Yellow duck Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⢰⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡀⢠⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠿⣿⠀⢸⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⣿⡃⠸⣿⠿⡿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⡟⠙⢿⣷⡄⠀⣠⠖⣶⠀⣴⠒⣶⠀⣶⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢸⣿⣿⢰⡟⠺⣿⢰⡏⢹⡅⣼⠏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢀⣿⣿⠇⢠⡄⢀⡄⢀⣤⢄⠀⣠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣏⣀⣤⣿⡿⠋⠀⣾⠃⣾⠃⣿⠁⡈⢀⡿⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠙⠚⠁⠀⠉⠋⠁⠘⠁⠙⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣽⣯⡻⣿⣿⣿⣿⣿⣿⡿⣟⣩⠽⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⣻⣭⣯⡛⢿⣿⣿⣿⣿⣟⣛⣯⣽⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⠏⡁⠀⢀⠙⡾⣻⣿⣿⣿⡿⣽⢋⠀⠀⡈⢳⣿⣿⣿⣿⣿⡿⣿⣿⣝⡑⣭⣿⣾⣿⣿⣟⣱⣿⣭⢁⣮⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣽⢘⡆⠁⠛⠂⢠⣗⢽⣿⣿⣏⡷⢳⠈⠓⠓⠂⢸⡻⢿⣿⣿⣿⣯⣿⣽⣿⢿⣿⣷⣿⠾⣿⡿⣻⣿⣿⣿⣿⣯⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡵⠉⠀⠀⠀⠀⠀⠈⢶⣹⣿⣿⡞⠁⠀⠀⠀⠀⠀⠙⡆⣿⣿⣯⡿⢻⣹⣿⣿⣿⣯⢿⣷⡹⣿⢿⣭⣿⣿⣿⣷⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆⠀⠀⠀⠀⠀⣠⣋⣾⣿⣿⣳⡄⠀⠀⠀⠀⠀⡼⣃⣻⣿⣽⣻⣏⡾⣿⣿⠿⣃⣿⢟⡽⣛⣷⣽⣿⣿⡿⣿⣹⡿⣻⣿⣿⣿⡿⢿⣿⣿
⣿⣿⡟⠋⠉⠁⢜⣪⢿⡯⣳⣦⣤⣤⣞⢻⣿⣿⣿⣿⡿⢊⣲⣤⣤⣴⣏⣿⣿⣿⣿⣿⣷⢟⣿⣿⣿⣿⡟⢉⠮⣿⣿⠎⣙⣿⣿⣿⣿⣋⣾⣿⣿⣿⠟⢀⣤⣿⣿
⣿⣿⣿⣤⣤⣀⣼⣿⣿⡼⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣰⣿⣿⡺⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠋⠉⠉⠉⠉⠛⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠠⣿⠋⢹⡧⠀⠀⢻⣿⣷⣶⣶⣶⣶⣶
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠘⣿⣿⡆⠀⠀⠀⣸
⠀⠀⠀⣠⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⢠⣿
⠀⠀⣼⣿⡿⠃⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣀⣠⣶⡿⠋
⠀⣼⣿⡿⠁⠀⠀⠀⠀⠙⢿⣿⣷⣀⣀⣀⣀⣀⣹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠻⠛⠛⠉
⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠿⠿⠿⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿
⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⠀⠀⠈⢿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢀⠀⠀⢘⣇
⠀⠀⠀⠀⣠⠤⠖⠒⠒⠒⠒⠛⠛⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠛⠓⠚⡇⠀⠀⠀⢀⡤⠚⠉⠛⠦⣄⣀
⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠐⢈⣁⣡⣤⠤⠶⠶⠶⠒⠒⠶⠶⠶⠶⠶⢤⣤⣤⣀⣣⠀⠀⠀⠯⠤⢤⣤⣤⣤⣤⠼
⠀⠀⠀⠀⠀⢀⡠⠃⠀⣠⡴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠖⢎⣉
⠀⢀⡠⠔⢊⠁⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⣀⠤⠤⠠⠠⠐⠰⢰⠤⠤⠄⣄⡀⠀⡀⠀⠂⠀⢰⠙⣦⠀⠤⡉⠑⢦
⣞⠁⠀⠊⠡⠔⠀⠀⣿⠀⠀⠀⠀⠈⠐⠛⠤⠄⣀⣀⣀⣀⣤⣤⣀⣀⠠⠤⠛⠉⠀⠀⠀⠀⠈⠀⣸⠀⠀⠈⠀⣠⠃
⠈⠙⠒⠤⢔⣂⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡷⣾⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠙⠛⠲⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠞⠛⠋⣁⠔⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⣒⣒⣊⣉⣠⡤⠤⠤⠖⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢮⣀⠝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠚⣠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠰⣁⣈⢧⠀⠀⠀⠀⢸⠏⠁⠀⠉⠉⠉⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣬⡥⠊⠀⠀⠀⢠⠏⠀⠀⡀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢠⢊⡟⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡏⠀⠰⣷⣌⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠹⣄⠓⢒⡱⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠉⢲⣄⡜⠓⡄⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢠⡞⣵⠉⠙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣛⣋⡹⠋⠣⠴⠃⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠘⣇⡈⠒⢊⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠳⢄⡀⠀⠀⠀⠀⠀⣀⡴⠛⠦⠤⠤⠤⠤⠴⠞⠋⠹⡆⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⡀⠀⠀⠀⠀⣠⠴⠋⠉⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠱⣇⢀⠟⡄⠀⠀⡼⠃⠀⠀⠀⢀⡤⠒⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⣀⠀⠀⠀⣸⠀⠀⠀⣠⠴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣌⣩⠞⠀⠀⢸⠇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢠⣤⣖⠭⠊⡽⠀⠀⢠⡏⠀⠀⣸⠃⣾⠭⢈⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⡞⠀⠀⠀⠸⣆⡈⠛⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣷⡀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⣠⣯⣀⣀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠀⣴⠛⠲⢤⣀⣀⣀⡀⠉⠉⠉⠉⠉⠁⠀⢀⣀⣠⠞⠓⣆⠀⠈⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠈⠙⠒⠶⠶⠭⣭⣭⣭⣭⣍⣉⣩⣭⣭⣭⡭⠴⠖⠚⠁⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠶⠶⠤⠤⠤⠤⣤⡤⠤⠤⠤⠴⠶⠶⠶⠚⠛⠋⠉





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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⡖⠊⠉⠉⠉⠉⠉⢉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠉⠉⡇⠀⠀⢀⡤⠊⠁⠈⠑⠲⢤
⠀⠀⠀⠀⠈⠑⢄⠀⠀⢀⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠲⠶⠼⠀⠀⠈⢓⣒⡲⠖⠒⠒⠚
⠀⠀⠀⣀⠤⠒⠁⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⠉⠒⠦⢤⡀
⡤⠒⠉⠔⢂⠀⠀⢼⠁⠀⠀⠀⠠⠤⣖⠋⠉⠉⠀⠀⠉⠛⠛⠉⢙⡲⠄⠂⠀⠀⠀⠸⠈⡇⠀⠑⠀⠈⡆
⠑⠢⢄⣀⡡⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⡤⠊
⠀⠀⠀⠀⠉⡇⠀⠀⠘⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠈⠛⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠞⠋⣁⠔⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⣒⣒⣊⣩⠤⠤⠤⠔⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⢷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⠀⣴⢤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⣾⣿⣷⣭⣾⣧⣴⣯⣿⣶⣶⣖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠘⣿⣿⣿⡿⠟⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⢠⣽⣿⣛⣻⣷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣧⣻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢟⣻⣿⣛⣿⣷⣽⣿⣿⣿⣿⣿⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣀⣤⢴⣞⣻⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣟⣛⣭⠿⠿⢿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠀⠈⠙⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣟⣦⣀⣀⣀⣀⣿⣷⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠾⠿⠿⠷⠿⠿⠿⠷⠶⠿⠿⠿⠿⠷⠶⠿⠿⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣜⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⠿⣷⠟⠻⠎⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣠⡇⣤⡀⠘⢣⣾⣶⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠯⠙⠒⠩⠅⢚⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠘⡷⢙⠿⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⣶⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠚⢼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣾⢡⡶⠒⠢⠤⢽⣿⣿⣿⣇⡈⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣯⣿⡓⠲⢾⣿⣿⣿⡟⢳⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣉⢻⣷⣾⢿⣿⣿⣿⣿⣿⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣫⣧⢛⣿⣿⣟⠿⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⠉⠉⠉⠉⠙⣷⣤⣴⣿⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⡖⠂⠴⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣲⣿⣽⣯⣻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣛⣿⣶⣻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣶⣿⣻⣿⣿⣷⡦⢻⡀⠀⠀⠀⠀⠀⠀⠀⡞⢰⣿⣿⣿⡿⣷⡶⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣿⣿⣿⣿⣷⣿⣧⣸⠇⠀⠀⠀⠀⠀⠀⠀⣟⢯⣿⣾⣿⣿⣾⣧⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣼⣿⣿⣿⣶⣿⣿⡁
⠀⠀⠀⠀⠀⠀⢠⢾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⡀⠀⠀⢀⡴⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣏⣾⡿⠻⢿⣿⣿⣿⣿⣿⣿⡿⢛⣯⡇⠀⠀⢼⣸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⢻
⠀⠀⠀⠀⠀⠀⠉⢻⡀⣀⣴⣿⣿⣿⣿⣿⡟⢵⣿⡏⠁⠀⠀⠈⠹⡄⣀⣿⣿⣿⣿⣿⣿⡏⣹⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢮⣟⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣧⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠿⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⡿⢿⡿⠿⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠫⣿⣿⣿⣿⣿⠝⠋⠛⢶⣾⣿⣿⣿⢋⣭⣶⣭⢳⣿⣿⣿⠝⣩⣴⣦⡙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣟⡇⠁⠂⠁⣿⣿⣿⣿⣿⠈⠐⠈⢸⣿⣿⣿⡧⢹⣯⣭⣿⠣⣾⣿⣿⠆⣿⣯⣽⡟⢸⣿⣿⣿⡋
⣿⣿⣿⣿⣿⣯⣏⠀⠀⠀⠀⢈⣿⣿⣳⡁⠀⠀⠀⠀⣹⢿⣟⢼⣿⣿⣿⣿⣿⢸⣿⠃⣿⣿⣿⣿⣿⡧⢹⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⢦⣀⣀⣠⢾⣾⣿⣷⡷⣄⣀⣀⡔⣻⣿⣿⣦⡙⠿⠿⠟⣣⣾⣿⣿⣌⠻⠿⠿⢟⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣹⣿⣿⣿⣿⣾⣿⣿⣏⣀⣀⠀⠀⣈⣿⣿⣿⣅⠀⣀⠀⣀⣽⣿⣿⣿⣿⣿
⠋⠉⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏⠉⠉⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠉⠁⠹⠿⠿⠿⠿⠿⠿⠷
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣿⣛⣿⣻⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠞⠛⠛⠛⠿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢠⡄⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢸⠇⠹⣆⣀⡼⠁⠀⠀⠀⣧⡀⠀⣀⡟⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣀⣀⣼⣄⣀⣈⣭⣤⣤⣀⣠⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠈⣧
⢀⣴⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣾⣁⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣼⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⢻⣄⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠘⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠙⠿⣶⣶⣶⡶⠶⠶⠶⠞⠳⠶⠶⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣦⣄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢠⡟⠉⢃⣤⣽⠇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠟⠀⢠⢿⣭⡉
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠶⠾⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠉⢻⣧⡀
⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⠀⢴⣿⠄⠀⠀⠀⠀⢿⡇
⠀⣀⣤⣶⡿⠟⠋⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠸⣿⣭⣤⣤⣤⣤⣤⣽⣿⠷⣶⣶⠆⠀⠀⠀⢠⡿⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⣴⡿⠋⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⣴⡿
⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⣼⡟⠀⠀⣀⣠⣴⡶⠿⠛⠛⠛⠻⢶⣤⣀⠀⠀⢀⣴⣿⣇⣴⣿⣿⠃⢀⣠⣶
⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣾⠿⠋⣿⠟⠉⢸⣿⡾⣿⡟⠁
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣄⣀⣀⣀⣀⣀⣤⣤⠄⠀⠀⠀⠈⠁⣰⡿
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢶⣤⣀⣀⡈⠉⠉⢉⣉⣥⠞⠁⠀⠀⡀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢳⡄⠀⠀⠘⢿⣦⣀⠀⠉⠉⠛⠋⠀⠀⠈⠛⠿⠿⠿⣻⡿⠋⠀⢠⡿⠁
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠉⠛⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠋⠀⠀⠀⣰⣟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⣠⡾⠋⠉⢳⡄
⠀⠀⠀⠀⠀⣼⠁⠀⠈⣻⠿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⢀⡀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠻⣧⡀⠀⠀⠀⠒⠶⠶⢶⣶⣶⣶⣶⣶⠶⠶⠟⠛⠉⠀⢀⣤⠟⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠙⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠋⠁⠀⢀⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣄⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣤⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠷⠶⠶⠶⠶⠶⠿⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣀⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢀⠸⡀⠀⠸⠘⡀⣀⢤⠀⠀⠀⠀⠀⠀⠀⢠⣝⡾⢷⣫⣤⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠄⠀⣀⡀⠀⠀⠈⠁⠀⠀⣴⣑⣁⠈⠀⠈⢣⣄⠙⡄⠀⢘⡿⣷⡾⢿⡛⠯⠝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣰⡀⠀⢠⠀⡈⡄⢰⢀⣀⣄⢺⣷⢷⡆⠁⠠⠐⡀⡂⡏⠀⠉⠉⠉⠉⠋⣿⡟⢻⠀⠀⠈⢹⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠰⢃⢀⡠⠐⠉⠀⠀⠀⢀⠤⠿⠚⠂⠑⡃⣚⣿⡠⢄⡅⠀⠀⠀⠀⠀⠀⣿⡧⢸⠀⠀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⡶⠤⠀⠀⠀⠠⠄⠀⠀⣀⣀⢀⡤⠖⠉⠀⠀⠉⠑⠫⢧⣤⡀⠀⠀⠠⣻⡅⢸⠀⠀⠀⠚⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⢐⠀⠀⡎⠠⠂⢀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣶⠀⠀⠀⠀⠀⠀⠀⣤⣽⡷⡤⠀⠀⢹⡇⢸⠀⠨⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠂⡋⠠⠁⠀⠐⠀⠀⠀⠀⠐⠂⡰⠁⠛⠻⠀⣾⢒⠶⡲⢦⠀⠿⠿⠙⣽⡀⠀⣸⣇⢸⠀⠀⢠⠒⠟⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢠⣆⣀⣈⠁⠊⣁⣀⣀⣀⡀⣰⠃⠀⠀⠈⠀⢸⣯⣶⣡⣾⠀⠐⠖⠂⠙⣿⣿⣿⣿⣿⣷⣃⣾⣷⠾⣷⣷⢦⡀
⠀⠀⠀⠀⠐⠀⠀⢀⡠⢒⠘⠊⠉⠉⠭⢙⣳⣧⣍⠀⠀⠈⠉⠻⠀⢰⠖⠒⢿⢳⣶⣴⠖⣾⡗⠒⡂⠑⠒⡛⠋⣛⡛⣛⠛⠓⢈⣕⡺⣿⣿⣞⢧
⠀⠀⠄⠀⠀⠀⠀⠀⣛⠙⠙⠚⠓⠺⢶⠋⠁⠀⢹⢀⠀⠀⠀⠀⠀⢸⠁⠆⢸⣿⢹⡿⣛⢽⠉⡞⢹⠀⠀⡏⠉⣿⡏⣹⠉⠉⠉⠉⠁⠻⢯⡁⠣⡀
⠀⠀⠀⠴⠤⣤⣤⣴⣟⣰⠀⡀⠀⠀⠰⠀⠉⠁⢸⣸⣤⣄⠴⠴⠀⣸⣦⣀⠾⠿⠾⠧⢥⣼⣶⣀⣲⣀⣺⣷⣴⣿⡷⠿⠿⠶⠶⠶⠗⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠀⠁⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⡶⢖⢲⠛⠛⠋⢉⡍⢍⡝⡻⠛⡳⠒⣶⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡚⠫⣍⠳⢌⠢⡙⢌⠀⠇⠀⡇⠸⠀⠜⠔⣡⡞⠡⢊⡡⠖⣋⠤⠞⢉⠹⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠲⢌⡑⡂⠍⡒⠅⠢⣈⣤⣬⣄⣡⠞⠛⠲⠞⠉⠉⠳⠴⠶⣭⣴⠶⡶⣄⠒⣩⡷⣤⠉⡓⣦⣀
⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠳⡄⠁⠀⣴⣾⣿⣿⣿⣿⣿⡴⢶⢶⠶⣶⠖⣶⡶⠒⢿⠾⠶⢷⣿⣰⡿⠧⣿⡟⠉⠁⠈⠳⢦⡀
⠀⠀⠀⣠⠞⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠶⣾⣿⣿⣿⣿⣿⣿⡿⠶⠶⡶⣶⢶⡾⠁⠀⠀⠀⢱⡄⢸⣿⢹⡇⠈⣿⡇⠀⠀⠀⢀⣠⠿⢦⡀
⠀⠀⡼⠃⠀⠀⠀⠁⠀⠀⢄⣠⣤⠞⠁⠀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣈⣓⣙⣙⣈⣻⠇⠀⠀⠀⠀⠀⣧⢸⣿⢸⡇⢰⣿⡇⠀⠀⠀⠈⢡⠀⢈⣷⡄
⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⠿⢿⣿⣟⣏⣙⣁⣛⣘⣃⣸⣤⣤⣤⣀⣀⣠⣯⣸⣿⣼⣅⣈⣿⣇⣀⣀⣀⣀⠀⠀⠈⠀⠻⡄
⣸⣷⣶⣶⣶⣦⣤⣤⣀⣀⣀⣠⣤⠤⠤⠶⠶⣟⣛⣿⡿⠿⡟⢛⣛⣯⠿⠟⠛⣋⣭⡤⠶⢚⣫⡭⠖⠋⠁⣠⡴⠛⠉⢀⣩⠟⠉⡽⠉⣟⠛⣟⠲⣶⢿
⣿⠢⠬⢭⣅⣉⢉⣙⠛⠻⠻⡿⣿⣶⣦⡶⠟⢉⣁⣀⣤⠾⠛⠉⠁⣀⣤⠶⠛⠋⢁⣤⠞⠋⠁⠄⣠⡴⢛⠁⠀⢀⡴⠋⠀⠀⡾⢁⢰⣗⢀⣹⣄⣈⣻
⣏⠑⠮⣄⡠⡉⠙⠓⢦⣴⣠⣠⣴⢛⡩⢀⣤⣞⡋⠉⠉⣀⣤⣶⣻⣥⣤⣤⣤⣞⠋⠀⠀⠀⣠⡾⠋⠀⢁⡀⢠⡟⣁⣤⠶⠟⣩⠉⠉⠉⢉⣉⣁⡤⢾
⢻⢳⢤⣤⣉⣳⣷⣿⣛⣫⣯⣥⣬⣩⣿⣿⣟⣉⣹⣻⣿⣽⣽⣭⣭⡁⠹⠛⠟⢻⢧⣀⣠⡾⠋⠀⠀⠀⡚⣵⠿⠭⠕⠒⠉⠀⠀⠀⠀⠠⢝⣛⣓⣟⣿
⠈⢿⣭⣼⣻⣿⣿⡿⣿⠷⣿⣷⣾⣷⣿⣿⣿⣿⡻⣿⣿⣿⠿⣿⣯⣟⡿⣷⢶⣤⣈⣻⣿⡟⣽⢳⣠⢄⣼⣟⣿⣟⣷⣖⣶⣦⣀⣤⣤⣀⣀⡈⠉⣨⠏
⠀⠈⢷⠦⣠⡠⠍⢿⣟⣷⣾⣅⣇⢉⢻⣷⡿⡻⣿⢤⢿⡿⣶⣿⣻⣿⣿⣿⣯⣽⡟⣛⣮⣏⡙⠾⢯⣿⣿⣽⢧⡿⣿⢻⣭⡟⣽⣛⢷⢶⡭⠽⣽⠏
⠀⠀⠀⠳⣄⠹⣯⠭⠇⡹⢤⢿⠿⣿⣦⣻⣶⣻⣫⢿⣷⣟⡻⣯⣿⣟⣯⣟⠿⡽⣷⢿⣆⡿⣓⣾⢧⣸⡟⣛⣧⠹⡷⣟⣲⡧⠯⣝⡟⣼⣭⡿⠁
⠀⠀⠀⠀⠈⠳⢿⡅⣢⢍⡛⣿⡁⣹⣿⡇⣿⣿⣟⣏⢿⣾⣷⣛⣟⣳⣝⣯⣾⡟⣫⣻⣞⢿⣭⢿⣦⣯⣿⣧⣞⣷⢛⡟⢾⣓⢦⣈⣳⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⣐⢢⣟⡙⣿⣿⣿⣿⣼⣿⣭⡑⢿⣚⣿⣴⣿⡷⢿⢯⣿⣫⣿⣿⡛⣾⡷⣾⣩⣿⣝⣿⣟⣿⣟⣽⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣥⣼⣿⣿⣿⡟⡷⢮⣉⠟⣾⡿⡻⣼⣗⡿⢳⣿⣿⣮⣽⣛⣷⣿⣿⣯⣴⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠿⢶⣟⣚⣇⣿⣯⣍⣽⣷⣿⣿⣿⣿⣭⣭⠾⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠒⢠
⠀⠀⠀⠘⠢⠐⣄⠀⠀⠀⠴⠢⡄⠀⢀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣀⡀⢠⣤⠀⠀⣀⠀⠀⣀⣤⣄
⢰⣤⣤⠴⠶⠤⠾⠶⠾⠀⠀⠀⠒⠂⠛⠓⠰⠿⠧⠴⠷⠾⠦⠤⠤⠴⠆⠀⣤⠤⢤⡄⠁⠀⠀⢰⣋⣁⡀⠉⡿⠔⠢⡄⠉⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠋⠙⠁⠛⠋⠁⠠⠾⠿⠿⠿⠶⠤⠤⠤⠧⠄⠘⠛
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠉⠀⠀⠠⣴⣞⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⡀
⠄⡀⠀⡀⢠⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⡉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠁⠁⠁⠈⠉⠉⠁⠉
⡆⣄⡷⠀⡼⣄⠀⢀⡀⠀⣸⠡⢛⣀⣧⣻⣽⣇⣀⣀⣀⣀⣀⠀⣀⣀⣴⡷⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡆⠏⡟⢡⣟⣾⣾⢀⣇⣆⣟⠰⠮⡉⠁⣀⠀⠀⠀⠂⠀⠀⠀⢠⡇⠀⠘⣻⢿⣯⡆⠆⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⠘⠀⡄
⠟⢰⣰⡧⣩⡎⠙⠞⠒⠈⠀⢀⡠⠔⠈⠀⠀⠀⢀⠐⢀⡠⣤⡚⠀⠀⠈⠻⢿⣷⢣⢸⡌⠆⢠⠀⢹⠀⡅⢀⠀⢀⠀⠰⢀
⣟⣸⡿⠛⠊⠁⠀⢀⣠⡴⠚⢉⠀⠄⠀⠀⠀⠄⠁⢀⠞⡤⠺⠁⠀⠀⠀⢀⣤⣶⢟⡋⢿⢀⢈⡄⡄⣀⢣⡈⠀⣸⠃⠀⣾⠈⡀
⠁⠀⠀⠀⢀⡤⠴⠋⢁⡀⠢⠀⠀⡠⣂⠄⠀⠀⡰⠋⠘⡽⠀⠈⢠⠀⠀⠀⢈⡿⣸⡅⣻⣈⡌⢰⡟⢋⠀⡇⠁⠇⠀⠂⢸⢸⣷
⢀⣠⠴⠚⠁⠀⢀⡸⠁⠀⠀⣐⣄⠣⠀⠀⠀⡜⢡⢠⣼⠃⠀⠀⣾⠀⠀⠀⢈⣸⣛⣛⣋⢿⣃⡘⣧⠄⠀⣷⢠⠀⡼⠀⡖⢨⡾
⠉⠀⠀⣠⣶⠙⠋⠀⢀⢠⣳⠹⠌⠀⠀⢠⠌⠄⣠⡻⠇⠀⠀⠐⠇⠀⠀⠀⠩⠑⠛⠋⢉⢴⡇⣧⢸⣧⠀⠁⡿⢡⣻⠀⡿⡘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⣤⣤⣴⡄⢀⡀⠀⠀⣀⣀⠀⠀⢠⣤⣿⣧⣤⣤⠀⡀⠀⣤⣤⣴⣾⣷⣄⣤⣤⣴⠦⣠⣾⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣶⣤⢖⣤⣤⣡⣸⣾
⠛⢻⢻⢛⠛⠃⡛⠛⠓⢛⠛⠻⠛⠛⠛⠛⠛⠃⠉⠁⠀⠈⠀⠈⠉⠙⠉⠉⠛⡿⠟⠛⠛⠉⠉⠀⠀⢰⠆⠀⠀⠀⠸⡭⠿⣿⣿⠾⣿⣿⣿⠿⣿
⢠⠁⠀⡀⠀⠢⠈⠀⢈⠀⠀⠐⠂⠀⠀⠀⠄⠀⠀⠀⠒⠂⢀⡀⠈⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠲⢤⡀⠉⠒⠤⣀⠒⠤
⡘⢰⠀⡧⠘⡀⠀⢄⠀⠑⠄⡀⠀⠢⠈⠁⠢⢀⠀⠢⢄⠀⠀⢀⠀⠂⠀⠤⠄⠀⣀⠤⠂⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠐⠦⢀⠙⠲⠤⣀⠙⠲
⠁⢼⠀⢰⠀⢠⠀⠀⢂⠀⠀⠙⢦⡀⠀⠁⠀⡀⠙⠢⡀⠙⠢⣀⠁⠦⣀⠀⠈⠉⠀⠀⠚⠀⠀⠐⠂⠀⠠⠔⠒⠈⣀⡠⠤⠂⢀⠁⠲⣄⠈⠑⢤
⠀⣼⠀⢸⡄⠀⠇⠀⠀⠳⡄⠀⠀⠹⠄⠀⠀⠈⠢⠄⠈⠲⠄⠈⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⠐⠖⠆⠀⠠⢠⠒⠈⠁⢄⠈⠙⢦⡀
⠀⠸⠀⠀⠧⠀⠘⠀⠀⠀⠡⠬⠍⠀⠀⠀⡀⠤⠈⠀⠀⢀⡐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠶⠆⠀⠀⡤⠤⠀⠳⠀⡀⠃
⠠⠀⠐⠀⠀⠂⠀⣀⠀⠠⡄⠀⠢⠀⠒⠀⠁⠀⠀⡀⠀⠀⠉⢀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠒⠀⠀⠠⠤⠀⠀⠲⠒⢀⠉⢀⠤
⢶⠀⠘⠀⠉⠁⠀⠀⡀⠀⠠⠤⠄⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠀⠐⢀⣤⠄⠀⠈⠁⣀⡤
⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣄⣀⡄⠀⠀⢀⣠⠄⠀⠀⠈⠀⠰
⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⡀⠀⠈⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣀⠀⠀⠀⠀⣠⡴⠆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⡠
⠀⠀⠀⠀⠉⠙⠒⠤⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠊⠁⠀⠀⣀⠀⠀⠈
⢾⣶⡄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠰⠓⢤⠄⡀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠉⠉⠉
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠉⠁
⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠚⠂⠀⠀⠀⠀⠀⠰⠗⠂⠂⠒⠀⠀⠀⠀⠚⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⢤⡤⠤⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⢀⣤⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠈⠉⠁⠄⠀⠈⠙⠛⠓⠀⠀⠀⠀⠀⢀⡴⠾⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⠀⠀⠄⠒⠂⠀⠀⠀⠘⠉⠉⠉


⠀⡀⠄⣠⠄⣀⡀⠀⡀⠀⣀⠀⡀
⢦⡈⠲⢄⡉⠒⢭⡑⠂⠤⢀⠋⠥⣂⠢⠤⣐⡂⠤⢀⣀
⠀⠙⢦⡀⠙⠢⣀⠈⠓⢦⣀⠉⠲⢤⣌⡁⠂⠬⣉⠓⠲⠭⣝⡲⠤⠤⣄⡀
⢳⡀⠀⠙⣦⠀⠈⠳⣄⠀⠈⠳⢶⣀⠈⠙⠳⢤⣀⡉⠑⠶⢤⣍⠙⠒⠦⣭⣙⠒⠦⠤⣄⣀
⠈⢻⣤⠀⠈⢳⡄⠀⠈⠻⣤⠀⠀⠉⠳⣤⡀⠀⠈⠑⠶⣤⣀⠈⠙⠲⢦⣀⠉⠙⠲⢦⣄⡉⠛⠲⢦⣄⡀
⠀⠀⢷⡀⠀⠀⠙⣤⠀⠀⠈⢣⣄⠀⠀⠈⠻⣦⣄⠀⠀⠈⠙⠷⣤⡀⠀⠉⠛⠶⣄⡀⠈⠙⠲⣦⣀⠈⠉⠛⠶⣄⣀
⡇⠀⠈⢿⡆⠀⠀⠙⣷⡀⠀⠀⠙⠷⡀⠀⠀⠀⠙⢷⣦⠀⠀⠀⠈⠛⢷⣤⡀⠀⠈⠛⠷⣤⣀⠀⠉⠳⢦⣤⣄⡈⠙⠳⢦
⣿⣶⠶⠾⠿⣶⣶⣶⣿⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣾⣿⣿⣿⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⣠⣤⣤⣴⣶⡾⠟⠻⣷⡀⠀⠀⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⣏⠉⠁⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠘⠻⢷⣶⣤⣄⣀⣀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠉⠉⠛⠛⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠿⠛⠉⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢷⣶⣶⣶⣶⣶⣶⣶⡾⠿⠿⠟⠛⠋⠉

⠀⠄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠃⠓⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠂⠀⣒⣒⠲⣂⠀⠓⣀⣒⡂⠐⣖⣚⡀⠛⣂⣙⣂⡛⣆⠐⢂⣘⣳⠀⣲⣘⠃⠠⠓⠈⢻⠂⠛⢂⡼⠏⢻⡧⠛
⠂⢀⡒⠀⠀⢹⡆⠀⠘⢳⠀⠀⠉⣷⠆⠀⠈⠳⡀⠀⠒⣃⡀⠚⠃⡀⠘⠁⢠⡘⠃⠀⣬⡋⠀⢀⣍⠀⠀⣍
⣀⠘⠉⠀⠀⡈⠉⠀⠀⢘⣳⣀⠀⠉⢉⣥⡀⠈⠙⢀⣄⣉⠉⠀⢈⣹⡁⠀⠈⠍⠀⠀⠉⣁⣀⠀⠈⢀⣴⣤
⡛⢓⠄⠦⠀⢹⡓⠤⠒⠀⠍⢉⡁⠀⠈⣁⡈⠀⣀⠭⠉⢉⠁⡀⠈⢙⠋⡄⠈⠙⠣⠀⠀⢙⣙⡂⠄⠠⠉⠉⡄
⣿⣿⣾⣷⣶⣾⣿⣷⣾⣾⣾⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣾⣿⣿⣷⣾⣿⣷⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠄⠐⠤⠀⠴⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡌⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⠄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡊⠀⠈⡆⠀⠀⠀⠀⠀⢀⠀⢤⠈⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡏⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣀⣄⣀⢤⠔⠄
⠀⠀⠀⠀⠇⠀⠀⠐⢠⡤⢐⠂⠉⠀⠀⠀⠒⠀⠀⠁⠂⠄⠀⠀⣀⡀⣠⠔⠈⠔⠠⠠⡓⠄⠈⢄⡠⠄⠀⣀⢄⣠⠊⠒⠦⠠⠀⠀⠓⠊⠀⠀⠉
⠀⠀⠀⠀⢠⠀⠐⠀⢨⠑⠢⠌⡁⠒⠀⠄⠀⠀⠀⠀⠀⠄⠂⠈⠤⠿⠃⠀⠁⠸⠀⠀⠈⠢⠀⠀⠑⠀⠲⣁⣀⣠⣤⣤⣤⡤⠖⣶⢒⡲⣖⣲⣒⠒⠐⠄
⠀⠀⠀⠀⠀⠒⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠚⠀⠖⠈⠀⠀⠀⠀⠀⠈⠢⣀⠂⠀⠀⣀⡠⠔⣂⡥⠙⡊⠕⠋⡁⠔⠊⢁⠠⠐⡠⠒⡁⠔⡡⠔⠉⠩⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⠀⠘⠁⠀⠐⠳⠆⢉⡅⠊⢁⠠⢰⣍⣠⠔⢁⡠⠐⠈⡠⠐⢁⠄⠊⡠⠊⠀⢀⠔⠁⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠬⢑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢺⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⠃⠀⢰⠆⣁⡠⠒⢁⠠⠂⠁⠔⠁⠀⡠⠂⠁⡠⠈⢀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠑⡀⠁⠂⠄⡀⠀⠀⡀⠀⠈⠉⣨⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣠⣰⠀⠈⢉⡘⡧⢤⡊⠁⡀⠔⠁⠀⡠⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠂⠒⠒⡈⠁⢀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠑⠋⠈⡁⠠⠀⠂⣉⣙⠈⠱⠒⡰⠣⡄⣠⠂⡠⠔
⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠒⠃⠀⠀⢀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠈⢉⡁⠠⠂⡰⠀⠀⠀⠀⠀⢀⠠⠒⠉⢄⡒⠢⣌⣉⠒⠩⢴⡒⢬⠉⡑⢄⡈⣑⠒⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢀⡧⠀⠒⡿⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠀⠠⠒⠈⠀⠀⠐⠀⣠⢊⡀⠎⡉⠒⠠⢍⣉⠒⠒⠅⣓⠢⠬⠢⣒⠆⢅⠙⠠⡁
⠀⠀⠀⠀⠀⠘⡗⠀⠁⠀⠀⡇⢀⣠⣿⠀⢀⠤⠐⠀⠁⠀⠄⠂⠁⠀⠠⠀⠀⠀⡠⢒⢊⠣⣈⠦⡑⡂⠚⢷⡤⢀⡈⠓⠢⢤⡁⠒⢄⠈⠣⢄⠈⠓
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠰⡏⢁⡠⠚⠀⠁⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⢀⣤⣊⣀⠛⠩⣉⠲⠤⡀⡉⠂⠤⣍⠢⢉⡐⠢⠄⢈⡃⠂⢌⡐⠤⡁⠒⢀
⠀⠀⠀⠀⢀⡠⡇⠀⡁⣀⠤⠊⠁⠀⢀⠠⠂⠀⠀⠀⢀⣀⡄⠂⠀⠰⠐⢈⣘⠆⠁⡑⠦⠄⢉⡒⢄⢉⠒⠤⢈⠐⠢⠬⡉⠒⢢⡈⠒⠠⢈⠑⠢⢕⡂
⠀⠀⠀⠀⠀⢀⣡⠆⠙⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⠌⠀⠀⣠⠟⢁⡘⠉⡀⠱⡄⣈⠑⠂⣤⠜⣠⢄⠉⠲⢄⡙⠢⠀⡈⠢⢄⡉⠢⢀⡀⠉⠠⢀⡉
⠀⠀⠀⠀⠴⠛⠁⠀⠀⡀⠈⠐⠀⠀⠀⠀⠀⠀⠘⠀⢰⣤⠞⠃⢾⡁⠈⠢⣌⠒⢄⢀⠙⠂⢄⠀⠘⢄⠑⠢⠤⡈⠢⣄⠉⠢⡀⠈⠉⠂⢌⠠⢄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡞⠀⡎⠉⠦⡀⠑⠠⡀⠑⠆⣀⠙⠢⡀⠙⢤⡀⠉⠒⠢⣈⠒⠤⠉⠒⣌⡒⠤⡀⠀⠈⠢⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠒⠀⠉⠒⠀⠘⠂⠀⠀⠑⠀⠈⠐⠀⠈⠂⠀⠀⠈⠀⠀⠂⠀⠀⠁⠀⠉⠂⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⣴⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠁⠈⠉⢁⣘⣿⣿⣿⡟⠛⠀⠀⠀⠀⢀⡀⢀⣾⡿⠛⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⣿⣿⣦⠀⠀⢻⣿⣿⣿⣿⡇⢸⡀⠀⣠⣤⠘⠓⢸⣿⣶⣿⡶⠆⠁⡀
⠀⠀⠀⠀⡠⠐⠀⠈⠀⠀⠀⠀⢀⡀⠀⣀⡀⢀⣿⣿⣿⣿⣄⣀⣀⣿⣿⣿⣿⣧⣾⣄⠀⠙⣿⣷⣤⣤⣿⣿⣷⣶⣶⣗⣀⠄
⠀⠀⢰⣏⠀⣾⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣈⣻⣿⣿⣿⡟⣿⣥⣶⣿⣿⣿⣿⣿⣥⣤⣀⣿⣿⢰⠀⣿⣿⣯⣯⠰⢀⣴⣲⠖⡃
⠀⠸⠿⠯⣭⠄⠶⢷⡨⠉⠀⠀⠀⠀⠉⠉⠀⠉⢙⡛⠛⠛⠋⡛⡛⠋⠉⠙⠋⠉⠙⠋⠛⢛⠉⡉⠀⠀⠉⠉⠙⢃⠀⠁⠀⠀⠀⠠⠀⣀
⠀⠀⠀⢀⣂⡀⢁⣀⠀⠠⣀⢀⢠⣠⠄⡁⣄⡀⡡⣀⣄⠤⠀⠀⠀⠀⢠⠀⢀⠀⠀⡈⡀⠄⠄⢀⠀⠀⠀⠠⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⡈
⠀⠀⠘⡧⣥⠙⢠⠶⠁⢹⣇⡛⡒⣍⣳⡇⢠⣰⡗⢁⡺⣔⡧⠀⢰⠉⠋⢃⠛⣀⠇⢀⣴⢏⠉⡻⠰⢏⡔⢩⣬⣧⣘⡀⠁⢐⡄⢷⡃⢂⣀
⠀⠀⠠⣿⢸⢡⣞⠞⢠⡈⢻⡄⣰⣍⡏⢸⠊⢹⡇⠪⡽⢙⡿⣶⡆⠙⢰⢢⠟⠟⢠⠟⢙⣶⣋⡁⠜⣿⣌⡹⠄⢰⡴⣄⢠⢼⠁⢻⠿⠉⡉
⠀⠀⠐⣿⢸⡷⣻⠨⣄⣽⢿⡀⣷⣌⡷⠲⡗⢸⣧⣸⡵⠌⣃⢤⣹⡣⡆⣼⢖⠃⢰⡖⠁⠹⢘⢹⣇⣉⣮⠁⢈⡑⣚⣉⠙⣀⢠⡼⠳⢒
⠀⠀⠤⣯⣸⡇⣻⢰⡇⠀⣿⠂⠻⢮⣧⣈⣟⢼⡅⣽⣟⠈⡗⣘⢩⡅⠜⣩⣻⡇⢸⡇⠾⢧⣄⢨⣿⣡⢯⡿⠸⡷⣩⣯⡵⠈⠟⠶⠃⡤
⠀⠀⠠⠿⢤⣀⣹⡈⣁⠃⣿⠐⠶⢓⡷⠼⠇⢠⡇⣺⣁⣘⣇⠐⢱⣍⡎⠉⢹⡃⢜⡃⠶⡫⠅⢼⣯⠘⢡⣿⣸⡟⣩⣟⡛⢘⡟⠸⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠚⠓⠦⠤⢤⣧⣤⣄⣘⡇⠈⠁⢸⣟⠀⠉⠛⢘⡱⠈⠥⠀⢸⣟⠀⣀⣷⣸⡏⣰⠏⠋⢸⡟⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠓⠶⠦⠤⢼⣅⡀⣀⠀⠰⡿⠀⠀⠁⢸⡏⠁⠑⠒⢺⠇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠓⠲⠰⠦⠬⠧⣀⡀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢰⠀⠀⣿⠀⢰⠇⠀⣰⠂⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠙⢦⠀⠹⡀⠀⠘⡇⠀⡏⠀⡼⠀⢠⠃⠀⢀⡞⠁⠀⠀⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠙⢦⡀⠳⡀⠘⠀⠀⠃⠀⠃⠀⠃⢀⠃⠀⡠⠋⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀⠉⠢⢄⠙⠦⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠔⠁⢀⠴⠊⠀⠀⠀⠀⣀⣤⠴⠾⣭⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡽⠖⠒⠲⣤⣀⡈⠁⠀⢠⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠤⠔⠚⠩⠋⢀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠹⠞⠙⢆⢸⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠖⠂⠀⢼⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣦⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣐⣶⣲⣆⣾⣾⣿⣦⣼⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢼⣆⠀⠀⠀⠀⠐⢰⠑⢺⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣇⣀⣀⣀⣼⣿⣫⣿⣿⣿⣿⣿⣿⣷⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⣶⣶⣤⣄⣠⣯⡴⣯⠷⡶⢶⠗⡶⠲⡶⢦⡤⣤⣤⣦⣼⡀⢸⣯⣿⡽⠷⠿⣟⣛⣛⣿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⡟⣿⢩⠇⣿⢁⡏⢠⡏⣼⢁⡇⣸⠁⡾⢠⠏⠴⠡⠞⣱⠯⢛⣫⠥⠖⣂⣩⡭⠤⠔⠒⣒⣒⣒⣒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣸⢰⡇⣸⠁⠾⠀⣋⣨⡤⢤⠲⡖⢦⠒⡺⠖⣉⠔⢊⡩⠔⣚⣩⠥⠒⢒⣉⣉⡭⠭⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⣉⣴⢲⡙⣏⠳⡜⢆⠳⠈⡠⢊⡠⢊⡠⠚⣩⠔⢋⣡⠴⠚⣋⡩⠤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠷⠘⡆⢱⡘⢠⠎⡠⢋⡴⢋⡴⢋⡤⠚⢉⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠉⠀⠉






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

⠀⠀⠀⠀⠀⣀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠠⢤⡟⠄⢠⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠰⠄⠀⡈⣠⣤⠀⠀⠀⠀⠀⠞⠉⠉⠙⢦
⠀⠀⠀⢰⠙⠺⠐⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⡄⢧⠀⠀⠀⠰⠋⠐⣁⠉⠀⠀⠀⢶⢮⡑⡀⠈⠀⢸⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢨⠆⠀⠀⠀⠀⣰⣁⡀⢀⡰⠆⠀⠀⠀⠀⡴⠃⠀⠈⠊⠓⠀⠀⠀⠐⠁⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠛⠒⠒⠒⠒⠒⠉⡅
⠀⠀⣰⠃⠀⠀⠀⠀⠠⣤⣀⣈⣉⢴⠆⠁⠀⠀⠰⡷⠦⣤⠴⠆⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠎⠀⠈⣠⠔⠒⠒⠒⠒⠙⠀⢰⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⢀⠆⠀⠀⠀⢷⢦⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢆⠀⠀⠁⠀⠀⠀⢀⡾⢗⡴⠃
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣀⣀⡸⣣⠎⠀⠀⠀⠀⠀⠁⠉⠭⢍⣁⣀⣀⣠⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣬⡭⠥⠖⠋
⠀⠀⠀⠉⠲⠤⣄⣀⣀⣠⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠚⠋⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠃⠘⣤⣠⡀⠀⢀⠀⠀⠋⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠡⠖⠒⠀⡀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠊⠀⠼⠀⠀⠘⢧⡙⠆⠐⠂⠀⠀⠀⢸⠤⢶⢴⡀⠀⣠⠖⢄⡀⠀⠈⠻⢵⣮⠕⢙⠁
⠀⠀⣾⠦⣄⣀⣀⡠⠴⠒⠀⠀⠀⠲⢤⠀⠀⠀⠀⠘⠦⠽⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡇⠀⣀⣬⡭⣀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⢠⡀⠀⠀⠀⣤⠤⠒⠉⠁⠀⠀⠀⠁⠀⠀⠀⡆⠀⠘⠒⠂⠐⠒⠀⠀⠀⢀⣀⡄⡴⠈⡇⠪⠥⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠱⣄⠀⠀⠻⣀⣀⣀⣀⡴⠁⢀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠐⠋⠉⠉⠉⣠⡾⠃⠀⠈⢀⠁⣀⠀⢀⣠⠎⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠈⠑⠲⠤⠤⠬⠭⠤⠶⠒⠋⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣈⣒⠶⠾⠟⠋⠀⠀⠀⠀⠀⠑⠺⠭⣉⣀⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢀⡀⠀⠀⣀⣴⡇⠀⠀⣾⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠐⣏⠉⠛⠋⠉⠈⡀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠙⣆
⠀⠀⠀⠘⢷⣄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠈⠛⠶⠶⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠈⠙⠳⠶⠤⣤⣤⣤⣤⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠉⠙⠛⠛⠛⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠄⡀⣀⡘⡀⠙⠀⠀⠀⠀⠈⠀⠁⠈⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⡤⠤⠖⠀⠑⠀⠀⠀⠀⠩⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠱⠂⠓⠀⠀⠀⠂⠀⠑⠄
⠀⠀⠀⢀⠔⠀⠘⠀⠀⠀⠀⠈⡁⠁⠠⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠂⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⣶⡄⠀⠁⠐⠠⠀⠀⠀⠄⠀⡀⠐⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠙⢻⣤⣀⡫⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠠⠠⠀⣀⠄⠀⠀⠀⠀⠄⠂⢸⡄⡖⢲⡔⣶⢒⡶⠶⡖⡞⢳⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⢠⠀⡼⠉⢿⠾⣇⠹⠀⠀⠀⠃⠁⠸⢀⠀⠈⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢀⡤⠂⠃⠀⡓⠊⡕⡠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡎⠈⢀⠠⠀⠙⢻⡟⠁⢛⠃⢰⠋⠁⣴⢟⢎⡇⠀⠁⢤⢰⢢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠂⠈⣀⣸⡇⠀⢿⠰⡿⠦⡀⠻⣍⣉⠄⠀⠀⢀⢟
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⢠⠀⠀⣿⣉⡽⠉⠒⠢⠤⣧⠀⠤⠀⠀⠒⠀⢰⠄⠈⡙⡀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠸⠀⠀⠈⠉⠀⠀⠁⣆⢄⡇⠀⠀⡀⠈⠀⠀⢐⠣⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⢈⡳⠀⠀⠀⠰⡄⠁⠈⠀⠘⠁⠀⡀⠀⠊⠁⠀⠂⠁⠈⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠆⠊⠀⠀⠀⠀⠒⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁

⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣤⣤⣤⣄⠀⢴⣦⣤⣴⣤⣄⠀⠠⠄⡀⠀⠀⢀
⠘⠛⣷⠟⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠛⠛⠋⠀⠀⠙⡿⠻⣿⠇⠀⠘⠿⠋⠀⠀⠙⠛⠁⠀⠀⠘⠷
⠀⢸⣿⠀⠀⠀⠀⠀⠀⣴⣧⣼⣿⣿⣿⣿⣿⣍⣵⡀⠀⠀⠀⠀⣠⣄⣀⣀⣀⡀⠀⠀⣀⡁
⠀⢸⢹⠀⠀⠀⠀⢀⡞⢻⣿⣿⣿⡟⢻⣿⣿⣿⡟⢳⡄⠀⠀⠀⠀⠙⡿⠿⢿⠀⠀⠀⠈⣿⣦⡀⠀⠀⢰⣾⡷⠀⠀⠈⠶⠀⠀⠀⠐⢦⡄⢸⡇
⠀⠹⠸⠁⠀⠀⠀⣿⡷⠾⣿⡿⣛⡷⢞⣛⢻⣿⠷⢾⣿⠀⠀⠀⢀⠀⣁⢀⢉⡀⣀⢀⢀⡉⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇
⠀⠴⠀⡅⠀⠀⠀⣿⡇⠀⣿⣷⡿⣷⢸⢿⣿⣿⠀⢸⣿⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⢀⡀⠀⢀⡀⠀⢀⡀⠀⠱⠃⠽⠀⠀⢠⡄
⠄⠀⠀⠁⠀⠀⢀⣿⣿⣿⣿⣟⣿⡟⢸⣿⢿⣿⣿⣿⣿⡂⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠈⠇⠀⠸⠇⠀⠸⠇⠀⠀⠰⠀⠀⠀⠘⠇
⠀⣀⣤⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢿⠛⣿⣿⣷⣶⣿⣿⣿⣆⠀⣶⣶⣤⣤⣤⣤⣶⣄⠀⢶⣶⣶⣶⣶⣶⣶⣶⡄⠀⣼⣷⣦⣀⣀⣤⣀⠀⠀⠀⢰⣶⡖⣶⣾⣿⠇⣼⣿⣿⣿⣅
⠀⠀⠀⡹⣟⠛⠋⠙⢿⡝⢿⡆⠈⠹⣿⣿⣿⣿⣿⣏⠀⠈⠹⣿⡿⢿⡿⢿⣿⠁⠀⠀⠈⢿⠿⠿⠿⡟⠀⠀⠀⠘⣿⣷⠿⠿⢿⣿⣿⣿⣟⣻⣿
⠀⠀⠀⠑⡄⠀⠀⠀⠃⠇⠀⠀⠀⠀⠸⡇⠀⠈⠹⠏⠀⠀⠀⢸⠁⠀⠀⡸⠻⠀⠀⠀⠀⠸⠂⠀⠀⠟⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠈⠻⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⡴⠚⠋⠉⠛⢦⡈⠙⢦⡖⠛⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣸⠥⢤⠤⠤⢤⠤⣷⠀⠀⠹⣦⠤⠤⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢻⠒⠚⠛⠛⠋⢛⡟⠀⠀⠀⢹⠛⠛⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⠴⠚⠀⢀⡤⠒⠚⠓⢦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠙⠲⠦⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠴⢤⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣠⣤⢭⣍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⠤⢤⣄⣀⣀⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⡠⠤⢄⡀⠀⠀⠈⠉⠉⠛⠲⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⢦⡀
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⡔⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁

⠲⣾⣴⡶⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒
⢺⡟⡿⠿⡷⠀⠀⠀⠀⠀⠠⠞⠛⠒⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⣾⣿⣟⣤⣰⣾⣦⠛⣶⣿⣿⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣚⣳⣶⣶⣦⣾⣿⣿⣷⣶⡶⠀⣠⠀⢶⣶⣾⣾⣿⣶⣆⣀⣀⣤⣠⣄⡀⣀⣤⡀⢰⣷⣶⣶⣂⡀
⠻⣿⠿⠿⣿⠿⠿⠳⠾⠿⠿⠤⠁⠀⠀⠀⠀⠸⠆⠀⠀⠉⠉⠉⠉⠉⠿⠏⠁⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠏⠋⡉⠁⠉⠉⠉⠉⡉⡍⡛⢛⠋
⡋⠤⠚⣁⠤⠖⠊⠉⣀⠴⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠠⠉⠈⢉⡉⠀⠒⢀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠡⠀⢈⠀⠈⠀⠂⠠⢀⠀⡀⢆
⣠⠔⠋⢁⡠⠴⠒⢉⡠⠔⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠠⢄⡀⠀⠠⣄⠀⠐⠀⢀⠀⠀⢀⠄⠂⠀⠠⠄⠈⠀⠀⠀⠀⠀⠄⠁⠀⠐⠀⢀⠀⢸⠀⠇⠸
⢀⣠⠔⠉⠀⡠⠀⠉⠀⠠⠄⣀⡀⠑⠒⠤⠄⡀⠁⠐⠀⠀⠀⠐⠂⠀⠉⠋⠀⠀⢀⡤⠀⢀⠠⠊⠁⡀⠔⠁⠀⠀⠊⠀⠀⣠⠞⠀⠀⠀⠌⠀⢀⠄⠀⡀⠀⢷
⠋⠁⢀⠔⠋⠀⡀⠚⠀⢤⠀⡀⠉⠠⠶⡶⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠖⠉⢀⡠⠊⠁⣀⠄⠁⠀⠀⢀⠞⠀⠀⠀⣠⠋⠀⠀⠐⠀⢀⡇⠀⣸
⠀⠐⠍⠀⣠⠎⠀⣀⣀⠀⠁⢀⣄⡄⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⡀⠂⠀⠀⠀⡄⠀⣼⠀⠀⡿
⠀⣀⠐⠢⠀⠠⣄⡈⠉⢀⡀⠀⠐⠀⠠⣤⡖⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠀⠁⠀⠚⠀⠤⠀⢀⠀⠀⡐⠀⠀⠄⠀⠠⠀⠀⣀⠀⢀
⠣⠈⠁⠀⠐⠦⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⡀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⣀⠀⠁⠀⠘⠃⠀⠰⠖⠀⡤⠀⢈

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠄⠒⡏⢡⡆⠂⠀⠐⡆⢹⡃⠂⢄
⠀⠀⠀⠀⠀⠀⠻⠄⣀⢸⠀⢰⠂⠁⡈⠀⠀⡆⠱⣇⠀⠀⠠⠆⢰⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠏⠀⠠⠄⠠⠄⠤⠄⠀⠀⠄⠠⠀⠠⠤⠀⠄⠧⢠⠈⠀⠀⠙⠵⣆⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠤⠤⠀⠄⠀⡄⠀⠀⡈⠀⠀⠀⠀⠀⠘⠢⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠐⠀⠀⠐
⠀⠀⠈⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢀
⠀⠠⠄⠀⠀⢂⢀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠤⠀⠀⠀⠀⠎⠀⠀⣀⡀
⠀⠀⢀⠐⠂⠂⣂⠀⢢⠃⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⢴⠆⠀⠀⠀⠀⠀⠘⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠁⠀⠀⠀⠻⠀⠭⠡⠼⠁⠀⣉⡅⢙⠀⣈⠁
⢀⣀⣀⢠⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡶⠂⠈⠉⠲⣟⣨⠉⣄⠐⠆⠀⠀⣠⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠧⠤⠟⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢊⠋⠀⡭⠘⢃⠀⢳⡏⠡⠈⡈⠁⡏⠀⠀⠁⣈⠀⠋⠛
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣤⡄⢀⠀⢰⣤⣀⡄⠀⠈⠁⠀⠀⠀⠀⠧⣄⠀⢶⡀⠀⠀⠀⠀⠀⢸⣙⡄⠘⣧⣭⠀⠀⠀⠧⠄⠠⡀⠅⠠⠄⠸⠄⠀⢄⡁
⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠙⠋⡀⠀⠘⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⣑⠁⠀⠀⠉⠀⠀⠈⠁⠀⠀⢀⠐⠀⠀⢹⠆⠀⢰⡀⠂⢀⠘⡇
⠀⠀⢤⠏⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠐⢀⢀⠀⠀⢠⣤⠀⡐⠙⡀⠿⣤⠙⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠀⠄⢀⢠⡄⢺⡇⠐⣿⢂⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠠⡧⠀⠰⣆⡀⠀⢠⡾⠀⠈⣧⠀⣜⠣⢠⣄⠊⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠤⠁⣀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⠋⠀⣮⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠈⠉
⣿⣟⠛⣿⠏⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿
⣿⣦⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠇⠀⢠⡿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠉⠙⠛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠤⠤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⢠⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⡾⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣸⠃⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣤⣤⣤⣤⡤⠴⠞⢉⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⣷⡲⠦⢤⣤⣤⣤⣤⠤⠶⠚⠋⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⡟⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠲⠶⠶⠖⠒⠒⠛⠛⠋⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⣀⣀⣀⠀⠀⠀⠀⢤⣀⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣬⡤⠠
⣶⠶⠶⠆⠀⠀⠐⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠀⠈⠉⠉⠉⠭⠅⠈⠉⠩⠍⠁⠠⠈⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⠤⠼⠇⠐⠀⠐⠐⠓⠒⠒⠀⠀⠀⠀⠒⠒⠀⠄⠀⠠⡄⣀⠀⠠⠄⠒⠂⠀⠚⠛⠒⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⠛⣛⡋⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒⠒⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠺⣿⠋⠀⣿⣿⣧⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠛⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠀⢸⠷⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠉⠉⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠀⢀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠉⠁
⠀⠀⠀⠀⡼⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢰⠇⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⣸⠀⠀⠀⠀⠀⣈⠙⠒⠶⠦⠤⠴⠖⠚⣉⡤⠖⠦⣄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣭⡟⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢸⡀⠀⠀⠀⠀⢹⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠺⣷⣦⠄⢠⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠼⠽⡿⣆⣠⣤⣄⠀⠀⢀⣀⣉⣴⣧⣉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⣀⣽⣶⣶⣶⡶⠿⠟⠛⢻⣿⣿⡟⠀⠲⠿⢛⠉⣬⡄⢿⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⣍⣳⡀⠙⡟⢶⣄⠀⠀⣾⣿⣿⠿⣏⠀⠒⡖⠀⢾⠋⣿⠋⠀⠀⠀⠀⣸⠀⢿⡧⢸⡇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣍⣉⠳⡈⠹⡿⢶⣷⡀⢙⠻⣆⠙⠿⢿⣆⠘⠀⠀⢀⠤⠈⠆⢸⠀⠀⠀⠀⠀⡏⠀⣀⠤⣼⣿
⠀⠀⠀⠀⠀⣼⣿⠛⠛⢯⠉⠻⡿⢶⣷⡀⢹⠻⣿⣦⣿⣄⠀⠀⠀⠹⣆⠀⠀⠃⠄⠁⡏⠀⠀⠀⠤⠤⠧⠤⠿⠤⠼⠿⣤⣄⡀
⠀⠀⠀⠀⢸⣿⣇⣶⡔⠀⠑⢢⣧⡀⢹⠻⣿⣦⣿⣌⡛⢿⣷⣦⣠⢰⡇⠙⠶⣦⣤⣶⣅⣀⠀⠀⠀⠉⠙⣛⣛⣛⣓⡒⠂
⠀⠀⠀⠀⣰⣿⣯⣉⣛⣿⣿⣤⣀⡤⠛⣢⣿⣬⡙⢿⣿⣦⣝⢿⣿⣮⡙⠓⠶⢤⣉⡿⠋⢿⣿⠛⠒⢦⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣹⣿⠿⢿⣤⣤⡔⠛⠙⣻⢿⣯⣙⠿⣿⣷⣌⡻⣿⣷⣝⠻⣿⢦⡈⠁⠈⠁⠀⠘⣿⣧⡆⠀⠈⢷⡄
⠀⠀⠀⠀⣿⣿⣷⡖⠊⠉⡻⠿⢿⣶⣶⠿⢿⣷⣮⣙⢿⣿⣮⡙⢯⣷⣌⢷⣽⣦⠀⠀⣀⣀⣽⣿⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣦⣤⣖⣉⣽⣿⣶⡿⢋⡿⣷⣬⡻⣿⣷⣝⢿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡛⢋⠀⠈⠐⢹⣿⣿⣮⡻⣿⣷⡝⣿⣷⡹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣭⣂⣠⣾⣿⣬⡻⣿⣾⣿⣿⣮⡻⣿⣮⢿⣿⣿⣿⣿⣿⡦⠄⠐⠒⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠿⠿⢿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣾⢿⣷⣽⣿⣿⠿⠛⠛⠉⠙⠶⣄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣇⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣏⣉⣩⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢾⣿⡟⠀⣿⣿⣿⡿⠟⠋⢁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⣿⣿⣿⣿⣧⡄⠈⠢⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡙⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⢏⣼⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠓⠘⠁⠛⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣀⣦⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠈⢻⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⡿⠿⣿⢿⡇⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⣯⣾⣿⡿⠀⠀⠀⠀⠀⢀⣿⣀⣠⣶⡄⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢠⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠉⣹⢋⡏⠀⠀⠀⠀⠀⠘⠛⠿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⠛⠉⠁⠀⠀⠀⢾⣷⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⢠⣿⣦⣤⣤⣄⣀⣀⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠙⠉⠻⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠛⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠘⣿⡿⠛⠻⠛⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣦⣀⡶⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣿⣀⡄⠀⠀⠀⠀⠘⠛⣿⠿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡠⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⣠⣰⣿⡿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠻⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣅⡀
⠀⠀⠀⠘⠋⠀⢹⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠐⣾⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠈⠉⠉⠉⠛⠛⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⢰⣿⢽⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠀⣹⣄⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠋
⠀⠀⠀⠀⠀⡼⣿⢸⡿⡄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⢧⡇⡸⣧⣇⠀⠀⠀⠀⠀⣴⡧⠀⢸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⢸⣧⠀⠀⠰⡗⠠⡄⠀⠀⢰⣦⠀⠀⠀⢸⡆⠀⠷⡶⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣨⢩⠇⡐⣏⢈⠀⠀⠀⠀⢸⣿⣿⢒⡛⣛⣛⡻⠿⠿⠟⠿⠿⠿⠟⣛⣛⣛⡒⣿⣿⡇⠀⠀⠀⠀⠁⠀⠀⠘⠋⠀⠀⠀⠘⠃⠀⠀⠃⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣏⣸⡄⡁⣿⡀⡇⠀⠀⠀⣸⣿⡇⠀⠀⣿⣿⢤⣿⣿⡆⢰⣿⣿⣆⣿⣿⠀⠀⢸⣿⡇⠀⢰⣆⣦⣶⣰⣤⣆⣦⣴⣴⣆⣦⣴⣰⣦⣦⣶⠀⠀⠀⢋
⠀⠀⠀⢸⠁⢸⠀⠀⢹⠀⢱⠀⠀⠀⣿⣿⣇⣀⣀⣿⣿⢘⣟⣹⡇⢸⣟⣻⡇⣿⣿⣀⣀⣸⣿⡇⠀⢸⡏⡏⣿⢹⣿⡏⣿⢹⢹⡏⣯⢿⢹⡏⡏⣿⠀⠀⠈⣿⡀
⠀⠀⠀⡎⠀⣾⠀⠀⢸⠀⠈⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⡇⢸⣿⣿⡃⣿⣿⣿⣿⣿⣿⣏⠀⢸⣧⣧⣿⣼⣷⣧⣿⣼⣼⣧⣿⣾⣼⣧⣧⣿⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠀⠘⠃⠋⠙⠘⠉⠃⠛⠘⠘⠃⠋⠙⠘⠃⠋⠛⠀⠀⠀⠉

⠀⢐⣾⣿⣿⣿⣶⣤⣀⣀⣀⣤⣄⣀⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢶⣄
⠀⠀⣿⠃⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⡀⠀⢻⣿⣿⣶⣷⣶⣶⣶⣾⣿⣿⡆⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⣿⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢻⣿⠿⠛⠛⠋⠻⣿⣏⠸⣿⣷⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⠫
⠀⠀⠀⠀⠰⡋⢹⠀⠀⠀⠀⠀⡼⢻⡆⠹⠿⠀⠀⠀⠈⢻⣿⡟⠛⠛⢿⣿⣿⣷⠀⠀⠀⠀⠀⠈⢻⣿⠉⠉⠛⠉⠈⣿⣿⠈⠀⠀⠀⠀⠀⣿⠈⠉⠁⠀⢻⡆
⠀⠀⠀⠀⠀⠙⠾⠁⠀⠀⠀⠘⠁⡼⠀⠀⠀⠀⠀⠀⠀⠸⢹⠇⠀⠀⠀⠸⢷⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡼⢃⡟⠀⠀⠀⠀⠀⠠⢿⠂⠀⠀⢀⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀⠐⣶⡄⠀⢠⣿⠁⠀⠀⠀⢰⡆⠀⠀⢀
⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⢠⡤⠤⠼⣷⡤⣿⠤⢴⠽⢦⠦⣾⡤⠤⠤⠤⣾⠤⠤⠤⣿⠧⢴⡤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠀⢸⡹⢶⣄⠘⡧⠘⠃⠘⠁⠀⠀⠉⠀⠀⠀⠈⠙⠒⠂⢼⠃⣠⠟⠤⠀⠃⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⡰⠄⠀⡄⠀⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡼⢯⡀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⣀⢀⣠⣸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⡾⢛⡿
⣤⣤⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠻⠾⡿⠋⠀⠀⠀⠠⠤⠄⠀⠠⠤⠶⠠⠄⠐⠶⠶⠤⠔⠶⠶⠶⠶⠶⠖⠒⠒⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣆⠀⠀⠀⠀⠀⡀⠀⡆⠠⣄⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠐⠋⠙⠃⠀⠀⠀⠒⡈⠛⢀⣠⣤⣠⣤⡀
⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⣶⣶⣦⣤⣤⣤⣦⣵⣾⡿⡏⠤⢿⣿⣿⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡉⠉⠀⠀⠀⠁⠀⠀⠀⠘⠙⠀⠁⠙⣄⠀⢴⢺⠗⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣶⡄⣐⣆⣀⢠⢀⠀⠀⠀⠰⣀⡙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⣿⣿⣿⡿⢻⣿⣋⣿⢋⡄⣀⢤⡴⠉⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣛⠉⠉⠉⠁⠙⠉⠛⠁⠋⢿⣿⠟⠱⠿⠋⠀⠀⠀⠀⢀⣠⢀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣷⣶⣶⣶⣶⣦⣤⣤⣤⡤⢀⣤⣤⣤⣤⣥⣼⣦⣤⣤⣤⣶⣶⣶⣿⣷⣞⣷⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⢿⣧⠛⢿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣼⣮⣄⠙⣧⡀⠻⠿⠟⠐⠙⠛⠛⠋⠻⢿⣿⣿⣿⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣮⣵⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠧⠀⠀⠀⠀⣻⣿⣿⣿⣿⠟⠋⠉⠁⠁
⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣠⢀⣀⣤⣤⣤⣿⣦⣄⡀⠈⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣦⣽⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⠿⢿⠭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠟⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠻⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡼⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣏⣳⡇⠀⠀⣿⠇
⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠓⠒⠒⠒⠲⠦⢤⣀⠀⠙⠿⠿⠟⠁⠀⢠⡿
⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⡤⠤⠖⢀⣀⡴⠞⠁⠀⠀⠀⠀⢠⡿⠁⠀⣀⣀⣤⠶⠶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⡾⠋⠉⠁⠀⠀⠸⠷⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠓⣦
⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠉⣆⠀⠀⠈⣷
⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⢀⡞⠀⠀⠀⣿⡄⠀⠀⠸
⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡇
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡿⠀⠀⢰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⡿
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠤⠖⠋⠀⢀⣴⡟⠁
⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋
⠀⠀⠈⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣶⡶⠿⠛⠉

⠀⠠⠀⠀⠀⠀⠀⠠⠤⠤⠄⠠⠤⠤⠀⠀⠀⠤⠤⣄⣠⣤⠤⠀⠀⠠⠀⠀⠀⠤⠄⠀⠠⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢀⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⣶⣾⣿⣚
⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣫⣷⢮⣕⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠡⣿⡟⠆
⠀⢠⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣬⢴⣿⣤⣷⣷⣦⣥⣶⠠⡾⣛⣿⣤⣄⠀⣐⣟⡁⠀⣀⣀⣠⣤⡀
⠀⠐⠒⠦⠤⢤⣬⡍⠛⢛⣻⣟⣿⣿⣺⣗⣿⣿⣿⣏⣭⣭⣽⡟⠋⠛⣿⣅⣠⣬⣿⡿⠯⠁⠀⠀⠀⠉
⠀⣴⣶⣶⣶⡶⠶⠾⠿⠿⣛⠛⠋⠉⠉⠉⢽⣿⠍⠁⠉⠉⠈⣉⠀⠈⠙⠛⠋⠙⣿⣶⣿⣶⣶⣶⣶⣶⡀
⠀⠈⣭⢅⣀⡀⢠⣀⡔⢿⡿⠁⠀⠀⠀⠀⠰⣿⣿⣿⣏⡟⢃⣹⣿⢋⡁⢶⣆⡐⠶⢏⣉⡩⠉⠁⠀⢉
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⣿⣦⡄⠀⢀⠀⠀⠉⠻⢿⣿⣷⣸⢿⡿⣼⡇⢸⡿⣧⠐⣿⣿⣷⣶⣷⣾⣿
⠀⢺⣿⣿⣿⣿⣿⣟⠛⠛⠻⣿⡉⠉⣹⠁⠀⠀⠀⠀⠙⠻⢿⣾⣵⣿⣏⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢺⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠠⣾⣡⡀⠀⠀⣤⣤⡀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⢼⣛⢦⣽⠿⣷⡄⠻⠿⠃⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣟⠉⠉⠁⠀⢀⣠⣿⣿⣄⣀⣀⣤⣤⡤⠖⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠷⣶⣶⣶⡿⠿⠻⠿⠛⠛⠻⢶⣄⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⢠⣶⣒⣀⣀⣠⣿⡿⣿⠢⣤⠾⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠐⢦⣉⠉⠉⠉⢉⣁⣴⡿⠁⠀⣰⣿⠃⠀⣠⣴⡾⠟⠛⠛⠛⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠋⠁⠀⣠⣾⡿⠋⣠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠻⠷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡿⠟⠋⠀⣰⣿⡟⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⢀⡘⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⣠⣞⣩⡿⠛⣩⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠛⠿⠛⠁⣴⠿⠟⢛⣩⡴⠾⠛⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠙⠛⠛⠛⠶⢶⣾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠉⠛⠛⠛⠓⢲⣦⣤⣤⣶⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠟⠛⠛⠿⠿⠯⠻⢿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⣀⣴⣾⣿⣵⠶⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠷⠟⢉⣿⠻⣿⣿⣷⣦⣤⣤⣤⣬⣭⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠹⣿⣧⡀⠀⠉⠉⠉⠉⠛⠛⠛⠉⠁⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠈⠛⢿⣿⣶⣶⣦⣤⣤⣤⣴⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢸⣠⢤⠜⡏⠉⡀⠀⠀⣐⡁⠈⠀⠀⠁⡤⠀⣀
⠀⠀⠀⠀⠀⠀⢴⠂⠀⠀⠁⠀⠀⡄⠀⢀⠀⠀⠰⠄⠴⣖⠒⠋⠠⠇⠀⠀⠀⠈⠂⠂⠉
⠀⠀⠀⠀⠀⠀⣘⠄⠀⠀⠜⣠⢀⠔⠋⢝⡀⠀⠈⡡⠀⠈⠂⠀⠀⠃⠀⣄⠀⠀⡄
⠀⠀⠀⠴⠋⠀⡅⠀⠀⠀⠀⢸⠀⠈⠃⢠⡁⠉⠉⠁⠀⢠⠄⠈⠀⠈⠂⠒⠀⠂⠀⡀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠈⢻⣦⣄⣯⠇⠀⠀⠂⠒⡠⠀⠘⠉⡴⠊⠁⠀⠉⠉⠂⡤
⠀⠀⠀⠀⠀⠔⠈⠈⠀⠀⠀⠁⠀⠀⠀⢰⣼⡇⠀⡤⡀⠀⠡⠀⡢⠐⠀⠀⠈⠀⠈⠠⠀⡄
⠀⠀⠀⠀⠀⢀⠀⢐⠂⠀⠈⢀⠀⠀⠒⡀⢸⡟⢒⣛⢀⣀⣀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⢨⠴⠛⠠⠂⠀⠀⠈⠈⢸⡧⣯⣹⡇⢿⠛⠋⢹⡟⠇⣷⠐⠒⠄⠀⠥⠰⣠⢤⠔⠀⠂
⠀⠀⠀⠀⠀⠀⡇⢌⠀⠀⡔⡠⡤⠀⢮⡣⢞⢄⠉⠉⠛⠉⠀⢀⡀⠀⠠⠉⢢⠀⠀⢀⢀⡜⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣧⢠⡟⠃⡀⠀⡱⣤⡷⠞⢶⠆⢠⠖⠂⣠⣴⣢⡀⠕⠐⣁⣠⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢀⠟⠚⠁⠠⢃⡁⠂⠀⡇⠀⣸⢠⣾⣀⢠⣿⡚⠛⠁⡀⢈⢹⡇⠛⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠂⠂⠀⠀⣀⠀⢰⠟⢻⠗⠤⢌⣀⣗⢈⣁⠈⡉⣍⠀⢠⡀⠓⡇⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠟⠀⠸⠀⠀⡇⠠⢈⠛⠋⠆⠆⡠⡀⡏⠀⠀⣀⠻⠊⠊⢸⡂⠺⠊⠊⠊⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠈⡁⢀⢠⠄⠓⡄⠤⢀⠠⣄⠙⠚⠁⠰⠎⢐⡀⡀⠒⠉⠰⠐⠇⠣⠒⠒⠐
⠀⠀⠀⠀⠀⠀⠐⠈⠈⠡⠊⠀⠉⠀⠬⠒⠁⠉⠐⠂⠒⠀⠈⠨⠅⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠒⠄⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠠⠀⠉⠐⠀⠀⠀⠀⠀⠀⡆⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡟⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣯⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠢⠤⠀⠀⠀⠒⠒⢰⠃
⠄⠀⠀⣦⡄⠀⠀⢹⣿⣿⣿⣿⣿⠀⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠂⢸
⠐⠀⠰⢿⣿⠆⠀⠀⠙⠁⠈⠛⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠙⠀⠒⠀⠐⠂⡀⠐⠀⠀⠀⠀⠁
⠁⠀⠈⠀⠀⠁⠀⠈⠁⠀⠈⠉⠉⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁


⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⢀⢀⢀
⣿⣻⣿⣻⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣻⣿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡀⢀⣀⠠⠈⢈⠁⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠁⠀⠠⢀⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣇⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠰⠀⠀⣀⡀⠠
⣾⣿⣏⣡⣤⡴⣤⣴⣯⡀⠀⠀⠀⠀⠀⠀⣶⡦⠶⣤⣤⣤⣾⣷⣤⣤⡄⠀⠂⣷⣴⣿⣧⣤⢀⠊⣀⣀⡀⣀⣄⢤⣶⣥⣴
⢿⠿⠿⡿⠿⢷⠾⠿⠧⠅⠀⠀⠀⠸⠆⠀⠉⠉⠉⠛⠻⠏⠉⠉⠉⠉⠀⠉⠀⠀⠁⠈⠉⠉⠛⠛⠛⠛⠃⠉⠉⠈⠹⠛⠛
⠅⢂⡡⠐⠊⣀⠄⠒⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠀⠀⠈
⠚⢁⡤⠒⢉⠠⠀⠁⠀⠀⠄⣀⠀⠀⠄⢀⠀⠀⣀⠐⠢⠄⠑⠂⢀⠀⠀⡠⠔⢀⡠⠀⠁⠄⠀⠀⡤⠈⠀⠀⠀⠀⠁⠃⢨
⠚⠁⡠⠖⠁⠠⠆⢀⢈⠐⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠔⠊⣀⠔⠁⡀⠀⠀⠀⡠⠈⠀⢀⡔⠀⠀⠃⢀⠇⢨
⠀⠪⠁⠠⠂⢀⣀⠈⠀⣤⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠼⠀⢸
⡀⢤⠉⢀⠐⠆⠀⠠⠤⠀⠀⠐⠚⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠁⠐⠀⠤⠀⠠⠀⢀
⡀⠐⢤⠀⠁⠀⠀⢤⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠈⠁⠐⠁
⠛⠀⠀⠀⠀⠐⠠⠄⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠒⠒⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠫⠥⡀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠘⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⡩⠀⠀⠀⠀⠀⠀⢀⣶⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠨⣈⣉⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠑⠂⠠⢄⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺⢋⠜⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣁⣐⠒⠀⠤⠄⠤⢀⣀⡱⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⣀⠀⠤⠀⠐⠈⠀⠁⠊⠔⠁⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢞⢿⣿⣿⣷⣶⣶⣾⠟⣁⠠⠄⠂⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠢⠝⣛⡛⠫⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⣀⠠⠔⢚⡄⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⡠⠔⠊⣠⢆⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠈⢀⡠⠔⢉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠁⣀⠔⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠈⠁⠀⡠⠔⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⢀⡒⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠐⠒⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⢲⣶⠶⣦⣀⣤⡀⢀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⣴⡆⠀⢤⠄⣶⡖⠒⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣇⣀⢈⣿⣄⣹⢻⡟⢻⣾⣿⠋⢻⣦⢶⣆⠀⠀⣹⡇⠀⣼⠀⣿⣥⣤⣾⣋⣭⡷
⠀⠀⠀⠀⠀⠀⢸⡏⠉⢻⣏⢀⣿⠘⡇⠀⠀⡇⠀⣾⠇⢠⣿⠀⠀⢸⣤⣤⣿⠋⢻⡇⠘⣿⣉⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⣉⡤⢧⡀⡀⢁⣀⣴⡤⣬⢥⣀⣀⡀⠀⣀⣉⢀⣼⡃⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⢿⡇⠀⣿⡇⠸⡇⡟⠀⣿⣾⣿⠁⢹⣾⡷⠚⢛⢷⣍⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠁⠈⠙⠊⠁⠙⠛⠃⠛⠚⠛⠛⠘⠀⠉⠉⠓⠚⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⢀⠀⢀⣀⡠⠐⠃⠀⠀⠀⠀⠀⠁⠐⠂⠤⠀⣀⡀⠀⠀⠠⢄⢐⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⣀⣀⣀⣀⣙⡓⠄⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣈⣳⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣈⣓⠲⠶⠶⠖⠒
⣶⣶⠾⠷⠒⠀⠒⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⢤⠠⠀⠀⠠⠤⠤⠤⠠⠤⠄⣀⠀⠬⠁⡀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣸⣇⠀⡐⠀⣀⣀⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⣀⣀⡀⠩⢴⡤⠤⢤⡀⠀⠀⠀⠀⠀⠠⡄⠀⢀⠠
⠖⠚⠛⠋⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠘⠓⠦⠔⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠠⠀⠁⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⡀⣀⠤⠴⠒⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠈⠙⠛⣛⡋⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⣀⣀⡄⠤⠖⠒⠒⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢰⣾⣿⡿⠀⣾⣿⣿⣧⠀⠀⢀⣀⠠⠅⠒⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⢀⠀⠾⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉