼⠊⣀⠉⠲⢟⠷⢱⡉⣽⡧⢳⡟⠘⡠⠓⣧⣈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣤⣤⣤⠁⠐⠀⡔⡀⠲⠎⢐⣿⡿⣯⢤⡶⢧⡠⠂⢬⣣⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣱⡃⢈⡿⣴⡆⣄⡅⠓⢀⠠⠀⠀⣽⣿⣿⡿⠓⣖⣄⡐⠂⡸⢿⠗⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢴⠶⡗⠉⠉⠁⢛⢂⠰⡀⣤⣲⠼⣿⣿⣧⡶⢽⣙⡀⣀⡐⢀⠀⠂⠀⠀⠐⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢠⣼⣟⡾⢁⣶⡇⠂⡀⠉⠉⠲⢗⣲⣽⣿⣟⠳⠩⠁⠂⠘⠀⠛⠀⠀⢠⢴⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣭⠙⠿⣹⣯⠋⠀⢸⠓⢶⡴⠁⢟⣿⣻⡓⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⠃⠀⠀⠹⠟⢐⠈⠙⠀⣠⡕⣖⠟⠋⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡆⡰⠃⠀⠀⠁⡀⢄⣤⣷⣾⡿⠛⢣⠤⠤⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠖⠳⠼⢿⢍⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣨⠋⠉⡄⠀⠀⠒⠒⠀⠀⠀⠀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠞⠀⠸⡁⠀⠀⢃⠀⠀⠀⠀⠀⠸⣦⠞⠁⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠄⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠸⣆⣤⡀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠐⠊⠙⠒⢦⡶⡀⠙⣷⡠⠆⠀⠀⠀⣿⠉⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⢷⠀⠀⢳⣄⠀⠀⢀⠿⢤⣤⣴⣋⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠩⣭⣍⡑⢾⡟⠀⠀⠀⠉⠓⠴⠋⠀⠀⣤⡄⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⣤⣤⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣅⠴⠛⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠀⠀⣀⣑⣈⣤⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡡⠊⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡁⠀⠀⠀⠀⠀⠀⣠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⡴⠇⠀⢀⣀⡀⠀⢈⠁⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡀⠘⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⢠⠁⠀⠀⠀⠀⡄⡰⠊⣉⣠⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣨⣃⠔⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⠃⡀⢦⡽⣂⠴⠋⣸⣀⣀⣀⣠⠤⢴⠒⢋⣡⠗⠀⢙⣪⠞⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠙⢄⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠒⠛⠁⠠⠵⣻⠄⠀⡠⠛⢆⡞⡟⠉⠀⣠⠞⠁
⠀⢰⠂⠀⡄⠀⡾⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠞⠀⠀⠈⠉⣇⣠⠞⠁
⠀⠸⠀⠸⠀⠸⡇⠀⠀⠀⠀⠀⠈⠳⣤⣀⡤⠤⠤⠖⠒⠢⠤⣀⠀⠀⠀⠀⢠⠟⠒⠶⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢤⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠹⡒⠂⠐⠶⠆⠀⠶⠆⠀⠀⢠⡀⠀⠀⢀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⠋⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣠⠄⠀⠚⠁⠀⠀⠸⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠥⣏⣓⡄⠀⠀⠀⠀⠀⢶⣀⡇⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⣿⣿⣿⠏⡽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠐⢚⣃⣿⢟⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⠂⢧⠹⡜⡇⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⢂⡀⠀⠡⠉⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣀⠤⠥⣖⣂⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠖⠛⠛⠙⠹⣼⠇⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠚⠉⠉⠛⠚⡣⢭⢭⣉⠈⠛⠛⠶⠚⡟⣭⣀⣀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡇⠀⠙⠂⢢⡓⣛⣛⣈⣿⣞⠘⣋⣓⣛⣉⣀⣈⣓⡒⠦⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠉⠀⢀⡀⠩⠟⠋⡉⢉⠩⢸⣍⣉⠽⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣟⡥⠐⠒⠒⠒⠛⢿⡏⠡⠠⢴⢰⠀⣄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠁⠀⠀⠀⠀⠀⠀⠘⣷⣼⣇⣴⣼⡶⢼⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣶⣷⣾⣿⣿⠊⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⢿⣿⣿⣿⣶⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⢿⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣁⣴⣤⣤⣴⣿⣯⡙⣾⣿⣷⡄⠀⠀⠀⡔⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡀⠀⢸⠀⠀⠻⣦⡀⠀⣀⣠⣀⡀⢀⣴⠟⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣀⣴⣾⣿⣃⠀⠸⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣵⣦⣤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⠦⠀⠣⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣟⣃⣲⣿⣿⣻⣿⣿⡇⠀⢸⣿⣿⣿⠋⠀⢸⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⡟⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣦⡄⠝⠁⣈⠠⣠⣴⣿⣿⡇
⠀⠀⠀⠀⠀⣠⣤⣾⣾⣿⣿⡏⠙⠿⣿⣿⣯⣾⣿⣿⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠒⡄⠀⠻⠟⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠟⢱⡀⡀⠠⠌⡻⠟⣿⣿⣿⡝⠙⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣄⠠⢵⣤⣾⣀⣀⠜⣰⣿⠟⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣤⡀⠀⢸⠁⠘⡆⠀⢹⢀⢸⠛⢿⠓⠐⡄⠒⢺⠛⠻⣿⣿⣿⣿⣿⣿⣩⣛⡻⢻⢲⣽⣥⣼⣶⣿⣿⠿⢿⠛⠻⣟⠛⣦
⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣦⠘⠤⣦⠗⢿⠚⠺⠋⠀⢸⡀⣤⣳⢠⣸⠀⣦⠟⠛⠻⠿⠿⠿⠛⠉⠁⠀⠀⠉⢻⣿⣿⣿⣏⣰⣬⣇⣶⣿⣼⡾
⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠘⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠉
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠂⠀⠀⣤⠄⠀⠀⠂⠤⣌⢰⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣤⣶⣷⠆⠀⠈⠀⠠⠶⣿⡶⠈⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢫⢾⠀⣩⠀⣀⣼⣶⣤⣤⣄⠀⠄⠀⣼⠟⡿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠗⠂⣸⡆⠈⠀⢹⣿⣿⣿⣿⠋⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣤⣿⣿⣿⣧⡀⠀⣠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠰⢿⣿⣿⣿⡿⠿⠀⢯⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⢀⠈⠋⠉⢀⣤⠴⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢻⣶⡿⣿⠁⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡼⢿⢓⠀⣷⣼⡇⢠⣢⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⣤⣽⣦⣻⣏⠤⠚⠁⠄⢻⣿⣿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣰⣿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⠀⢸⣿⣏⢉⣛⡿⢾⣿⣿⣄⠀⣄
⠀⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⡟⠉⠀⢀⣸⣿⢹⣿⣿⡿⠋⠙⢿⣿⣯⠀⠈⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡀⠻⠇⠀⠀⡀⠀⠉⠉⠢⠀⢿⠛⠟⠻⠛⠻⡿⡟⢻⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢿⠿⠏⠩⣾⣿⣿⣿⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣛⣛⣃⣙⣉⣭⣭⣭⣤⡤⠤⠤⢤⡴⠶⠶⠶⠶⠾⠿⠿⠇⣿⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣿⡯⢭⠍⠉⠉⠀⢀⢐⠒⠂⠲⠆⠀⠀⠄⢩⣉⣉⣉⣲⠂⡀⠆⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢰⣿⣿⠶⣄⡐⣿⣿⣿⣃⣒⠒⠒⠐⠂⠠⠁⠉⠉⠉⠋⠀⣒⣺⣾⠷⠾⡾⠁⣴⠈⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣾⣿⣷⣦⣈⠙⢷⠒⠲⠦⠬⠄⠁⠄⠀⢐⡃⠐⠒⠀⠖⠀⠨⠬⡍⢉⣉⣣⡆⢀⡤⠀⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⡿⣡⡈⠙⢶⡏⢉⠀⠛⠂⠒⠂⠀⠀⠤⠉⠩⠉⠉⢘⠀⠀⠂⠀⠀⢽⠁⠄⣠⠄⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⡉⣁⡈⠳⣝⣲⡒⠂⠀⠠⠈⠩⠍⠉⠉⠉⠒⠂⠒⠒⠀⠀⣠⣄⣬⡙⠙⠷⠃⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣧⠀⠙⠒⠋⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣿⣿⣷⣄⠀⣀⠤⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡆⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢺⣿⣿⣿⣿⡔⢶⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢡⣄⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠘⢿⣿⣿⣿⠧⠀⠙⢹⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⢁⣤⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣤⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⡿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠄
⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠠⣤⣶⣤⣄⡈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⣿⣶⣆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣤⣤⣿⣿⣿⠻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⠋⠀⠀⢀⣺⣿⣿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣿⣿⣿⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠈⢹⣿⣿⡫⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠟⠁⠀⠀⠀⠀⣤⣶⣿⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⡷⢶⣄⡀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡿⠀⠀⠀⠀⠀⣾⣿⡦⣈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣠⣾⣿⣷⡄⠀⠀⠀⠀⣹⣿⣿⣿⣿⠘
⠀⠀⠀⠀⠀⡀⠰⠘⣿⣿⠃⠀⠀⠀⠀⣸⣽⣿⣶⣿⣷⡈⣧⠀⣀⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⢾⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⢠⡼⣶⣿⣿⡆⠀⠀⢠⣴⣿⣾⣟⣿⣿⡁⢹⣿⣿⡿⠛⠁⠀⠁⠀⠀⠀⠀⠈⢧⣴⣾⣧⣀⣬⣽⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠑⣻⣿⣿⡛⠀⢐⣾⣿⣿⣿⣿⣿⣿⣥⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢡⣿⡿⠁⢉⣻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢀⡀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣴⣒⣾⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠋⣵⢾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠻⣀⣀⣀⣶⣶⠀⢀⣴⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠖⠳⣺⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠠⢠⡙⠛⠟⠛⠋⠀⠀⢰⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⣿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⡿⠶⠄⠀⠀⠄⠀⢤⣠⣼⣿⣿⣶⣶⣷⣦⣀⡘⠦⠔⠲⠶⠞⠿⣿⣿⣿⣷⣿⣷⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣿⣿⣴⣦⣀⣴⣲⣾⣷⣿⣿⣿⣿⣻⡿⣿⡿⣿⣿⣿⣶⣦⣤⣄⣀⣻⣭⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡿⡿⠿⠿⠿⠟⠛⠛⠻⠭⠿⠦⠾⠡⠿⠟⠿⠟⠻⠿⠿⠿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣯⢿⠿⠯⠇⠋⠱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣰⣾⡏⢀⠤⣠⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣾⡶⠟⠉⠁⠀⠀⢹⠉⡜⠛⠟⢋⡀⣆⣢⣦⢄⣀⡀
⠀⠀⠀⣀⣴⣾⣿⠿⠀⠀⠀⠀⠀⠀⢀⠾⠁⢠⣌⠉⢉⠹⠦⠠⠈⠛⣳⣖⣤⡀
⠀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⣠⡥⣤⣤⡄⢩⣈⠛⠢⣍⠿⣷⡄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡄⠚⣃⠐⠺⠣⠾⢷⣽⡐⢤⣆⡏⠻⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣼⣷⡄⠿⠆⢩⣶⠲⠀⢿⣟⣉⣥⣿⣿⣻⣷⣶⡈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠉⠉⠀⡁⠐⢁⠚⠿⣠⣆⢉⣉⣩⣶⣟⡛⠻⢟⢻⢏⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠸⠀⠀⡀⠤⠰⠆⠉⢙⠀⠵⠉⠯⣍⠛⠿⠟⣙⡓⠋⣨⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣃⠐⠘⠧⠱⠈⠃⠀⠳⣄⠀⣈⠛⢷⠄⢦⣤⣾⠿⣞⠓⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠞⢇⠛⠸⠇⣸⡂⢐⢈⢴⣦⣍⡛⢷⣦⡻⣯⣟⣷⠶⠾⣽⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠙⠻⠾⢿⡿⠖⣭⣿⣿⣮⣭⣛⣛⣶⠾⠭⠿⡦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠛⠒⠒⠛⠿⢿⣿⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⠁⠀⠠⠄⣀⠁⠀⠀⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠦⠬⠷⠚⠲⠻⠝⣇⢤⡤⠕⠳⡅⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠇⠘⠣⠘⢧⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠒⣰⠀⠒⠙⠂⠤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡆⠀⢀⣍⢤⡄⠀⢀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣸⢸⠋⢁⣠⣞⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡞⠁⢘⣻⡽⠁⠀⠀⠀⠈⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠕⠊⠉⠣⣀⣀⡾⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠈⢹⠉⠉⠙⢢⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢀⣠⢴⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣸⢤⡀⠼⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣳⠀⠀⠰⠵⢢⠀⡠⣴⡽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢉⡴⠂⣀⣤⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠳⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⠉⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠉⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⣀⠤⠂⠉⠉⠉⠢⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡀⠀⠪⡁⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⠆⠀⠁⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢀⠀⢣⠀⠀⠀⢠⠁⠀⡀⠀⠀⠀⠀⠒⠂⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡰⢛⢀⡈⢢⠀⠀⠘⡄⠈⠄⣀⠤⠤⠀⠀⢀⠤⠔⠁⠉⠁⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⢻⡇⠀⢆⠀⠀⢀⠼⠀⣤⠂⠀⠀⠐⠐⠢⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠥⡉⠋⠀⠀⠑⠛⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⡔⢸⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⡎⠹⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠼⢆⠀⠀⠀⠀⢠⠀⠤⣀⡈⠲⠒⠀⠠⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢸⠄⠀⠀⢰⣼⠤⣄⣇⡥⠊⠀⡠⠴⠉⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡇⠀⠀⠀⠁⣸⡉⠉⢓⠁⠀⠀⠘⢄⠤⠐⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⢹⡿⠐⠋⠆⠀⢀⡤⣫⣝⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠛⡃⠀⠀⠈⠂⢹⣶⠋⠙⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⣀⠀⠀⠆⠃⠀⠀⠀⢤⡜⢰⢸⢀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠁⡇⠖⠤⠤⢤⣼⠶⡾⣏⠏⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠓⠋⠁⠀⢾⣆⡼⠶⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⢦⣄⠀⠀⢻⣸⡄⠀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⠉⠓⢀⠟⠁⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠐⠒⠒⠊⠯⠉⠛⠟⠃⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣬⣿⣺⣼⣿⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⠟⠋⢹⣿⣙⣿⣿⠜
⣤⡤⣼⣴⡀⠀⠀⢠⢀⢈⣦⣄⣾⣧⣼⣿⣷⣦⣤⣶⣶⠾⠟⠛⠉⠀⠛⡀⠉⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿
⠉⠉⠉⣽⠦⠿⠿⠛⠚⣾⡏⢛⡋⠉⠘⠋⠀⠤⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣹⣿⣷⣿⣻⡿⣿⠿⠿⢿
⠀⠀⢀⠘⠑⠂⣦⣦⠸⠧⣌⣆⣻⣿⣶⣖⠠⣦⣄⢄⢀⣀⣀⣸⡟⣷⠶⠶⣿⣽⣿⣿⠿⠛⠛⠚⠶⠶⣼
⢻⣿⠴⢾⡏⠓⠀⠀⠉⠀⠘⠛⠛⢉⠀⠉⠀⠺⡉⢻⣿⣿⣿⢿⣷⣿⣾⢿⣏⣘⣰⣦⡤⢤⣄⣀⣀⡀
⢿⠟⠃⣸⡷⠆⠀⠀⣡⠀⠀⠀⠀⠈⣧⡀⠀⠀⠛⠿⠛⠋⠉⠈⠛⣿⡤⠊⠉⠋⠉⠉⢹⡿⠛⠻⣿⡿⠭
⠀⠀⠈⠃⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⡀⠀⢀⣀⣤⣤⡄⣟⠀⠀⢀⠀⠀⢀⠈⠀⠀⠀⠁⡀
⠀⠀⠠⡴⠃⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠹⣿⣷⣦⣽⢿⣿⣛⣿⡟⣶⠐⢭⡁⠒⠛⢂⣀⢰
⣠⣿⡇⣏⣷⣾⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣱⠟⣕⠾⠾⣿⣿⡇⣿⠀⣿⣿⡗⣿⢻⡀⢸⠷⠀⠴⣾
⣿⣿⡇⡏⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠖⠉⠉⡇⢿⣀⣿⣿⠇⣿⣸⣿⣲⠀⠀⠀⣴
⣿⣿⢓⣧⣭⣵⠀⢰⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⢤⡗⠢⢍⠛⠻⢢⣍⠈⠓⢽⣶⢶⣶⣿
⠋⣾⢿⣿⣿⣿⡇⠁⠀⠀⠀⠀⡭⠱⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⣘⣿⣧⡀⠀⣿⢸⣿⣿
⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠈⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄⠀⠀⢹⣿
⣁⣿⢿⡿⣿⣿⡿⠀⠀⠀⢠⡆⠀⠀⠃⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⡄⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠒⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣣⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠭⢛⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡀⢀⠀⠀⢳⡀⠀⠈⠂⠀⠀⠀⠀⠀⠠⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⢯⡔⠋⢁⢱⠀⠁⠀⠀⢀⠐⠀⠀⠀⠀⠀⢫⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠑⠈⠢⣀⢼⡀⠀⣠⠃⠀⠀⠀⠠⠁⢀⠠⠤⠄⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⠂⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡅⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⢀⡀⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⢏⠟⣧⢇⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠠⡄⠀⢻⠈⢳⡇⠐⠁⠊⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠘⢯⠇⡀⠘⠀⢰⠀⠸⠀⠀⠀⠀⠸⣋⣀⠀⠠⠄⠠⠤⠤⠤⠀⠤⠤⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠨⣗⠠⣛⠀⠉⠓⠲⠄⠒⠀⠐⠀⠀⠀⠀⢸⠉⠉⠁⠀⠉⠉⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠐⣞⣇⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣐⣶⠧⣼⣄⣀⡀⠘⡆⠁⢘⡛⠉⠉⣟⡖⡗⠒⡛⠋⠉⠁⠀⠀⢹⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠞⢿⣤⣮⣭⣾⣧⡤⠈⡧⣆⠀⠀⠀⠀⠡⣵⠠⠀⠧⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⢘⡇⠀⠉⠀⠀⠀⠀⠀⠘⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐