Dkg Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠄⠀⠀⠁⠀⠀⠐⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙⠂
⡔⠈⠁⠀⠀⠀⠀⡦⠀⣀⡀⠀⢀⡀⢂⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈
⡇⠀⠀⢀⠔⠀⠀⢀⠤⣤⣄⡁⠈⠁⠀⠃⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠈⠆
⠘⣄⠀⠀⠀⠀⠀⢁⠰⣿⣿⣿⠀⠀⠐⡀⠀⠀⠀⠀⠑⢄⠀⠀⡀⠐⠄⠀⢠⠀⠀⠰⣶⠄⠘⠁
⠀⠸⠀⠀⠀⠀⠀⠀⣐⣚⠉⠁⠀⠀⠀⣷⠀⠀⠀⢀⣠⠞⠀⠀⡇⠀⠀⠀⠀⠀⠂⠽⠋⠤
⠀⢰⠀⠀⠀⠀⠁⠊⠀⠀⠑⠒⠈⠀⠔⡍⠀⡰⠚⠉⠀⠀⠀⠀⢇⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⢀
⠀⠀⠛⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⠁⠀⠈⠦⣀⡴⠋⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⠀⠀⢀⠆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠰⠂⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⡉⠓⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡁⠀⠀⠀⠐⡈⢆⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠇⠀⠀⠀⠀⠻⠈⢣⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢣⠀⠀⠢⡀⠈⠐⡄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⣀⣀⠀⠸⠀⠀⠑⠄⠀⠈⢦⡀
⠀⠀⠀⠀⡠⠄⠐⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⢠⣶⣶⢿⡇⠐⢼⠀⠀⠀⠀⠀⠀⠉⠢⢀
⠀⠀⠀⠀⠓⠒⠒⠒⠒⠲⠤⠔⠒⠁⣆⠀⠀⠀⠛⡿⠋⠀⢀⡸⠂⠀⠤⠤⠤⠤⠤⠄⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⣀⣤⣴⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣟⠁⢻⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠘⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⡿⠿⠁⠀⠘⢻⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⣤⣤⣤⢿⣿⣿⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦⣀⠻⡿⢋⣼⡟⠁⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠙⣟⠛⣿⠋⢠⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠛⠋⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⡅⠀⠀⠀⢸⡇⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣿⠏⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⣿⣆⣴⣿⣿⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢿⡄⠀⠀⠈⢻⣿⣿⠏⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⠈⠇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠛⠙⠻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠑⢶⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠠⠀⠤⠤⡏⠀⡀⠀⠄⠀⠀⠀⠀⠀⠠⠠⠤⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠁⠈⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠈⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡈⢆
⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⠀⠀⢀⡰⠟⠋⠁⠀⠀⢀⣠⠀⠂⠘⠦⠀⠤⠀⠙⠛⢷⡖⠀⠀⠀⠀⠀⡀⠄⠁
⠀⠀⠀⠀⠀⢨⠱⠓⢸⡇⠀⠀⢀⡴⠛⠀⠀⠀⠈⠀⠀⠻⠁⠀⠀⠀⠀⠘⣔⠂⠀⠀⠀⠉⠀⠀⠀⠀⡜⠃⠀⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠨⣝⣶⠆⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢦⡁⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⢀⣰⠾⠞⠀⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⡠
⠀⠀⠀⠀⠀⠀⠘⣡⠋⠀⠀⡀⠀⢠⠦⢤⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠜⠦⢀⡔⣵⣶⣿⣶⣝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢻⣿⣿⣻⣿⣹⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠈⢎⣼⣿⣿⣿⣿⣿⠏⢡
⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠹⢿⠿⡿⠻⠉⡀⠀⠊⠈⢠⣄⣀⣀⣤⡀⠐⠤⡀⠈⠙⢛⠿⠿⢛⡧⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⣼⡀⠀⠤⠀⢈⣰⠆⠁⠀⠀⠀⠀⣠⡾⣛⣉⠉⠉⣙⠛⢷⣄⠉⠢⡀⠀⠙⣿⡟⠚⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⣞⠐⠀⠀⠔⠀⠀⠀⠀⠹⣴⣍⣿⡿⡧⣿⣇⣠⠇⠀⠀⠈⠰⡀⠈⠛
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠹⣍⠻⢸⣧⣈⣉⡽⠁⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⡿⡻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⢠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠶⣖⠈⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣇⣊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⡌⣑⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢁⡌⢠⣄⠀⣀⣴⡿⠋⠉⠉⠉⠉⣿⡿⠉⠉⠛⠻⣿⡟⠒⣠⣦⣨⣋⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠳⢿⢯⣿⣿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⣧⣬⣤⠰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣴⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⡛⠶⣦⣤⣀⣀⣠⣇⣀⡀⢀⣀⣼⣧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣬⣍⣯⣛⣛⣽⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⣿⣿⢿⣿⠿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠿⠿⠿⣿⣿⠿⠿⠿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⡿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢾⣿⠀⠸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⠁⢤⣄⢠⡴⠛⠉⠉⠙⠓⠒⠒⠛⠋⠉⠙⢷⣝⠠⠶⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠈⠿⠋⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠈⣿⡆⠀⠀⠙⣿⣿⡿⠁
⠀⠀⠀⢰⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣩⣬⡙⣿⠀⠀⠀⠀⣠⣤⡉⢻⣿⣿⠀⠀⠀⠈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠾⠃⠉⠀⠀⠀⠀⠻⠾⠟⠂⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠀⠀⠀⣤⣶⣶⣦⣄⠈⠙⠒⠶⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⣼⣿⣧⠛⠀⠀⠀⠀⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣡⠁⠀⠀⠀⠀⢀⡀⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣤⣾⣿⣷⣦⣤⣤⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⢁⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⣄⠀⠀⠀⠀⠀⢀⢴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⡆⠀⠀⠀⠀⣾⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣽⡧⠄⠀⠀⢴⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠎⠀⠀⢠⠄⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣱⣀⣠⣶⡄⢠⣶⣌⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠻⣿⣿⡤⢨⣿⡿⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⣿⣷⡇⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠻⣿⣿⣷⣶⣾⠏⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⢦⡰⡄⠙⡏⠻⠟⢫⡀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡖⠠⠚⠷⠽⢦⡼⡦⠴⠞⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡈⠁⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣶⣴⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⢿⣿⡆⠀⠉⠛⠟⠛⠻⠦⣤⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠻⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠙⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⠀⣸⠇⠀⠀⠀⠀⠀⢠⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⡆⠀⠀⠀⠀⣷⣏⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠳⣄⡀⢀⢥⡀⠀⠀⠀⢹⡿⠁⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣘⣿⢷⠟⠋⢻⡆⠀⠀⠘⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⠀⢀⡀⠀⠀⠀⢠⢋⣴⠛⢃⠀⡠⠄⠚⢿⠀⠀⠀⢱⠀⠈⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠉⢀⣄⣀⣴⣆⣀⡀⠾⠰⣿⣿⡷⠖⠋⠁⠀⠀⠀⠀⢱⡀⠀⠀⠆⠀⠀⢄⠀⠀⢃
⠀⠀⣀⣀⣤⣶⠞⠙⢻⣟⠋⠉⠙⠉⠈⠀⠑⠄⠀⡈⣷⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⡀⠀⠸⣤⡀⠈⠀⡀
⢴⣾⡿⢿⢿⠟⠂⡴⡂⠀⡐⠀⠀⠀⣀⣄⡀⠏⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⠀⠈⢷⣀⡀⠈
⠀⠈⠙⠛⠻⠾⠾⠻⠶⠾⠟⠚⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⣄⠢⣕⡀⠀⠉⠛⠲⠶⠤⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⡿⣳⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠈⠀⠈⠁⠀⠈⠉⠙⠲⠦⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢢⡀⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⡎⠀⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠀⣷⠀⠀⠙⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢰⢸⡄⠘⢀⣤⣤⡀⠀⠀⠀⠀⠀⣴⣿⣻⣦⣀⡞⢰⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢼⡈⢧⡤⠿⣿⣷⣿⡀⠀⠀⠀⠀⢾⣿⣿⠇⢸⠃⢸⡇⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⠀⠀⢸⠃⠘⡇⠀⠛⣻⠟⠀⢀⣤⣄⢠⡀⠉⠳⣄⢸⡀⠀⠁⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣄⠁⠀⢰⡿⠀⣴⠃⠀⠀⠘⠻⣿⠟⠀⠀⠀⠈⡿⢷⡀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣀⡾⠛⢶⣇⠀⠀⠀⠀⠀⣠⣀⠀⠀⢀⣠⠇⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⣸⠻⡳⠦⢤⡶⠚⣁⣈⣹⢟⢟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠓⠬⣑⡂⢨⠩⠤⠀⣊⠥⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡁⠀⠀⠀⠀⠉⣽⠶⢻⡍⠀⠀⠀⢬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⡀⠀⠀⢀⠀⠀⠈⠓⠋⠀⠀⠀⠐⢮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠁⡆⠀⠀⠀⠀⣰⠀⠀⠀⠈⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⢱⠀⠀⠀⠀⢟⠳⣄⣠⠾⢻⡄⠀⠀⠀⡇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡀⠀⠀⠀⢸⡄⠈⠁⠀⣾⠀⠀⠀⢀⡇⠀⣸⣃⣄⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠸⡇⠀⠀⠀⠈⣧⠀⠀⢠⡇⠀⠀⠀⢸⡇⣴⡿⠁⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠾⠿⢦⡀⣷⡀⠀⠀⠀⢹⡄⠀⣸⠃⠀⠀⠀⣼⠷⠚⠓⠲⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡐⢠⠂⠀⠀⠙⡿⠁⠀⠀⠀⠈⢧⣀⡟⠀⠀⠀⠀⠘⢦⡀⢢⠀⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣼⣄⣠⣤⣼⠁⠀⡄⠀⠀⡂⠈⣿⡇⠀⢠⠀⠀⣆⠀⣳⠾⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠳⠤⠶⠳⠚⠁⠙⠒⠛⠶⠶⠛⠚⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠉⠀⣤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠃⠀⣈⡏⠀⠀⣒⡀⠀⠀⠀⠀⠀⠀⠒⢂⣀⠀⠈⢷⡐⠀⠀⠈⢢
⠀⠀⠀⠀⡆⠀⠀⢀⣿⠀⠀⠼⣿⠿⠀⠀⠀⠀⠀⢁⡴⢿⣾⠗⢀⢸⣿⠆⢀⡄⠈⠣
⠀⠀⠀⠰⢃⡄⠀⠘⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⢿⡇⠘⠂⠀⠀⠀⠄
⠀⠀⠀⣶⣁⠀⠀⠀⣿⠀⠒⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⡁⣻⣿⡀⡀⠀⠀⡀⢊⠂
⠀⠀⠀⣿⣿⣿⣄⣤⢸⣾⠁⣤⠀⠀⢰⣿⣿⣿⣿⣿⠆⠠⠀⢰⣴⢸⣯⣿⡏⣿⣧⣼⡏⣺⠟
⠀⠀⠀⢿⣟⣏⣾⡾⢸⡜⠦⠹⡇⠀⠈⠙⠿⣿⠟⠋⠀⠀⢠⠟⠠⢾⠟⢿⡇⣻⣿⠄⡼⡇
⠀⠀⠀⠀⠘⣿⣿⡇⡼⢣⠀⠀⢱⡀⠀⡀⣰⣤⣀⣀⠀⣀⢟⡄⠀⠠⠀⢾⣿⢹⣿⣖⡝
⠀⠀⠀⠀⠀⠈⠻⣿⠛⠋⠀⠰⠌⠫⣿⡛⠉⠙⠛⢙⣿⡕⠉⠀⠀⢀⠀⠀⢙⡎⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠘⣷⣤⣀⣠⡿⠏⠀⠀⠀⠀⢄⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣆⢀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⠀⢈⣦⣼⡿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠋⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠈⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣄⣷⣠⣀⣠⣤⠄⠘⠃⠀⠀⠀⠀⠉⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⢰⠈⠀⠀⠀⣮⠉⠦⠠
⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⡟⠀⠀⢀⣮⠡⣀
⠀⠀⠴⡒⠁⠀⠀⠈⠀⠀⠀⢧⠀⣠⠞⣣⠀⠈⠑⡀
⠀⠀⠙⠥⠀⣀⡀⢴⡖⣲⠆⠈⠛⠁⠐⣟⠀⠀⠀⢸⣿⢲⣤⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣍⣠⠊⠉⠁⠂⠠⠀⠀⣀⡷⠀⠀⣰⠟⠁⢸⣿⡇⠘⢿⣿⣿⣟⡛⠛⠛⢋⣙⣉⡉⠛⠛⠒⠒⠠⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠓⠄⠀⠸⡇⠀⠀⠁⠀⠐⢿⣿⡇⠀⢸⡿⠏⠈⢹⣿⡟⢿⠙⠏⠉⠉⠀⠀⢀⠀⠀⢌⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠃⠀⠀⠀⠀⡴⠀⣿⠃⠀⠀⠇⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⡆⡄⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢼⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠃⠀⠀⠀⠀⠁⠡⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠠⡹⣆⠀⠀⠀⣴⢁⠀⠀⠀⠀⠀⠀⣀⠄⠀⢰⡶⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣦⣬⣵⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠓⠷⢌⠀⠀⠒⢩⡇⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⣷⠘⢿⣿⣧⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣼⠃⠀⠀⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠘⣿⣷⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⣿⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠹⣿⣿⣧⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠙⣿⡏⠻⡀⠸⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸⠃⠀⢱⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡆⠀⡼⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡘⠀⠀⠈⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣦⣀⡜⢁⣤⣤⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣙⣲⠇⠀⠀⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠶⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⠇⠲⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠋⠉⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠘⡄⠀⢆⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠔⠀⣀⣴⣼⣏⠁⠀⠀⠀⠁⠀⠀⠀⠀⢰⣆⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡌⢿⡇
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⢠⠴⠚⠛⠾⠿⠿⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⢸⣿
⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠚⠿⣧⣀
⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⣿⣿⣷⣄
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠹⣿⡄⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠙⣿⣦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⠟⢹
⠀⠀⠀⠀⠀⠈⠻⣿⣮⣦⠐⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣌⠄⠀⠀⠀⠀⢸⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⢠⣿⢇⠂⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⣾⣿⣿⣿⡇⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣭⣾⣿⣿⣿⣿⣿⢇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⢐⠨⠀⠀⠀⢠⣾⣿⣿⣷⣶⣶⣶⣶⡶⢿⣿⣿⣿⣿⣿⡿⢿⣷⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠩⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣯⠟⢛⣩⣷⣿⡿⠿⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠂⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠔⡁⠀⠔⡟⡿⣿⠏⠀⠀⠀⠻⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡜⣇⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠸⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣆⠀⠀⠀⠀⠀⠄⠀⠰⣔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠘⢦⠀⠀⠀⠀⠀⠀⠀⠘⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠎⣸⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⡰⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠂⠀⠁⠉⠉⠉⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣈⠁⠀⠀⠀⠓⠀⠀⠄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠘⠛⡁⠀⠀⠈⠭⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢸⠀⠀⠐⠄⢀⠀⠀⠀⢀⠀⢠⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠜⣄⢣⢀⡠⠤⠤⡤⢴⠋⡠⡞⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠢⡹⠀⠀⠀⡖⡡⠊⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⡇⠀⠀⠀⡋⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡀⠀⠱⢄⡠⠔⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⡀⠀⠀⢰⠀⠀⠀⢛⠀⠀⠀⠀⠀⡜⢇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠄⠑⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢠⠞⠀⠈⢆⠀⠀⠘⡀
⡔⠋⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢣⠀⠀⠘⡄⠀⡰⢻⠀⠀⠀⠈⢣⠀⠀⢃
⡇⢄⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⡟⠀⠀⠀⠀⠀⠘⡄⠀⠀⢣⠐⠁⣸⠀⠀⠀⠀⠀⢣⠀⠸⡀
⢣⠈⢦⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⡤⢖⣁⠀⠀⠀⠀⠀⠈⢇⠀⢣
⠀⠑⢤⣈⠉⠛⠉⠉⢳⡄⠀⠀⠢⣇⣀⠀⠀⠀⠀⠀⢀⣱⠀⠀⢸⡁⠀⢙⡆⠀⠀⠀⠀⠀⢣⠈⠓⠤⢄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠢⠼⠤⠴⠼⠀⠉⠉⠉⠉⠉⠁⠸⣀⢀⠀⢈⢻⠉⠁⠀⠀⠀⠀⠀⠀⠣⣀⣰⣀
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣹⠃⠀⢀⡀⠀⠀⢳⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡻⠆⠀⠀⠶⠂⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠂⠀⠀⠀⠀⠀⣸⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠀⠀⠀⠀⠀⠀⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⡤⢥⡴⢦⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠱⡄⠀⠈⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠘⡀⠀⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡤⠖⠛⠉⠛⢦⡀⠘⡀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢧⠀⠀⣸⠀⣠⡆⠀⢸
⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⢰⠞⠁⢳⠀⢸
⠀⠀⠀⠀⠀⡟⢧⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢈⡇⠀⠀⠀⠀⢸⠀⢸⡀
⠀⠀⠀⠀⠀⢷⡀⠓⢤⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡴⠋⣃⠀⢰⠀⠀⠘⡄⠘⡇
⠀⠀⠀⠀⠀⠀⢽⣦⡀⠉⠓⠠⠄⢳⣄⡀⠀⠀⠀⣠⡖⠋⣁⡤⢆⣉⡉⠉⢧⠀⠸⣄⠀⠀⠈⢄⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⠤⠖⠿⣀⣀⣀⣀⣀⣉⣉⡀⣠⡤⠎⠀⠀⠈⠣⣀⢀⣀⠄⠀⠈⠐⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⢄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠀⢰⠀⠀⠀⡴⠁⠀⠀⠀⠈⢃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⢠⠀⢀⡞⠀⠁⣀⡤⠤⠶⠖⠒⠺⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇
⠀⠀⠀⠀⠈⠦⠊⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠞⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡠⠴⠒⠒⠒⠒⠒⠤⠄⠀⠘⠀⡟
⠀⠀⠀⣀⠄⠈⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠐⣌⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣦⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢰⠁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠧⠞⠀⠐⠀⠀⢀⡠⠴⠒⠒⠓⠲⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢃⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⠀⠘⡟⠛⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢀⣀⠀⠀⢢⠜⠙⠛⢛⠟⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⡜⢁⡄⠀⢰⠃⠀⠀⡴⢃⣀⣀⡤⠖⠀⠤⢄⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠡⡎⠀⠀⠸⣤⡤⠞⠁⠀⠈⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠑⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡤⠤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠳⢄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠳⣄⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⠉⣀⠀⠉⠐⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢠⡙⣿⠁⣼⠟⣀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠉⠁⠃⠄⠹⠀⠋⢈⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢈⣿⣷⠀⠰⢲⢳⠢⠀⢠⣿⢽⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⣿⡀⣤⢠⣇⢠⠀⢸⣿⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢧⣥⢟⡹⢦⣀⣸⣏⣷⡍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣽⠃⢲⣿⠿⠊⠑⣫⣾⣿⠇⠘⡆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⢘⡇⠀⠀⢠⣿⣿⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣾⣷⣆⣴⣿⣿⣿⠁⠀⠀⠀⣾⠁⢠⠀⢸⣄⣤⣤⠀⠀⠀⠻⠦⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⣰⣿⠀⣾⠀⢸⣿⣿⣿⣤⡀⠀⠀⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠄⠀⠀⠙⠻⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣾⡟⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣀⡀⠸⣧⣤⣀⠀⢀⣠⣤⣀⣠⣶⠃⠀⢰⣿⣿⣿⡿⠛⠛⠻⢟⡁⠙⠻⡷⣷⡀⠰⠁⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣠⡝⠁⠀⠀⠈⠛⠿⣿⣿⡿⠿⠟⠋⠁⢀⠀⠀⠛⠉⠀⠀⠀⠀⠀⣼⣿⡤⠔⣃⡼⠃⠀⠁⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡰⠋⠁⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣠⣤⠞⠋⠁⠀⠀⠀⠀⠀⠈⢌⡉⠟⠋⠀⢸⡋⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿
⠀⠀⠄⠒⠉⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒
⡤⢀⢀⡄⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⠀⠁
⠓⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠀⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡠⠔⠒⠉⠉⠷⠿⣶⣦⣭⠭⠉⠉⠉⠙⠳⣆⠠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣴⠶⠆⠀⠐⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢺⡏⣠⠀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠘⡇⠀⠄⠀⠀⠀⠀⠈⣏⢧⠸⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⣨⣴⡇⠀⡇⠀⠀⠀⢀⡀⠀⠀⣀⡆⣠⠇⠀⠀⠀⠁⢦⣠⣶⣀⠤⠀⠀⢸⣾⠀⠃⠉⠻⣄
⠀⠀⠀⠀⠀⠀⣼⢸⣿⡇⠸⣿⣿⡇⢰⡇⠀⠀⣀⡾⣿⣻⣿⣿⣆⢿⠀⠀⠀⠀⠀⠀⠻⣿⣽⣷⠄⡀⠈⣟⡇⠀⠀⠀⠿⢷
⠀⠀⠀⠀⠀⠀⢹⣆⢻⡇⠀⢻⣿⡇⢸⡇⠀⠉⠉⠁⢼⡿⠉⣿⡏⠀⠀⠀⠀⣷⠀⠀⠰⡙⠧⠀⢀⡄⠀⣯⡇⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⢿⣷⠀⡿⡄⠀⢤⣀⠀⠀⢈⣿⠆⠀⠀⣀⣸⡟⠃⠀⠀⢀⣰⠿⠋⠀⠀⣿⣇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢸⣿⡀⡇⠀⠀⠀⠙⢻⡇⠀⡏⢀⡴⠛⠉⣠⣤⣄⠐⢶⣦⠙⣦⠀⠀⠀⣿⣏⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢸⣿⢣⣇⠀⠀⠀⠀⠊⠀⠀⠀⡜⠁⠀⠀⣭⣷⠄⣀⠸⣯⡅⠸⠀⠀⢠⣿⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠾⣃⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⡷⠞⠀⠀⠠⢇⠀⡿⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⢿⣿⡇⠀⠋⠘⣵⣆⠀⠀⠀⠀⡀⡀⢸⣿⣿⢈⣶⡆⠄⠀⢾⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠈⣿⣷⡀⠀⠀⠻⣿⣆⠀⠀⡄⡄⢤⠴⣿⢻⣾⣿⣷⣍⣀⠌⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⢹⠈⢳⣄⠀⠀⠘⡿⢿⣶⣤⣤⡴⣚⠛⠯⠋⠀⢹⡛⣉⠞⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡼⡆⠀⢇⠀⠉⠑⣦⡀⠈⠙⠛⠻⣏⣴⡙⠦⣀⠀⠀⠘⣿⠃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠈⣆⠀⠀⠈⠛⠂⠰⢤⣀⠙⠻⠿⠶⠶⠖⢚⡶⠋⠀⠀⠀⣼⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠈⠀⠀⢠⢠⠀⠀⠀⠈⠑⢶⣶⣶⠃⠈⠁⠀⠀⠀⠀⡀⢸⡟⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣻⣿⠃⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⡾⣿⣿⡀⠀⠀⠀⠀⠀⢠⠀⢸⠃⠀⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠘⢱⠃⡀⠀⠀⠀⠀⠙⢿⣟⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠁⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢿⣇⣤⠀⠀⠀⠀⠀⢸⣿⡇⢀⡄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡇⠀⠀⠀⠻⡿⣆⠀⠀⠀⠀⠈⠈⢿⣿⣧⣆⠀⣠⣶⣄⠀⣀⠀⠀⠀⠠⣹⡆⠀⠀⠀⡏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠁⠙⠻⢶⡏⠀⠉⠻⠇⠈⠁⠀⠀⢹⠃⠀⠀⡼⠃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠳⣄⢀⡀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠛⢷⣾⣷⣄⢲⣄⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠴⠒⠲⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⢋⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⡙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢰⠁⠀⠀⠀⣼⡏⣳⠀⠀⣀⣀⡀⠀⣞⢹⣇⠀⠀⠀⢸⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣼⣀⣀⣀⠀⠘⠛⣋⠴⠋⣀⣀⠉⠲⣝⡛⢃⣀⣀⣀⣀⣇⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⢀⡏⠀⠀⠈⠉⠉⠉⠀⢼⣿⣶⣶⣿⡆⠀⠉⠉⠀⠀⠀⠀⠹⡄⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⡀⢉⣽⢿⣁⣀⡠⠀⠀⠀⠀⠀⠀⢀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠉⣏⠁⠀⡹⠉⠀⠀⠀⠀⠀⠀⠀⣸⡵⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⣀⡤⠞⢹⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠉⠑⠒⠲⠶⠤⠤⠶⠖⠒⠒⠉⠉⠀⣇⢀⡼⣄⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢹⡎⠀⠀⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢸⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⡇⠘⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢇⠀⠀⠀⠈⠓⠦⢤⡤⠴⠚⠁⠀⠀⠀⣸⠁⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⣀⠘⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠃⢀⣠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠉⡰⠋⠓⠦⠶⠂⠀⢸⠀⠀⠠⠤⠤⠖⠛⢦⠉⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡇⢰⠀⢧⣶⠀⢰⠀⠀⢀⣸⢆⡀⠀⠀⡆⠀⣷⣸⠀⡆⢰⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠚⠓⠋⠉⠀⠀⠈⠙⠚⠓⠚⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⡤⠀⢒⣯⣻⣿⣿⣯⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⡄
⠀⠀⠀⠀⠸⡀⠂⠈⢟⣿⣽⣿⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⡄
⠀⠀⠀⠀⠀⠈⠑⢤⣼⣿⣿⣿⣿⡟⠛⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⠏⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣋⡉⠛⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣷⣿⡿⠟⠷⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣷⣿⣿⣯⡉⣸⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⡇⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠘⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣩⣭⣦⣦⣄⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⠀⢘⡟⠛⠛⠿⠗⠒⠒⠛⠉⠉⠀⠀⠀⠘⢿⣧⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠆⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡳⣄⡐⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢨⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠏⢻⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣥⣀⡼⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣁⠼⠀⢸⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣄⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣠⣄⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⠀⠀⠀⢠⠀⠀⠈⠁⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠙⠓⠒⠒⠒⠒⠒⠚⠋⠁⠀⠉⠀⣀⡤⠋⠀⠀⢀⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠢⢤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⢢⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠹⠶⠆⢀⣀⠤⣿⠀⠀⠀⠀⠀⠀⡼⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿
⠀⠀⠀⠀⠉⠁⠀⡏⠀⠀⠀⠀⣠⡞⠉⠉⣠⠆⠀⠲⢤⠠⢤⡤⠜⠀⠀⠀⢠⢧⡏
⠀⠀⠀⠀⠀⣠⠞⠀⢀⡠⠚⠉⠹⢧⡀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⢠⡏⠀⢰⠛⠁⠀⠀⠀⠀⠳⠀⠈⠢⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⠈⠓⢤⡀
⠀⠀⠀⠀⠀⡇⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠢⠴⠦⠃⠀⠀⠀⠀⠈⠙⢆⠀⠀⠓⢶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠤⠄⠤⠤⠀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⢠⠆⠀⠀⠀⠀⠀⠀⣀⢰⡀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠰⠂⠀⡏⢰⣿⡆⠀⠀⠀⣾⣷⠈⡇⠀⠀⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡄⢀⡁⠀⠀⢀⣾⢲⣦⠀⠀⠀⣿⠀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠔⣼⠁⠀⠀⢀⣿⣿⣏⠀⢀⠀⢸⣄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣸⡀⡾⣦⡜⠛⠟⠻⣤⣾⠀⢰⢩⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠦⢐⢈⡻⢦⣤⠾⢋⢈⡤⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣤⣀⣨⠀⣉⠁⠀⠈⠁⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠺⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣾⡏⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠙⣿⣿⣿⢿⣿⣿⣿⡿⣻⣿⠋⠶⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢰⡄⠘⣿⣿⣿⣿⣿⣿⡟⠱⣿⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠘⣘⡧⠀⠈⣿⢿⣿⡿⠃⠀⠀⣏⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣲⠞⣇⠀⠉⠀⠀⣃⢀⠀⠀⣤⠀⠀⠀⠠⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⢳⣄⠞⠈⠁⠛⠂⠴⠸⠀⠀⡔⠓⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠐⣆⠀⠀⠀⢠⡞⠀⠀⠀⡇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇⠀⠂⠀⠘⢣⡦⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢀⡴⢹⢇⠀⠀⠀⠀⣸⠿⠁⠀⡅⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⢸⠀⠙⠒⠒⠋⢩⠀⠀⠀⡇⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠖⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠳⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⡠⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢛⡻⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠉⠐⠂⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠐⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⡤
⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢐⣿⣾⣷
⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠣⣽⣿⣿⣷⠀⠀⠀⠀⠰⣄⣀
⠀⠀⠀⠠⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠗⣿⣿⡛⠓⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣿⣿⠛⠂⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠐⠀⠰⢿⣿⣿⣿⣿⣼⣂⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣠⣏⣿⠌⠙⠃⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⣷⡁⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠻⣿⣿⣿⡿⠶⢀⠀⠀⠈⠋⠙⢿⣿⣦⣶⣦⣄⣾⣿⠏⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⠟⢡⣌⠹⠙⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡤⠄⣤
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠈⠩⠭⠟⠩⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢦⣾⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠁⠀⠀⠀⠀⠀⠀⠰⠞⠉⠀⠀⢠⠀⠃⡀⢮⢃⡕
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡅⢠⣤⣿⣿⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆⣰⡷⠉⣿⡟⡆
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⣿⣾⣿⣿⡏⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣷⢸⠃⣀⡿⣿⡇
⠀⠀⢰⣼⣿⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣿⡆⠀⢹⣿⣿⡇⠄
⠀⢠⣿⣿⣿⣷⣾⣇⣠⠄⠀⠠⠀⡀⠀⠀⢀⣠⠀⠀⢸⣿⡿⣿⡭⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⣏⡿⢃⣶⢈⣿⡿⡇
⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣤⡤⠷⠛⠋⠁⠀⠀⠹⢻⣟⠻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⢠⡿⣻⣇⠀⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡃⣼⣾⡷⢰⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⡏⠁⠄⠀⠀⠰⣴⣤⡆⠀⠀⠀⠀⠀⠀⣀⠆⢰⡄⣧⠀⣿⣽⣿⣿⠁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡀⢠⣶⣯⣿⡿⠀⠂⠀⠀⠀⠀⣽⠇⡈⣴⠏⢰⣿⣿⡟⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠁⠀⠀⢠⠵⡋⣗⠀⢀⠦⠊⣠⠟⠐⣹⠊⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠂⠀⢀⠀⠀⠁⠻⠴⠛⠒⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢉⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⢀⡉⠀⣤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠣⣀
⠀⠀⠀⠀⠀⠀⠃⠀⣈⡏⠀⠀⣒⡀⠀⠀⠀⠀⠀⠀⠒⢂⣀⠀⠈⢷⡐⠀⠀⠈⢢
⠀⠀⠀⠀⡎⠀⠀⢀⣿⠀⠀⠾⣿⠿⠀⠀⠀⠀⠀⢁⡴⢿⣾⠗⢀⢸⣿⠆⢀⡄⠈⠣
⠀⠀⠀⢰⢇⡄⠀⠘⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⢿⡇⠘⠂⠀⠀⠀⠄
⠀⠀⠀⣾⣋⠀⠀⠀⣿⠀⠒⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⡁⣻⣿⡀⡀⠀⠀⡈⢚⠂
⠀⠀⠀⣿⣿⣿⣤⣤⢸⣾⠁⣦⠀⠀⢰⣿⣿⣿⣿⣿⠆⠀⠀⢰⣴⢸⣯⣿⡏⣿⣧⣼⡏⣾⠟
⠀⠀⠀⢿⣟⣏⣾⡾⢸⡜⠦⠹⡗⠀⠈⠙⠿⡿⠟⠋⠀⠀⢠⠟⠠⢾⠟⢿⡇⣻⣿⠄⡜⡇
⠀⠀⠀⠀⠘⣿⣿⡇⡼⢣⡀⠀⢰⣄⠀⡀⣰⣤⣀⣀⠀⣀⢟⡄⠠⠢⠐⣾⣿⢹⣿⣖⡽
⠀⠀⠀⠀⠀⠈⠿⣿⠛⠋⠀⠰⠌⢻⣿⡟⠉⠙⠛⢙⣿⡕⠉⠀⠀⢀⠀⠐⢽⡎⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠘⣷⣄⣀⣠⡿⠏⠀⠀⠀⠀⢄⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣆⢀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⠀⢈⣦⣼⡿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠙⠋⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⠈⠈⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⢶⣄⣷⣠⣀⣤⣴⠄⠘⠃⠀⠀⠀⠀⠉⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⠀⠀⠀⠀⠀⣰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠈⡇⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢁⣾⠀⢱⣤⣤⣿⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⡇⠀⣿⣿⣿⣿⡻⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣆⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠉⣭⣽⣆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⢹⡿⠃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢻⣿⣧⡀⠠⣄⡀⠀⠀⠀⠀⢹⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢿⣿⣶⣤⣭⣷⣶⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣯⣍⠉⠛⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⠀⠀⠀⠉⠛⠿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣤⣴⣶⣿⣿⣧⣼⣿⣿⣿⣿⣿⣻⣇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢟⣽⣿⣿⡄
⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⡟⣿⣿⢟⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢋⣴⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣿⡟⠹⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢊⣿⣇⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⠾⠿⠟⠸⣫⣯⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠃⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣛⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠸⡇⠀⠀⣠⣒⠲⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⠁⠀⠀⢿⣿⣿⣿⠃⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣿⠈⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⢦⣄⠈⠄⢰⡏⠀⠈⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠁⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⣶⣶⣶⣾⣿⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⡟⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡁⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣯⡆⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⢀⣤⠴⠚⠛⠉⠉⠓⣦⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠈⢽⢷⣶⣎⣩⣤⣤⣤⣶⣶⠾⠋⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢣⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⢿⡿⠛⠛⠁⠀⢠⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣾⠟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠶⣤⣴⣶⣤⣤⣶⡶⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠀⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢁⣤⣶⣶⣶⣶⡶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⣤⣯⣝⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣼⣿⢿⡿⡻⡿⠁
⠀⠀⠀⠀⠀⠴⠂⠉⠉⢀⡄⢸⣿⣿⣿⣇⠀⠀⡀⠀⣀⡀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⣠⠄⣠⣠⣿⠁⠀⠐⠂⠁
⠀⠀⠀⠀⠸⣤⠀⠀⠀⠘⢁⣾⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⣉⣩⣿⣿⡿⠂⠉⠀⠰⣿⣿⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡿⡆⠀⠀⢀⣾⣿⣿⣿⠻⠁⢠⣴⣶⣤⡀⠀⠀⠀⠰⣽⣿⠟⠁⠀⠀⠀⢀⢀⠛⡀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠐⠓⠃⣠⠴⠋⣄⠸⠯⡋⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠉⠁⠀⣠⣶⣶⣾⣿⣿⣷⣶⣆⠀⢀⡞
⠀⠀⠀⠀⠈⠐⠉⠁⠀⠀⠈⠂⣰⣿⣤⣶⣧⣉⡻⣿⣿⣿⡄⠀⠀⠀⠀⣴⣿⣿⣿⡿⢿⣿⣿⣿⣿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⣩⣍⢮⣿⣿⡇⠀⠀⠀⠀⣿⣿⡯⠚⣛⢦⣉⢛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⣝⣡⣾⣾⠟⠁⠀⠀⠀⠀⠉⠙⢀⣘⣛⣰⠟⠛⠉⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣋⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣛⣿⣿⣿⣿⠟⠁⠀⠀⣤⣴⣶⣶⣶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⢿⣿⡿⠟⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣠⡶⠆⠀⢠⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠿⣶⣮⣝⠷⣦⠄⡀⠐⠂⠄⢻⣽⡿⠇⠤⠀⠀⠀⡀⠀⣿⣤⣶⠲⡿⠋⢀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⣧⡀⠀⠉⠁⢹⡆⠈⠃⠠⡉⠉⣨⠄⣷⣄⠩⡌⢠⠀⡀⠀⢸⡿⠟⠁⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣯⣶⣦⡈⠙⠷⣄⠀⠈⠻⢦⡀⠂⠒⣀⣴⡾⠟⠻⡿⢶⣄⡒⣐⣠⣟⠀⠀⠀⠀⢀⣠⠞⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠘⢻⣍⣤⣤⡄⠈⠙⠶⢤⣄⣈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⢁⣀⣠⣤⠶⠛⠛⠃⠀⠴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠙⠻⣿⣿⡀⠐⠓⣀⣈⠉⠛⠻⠷⠶⠶⠤⠶⠶⠶⠖⠛⠛⠛⠉⠉⠀⠀⠀⣾⣷⣦⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠛⠿⣿⣿⣿⣧⠀⠰⠶⠂⣠⣴⣦⡀⠀⠲⠖⢠⣿⣶⣄⣀⣀⣴⠿⠛⠁⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠉⠉⠛⠳⠶⠶⠾⢿⣿⣿⣿⡶⠴⠾⠿⠟⠛⠛⠉⠁⠀⠀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣠⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠈⢳⡞⣛⣛⡓⣳⣤⠋⣼⣶⡟⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⠻⠷⠚⠛⡒⠒⠦⠽⠶⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⡄⠺⣿⣿⣿⣿⣿⣿⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠬⣟⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡺⠑⠤⢲⡞⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠒⢤⣐⡊⠁⠠⠀⠀⠀⠉⢽⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣽⠁⠞⠀⠀⠀⠀⠀⢠⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠁⠝⠛⠛⠛⠋⠀⠀⠀⢠⠄⠐⠂⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸⡅⡜⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠼⢶⠤⠔⠋⠙⠁⠀⣇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⡘⠀⠀⠈⠙⢦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣏⣉⠉⠒⠒⣚⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠐⠣⠋⠉⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠘⠳⢤⡀⠀⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠸⠞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠸⡄⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⢸⠀⠀⡇⣠⠖⠚⠛⠓⠲⢄⡠⠁⠹⢄⠀⠀⠀⢳⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠙⣇⠀⢻⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢳⡀⢠⠏⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠸⡄⢸⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠜⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡄⣀⡬⠽⢧⣸⡆⢀⡵⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢧⡰⠂⠀⠀⢀⣾⠀⢀⠀⠀⣠⣀⡀⠀⠀⢀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉⠈⠙⠛⠒⠚⠁⠀⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠄⠀⣀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁⠀⠀⠐⠉⠉⠀⠀⠈⠁⠀⠀⠐⠀⠒⠒⠂⠶⡶⢄⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⣿⡏⠠⠂⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀
⠀⠀⠀⠀⡀⢀⠀⠀⠀⢰⡆⠀⠀⣤⠏⡤⠀⠀⠀⠐⠂⡰⠦⠀⠀⠀⠄⠂⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⠛⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⢀⣴⣏⣜⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢳⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣡⡄⠀⠀⣀⣤⣔⢄⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡆⢿⠘⢠⠁⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣼⣟⣵⠶⠓⢠⣿⣿⣧⣿⡌⠹⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⢷⣶⡀⠀⠈⠛⢾⡇⠀⡇⠀⠀⠀⢉⠀⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠉⣿⣿⡿⣀⠀⠀⠑⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠺⠻⣟⡽⠳⠀⣸⠸⣿⠁⠀⠀⠀⠀⠀⠈⢸⠃
⠀⠀⠀⠀⠰⡟⡀⠀⠀⠀⡟⢰⣿⣿⠀⠈⠹⣿⣶⠀⠀⠀⠀⢀⣤⡄⠠⠀⡀⣀⠀⠀⠀⠣⡀⠀⢀⣤⠀⠘⡓⢿⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠈⠻⣆⠀⢀⠁⣾⠏⡿⠀⠀⣀⢹⣿⡀⠀⠀⣰⡿⣋⡀⠀⠌⠁⠈⠻⣄⠀⠀⠐⣶⣿⡏⠀⠀⣿⣿⢸⣇⠀⠀⠀⢰⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢇⡜⢴⣿⢸⡇⠀⠀⠛⡿⡭⠁⠀⢠⣿⣶⣿⣿⠁⡀⢺⣿⣷⣼⡄⠀⠀⠻⣿⠀⠀⠀⣽⣿⡘⢿⡀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣼⡇⣸⠗⠋⠁⠈⠀⠃⠀⠀⠀⠑⣧⡈⢡⣼⣗⣠⠉⣻⠿⠇⠀⠀⠀⠉⠲⣀⢀⡿⣹⣇⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⢃⣿⢀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢠⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⡿⣿⠐⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣻⡯⠸⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠈⣧⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣿⠚⣧⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣤⣿⣦⣡⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⡼⢏⣼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠸⡇⢻⣿⣿⣤⣄⣀⣠⣴⡿⣿⣟⣙⣧⣀⠀⠀⠀⠀⢠⠎⠁⠔⠃⠛⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣇⣿⣿⣿⣿⠗⠒⠂⢺⣿⡋⠀⠿⣷⣶⣶⣶⡿⠐⠀⠀⠛⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡷⠞⣨⠛⠁⠀⠀⠀⠙⠋⠁⠀⠀⠸⣯⣽⣟⠓⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠹⠿⣿⡿⠿⠛⣷⡶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠃



⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⡉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠻⠄⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢣⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠋⡃⠀⠔⢆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁⠰⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠈⠁⢈⡁⠀⠀⠀⠀⢠⠀⠀⠀⠐⢁⠀⢤⣿⠀⡀⢾⠀⠐⢗⡠⠄⣰⡆⠄⠀⠀⡀⠤⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢆⠘⠀⠴⠙⠋⠦⡀⠀⣠⠏⠀⠀⠀⠀⡠⠠⢄⢟⣤⡄⠈⠲⠤⣾⡄⠀⣼⡇⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⣈⠀⣾⢾⠈⡆⠈⠚⠁⠈⠀⠀⠀⠁⣦⠀⢼⢰⠀⠉⢁⣤⢀⣃⡀⢀⡄⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠑⠁⢃⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠢⠱⠄⠒⠺⢀⢢⣞⠀⠀⠙⣇⠀⣨⡆⠳⠄⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠹⠁⢤⠉⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⠐⠳⣵⠇⠙⢦⣤⣴⣿⡁⠀⣹⡄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠸⠋⢢⠘⠈⡁⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⢶⠿⠈⠁⠀⠀⠀⢎⠁⠉⣿⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠂⡙⡄⠁⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⢫⠳⠞⣳⠟⠰⢞⠋⠈⢻⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠁⠆⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠃⣌⣨⡀⠹⣄⣠⣼⠇⠈⠛⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣷⡆⠀⠀⠀⠈⠢⠀⠀⠀⠞⠀⢉⡘⣄⢘⡄⠀⢠⣾⣿⣈⠙⠀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠌⠓⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣀⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⡿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣿⣶⣆⡀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣿⡷⠀⠀⠀⠘⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣹⣟⣿⣿⣷⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⠟⠀⠐⠠⢄⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣯⣭⣽⣽⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣿⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⡀⠄⠀⠠⠤⠐⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣠⣾⣿⣾⣿⣿⣾⣿⣿⣶⣦⣠⡄⠀⠀⠀⠀⠁⠀⠂⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣿⣿⣿⡿⠟⠛⠻⠛⠛⠛⢿⣿⣿⣿⣷⣶⣤⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣽⣿⣿⣿⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣭⣿⣿⣿⠿⣿⣿⣿⠟⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣯⣿⣿⣿⣿⠇⠀⠀⠀⣠⣾⣿⣯⣿⣿⣿⣿⣵⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣾⣿⣿⣿⣿⣾⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣹⣿⣿⡄⠀⢀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢭⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠠⡀⣿⣿⣿⣿⠛⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠚⠂⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⡿⠋⠀⣤⣠⡄⠀⣀⠀⠈⠁⠈⢿⣿⣿⣵⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⣿⣿⣿⣿⣥⣴⣶⣾⣿⣷⣤⣌⠛⠾⠀⠐⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⠗⠀⡆⠀⠀⠀⡞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣄⠀⠋⠀⠆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠂⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡃⢸⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⢀⠄⠀⡔⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⠴⣮⣴⡂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⣛⠋⢉⠉⠉⠉⠙⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⢿⣿⣿⣿⣧⣤⣤⠆⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠽⠿⠿⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣖⣄⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠁⠀⠀⠀⠖⠁⠀⠀⠀⠸⣆⠀⠀⠘⡿⠿⢿⣿⣿⣿⠟⡀⠀⠀⢀⢀⡄⠀⠀⢠⠀⢸⠅⠀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢹⠄⠀⠀⠀⠘⣶⡆⢠⡖⣻⣿⣁⠤⡀⣠⣷⡟⣢⣤⣖⢸⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠼⡆⢀⠀⠀⠀⣾⠀⡀⠄⠀⠀⣸⢀⣠⠀⡈⡇⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣿⣼⣦⣀⣿⣧⣰⣄⣰⣶⣶⣿⣾⣷⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠀⠉⠛⠛⠋⠉⠀⠈⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⠿⠿⠷⠆⠀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡰⣿⡏⠀⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠁⢤⡀⣠⠞⠋⠉⠉⠙⠓⠒⠚⠛⠉⠉⠙⣷⡃⠴⠾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⠟⠁⠀⠀⠈⠟⠁⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠘⣷⡀⠀⠈⠻⣿⣿⡏
⠀⠀⠀⢰⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢊⣡⣬⡙⣿⠀⠀⠀⠀⣤⣤⡙⢿⣿⣇⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠞⠃⠁⠀⠀⠀⠈⠻⠿⠛⢈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⢀⣴⣶⣶⣶⡄⠉⠙⠓⠾⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠉⣾⣿⡧⠃⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⢀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⣴⣾⣿⣷⢦⣤⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠈⠁⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠛⠁




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠓⠀⠀⠰⣶⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡀⠀⢀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠐⠗⠀⢀⣀⠀⢹⠟⠀⠀⠀⠀⠀⢀⢸⡿⠃⠄⢀⣿⣄⠲⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠄⠿⠀⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠉⠀⣼⠀⠀⠀⠀⠀⣴⣿⠛⠳⣆⠀⠀⠉⠃⠀⣴⣆⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣶⣦⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⣆⠀⠀⣀⣄⡝⠀⠀⠀⠀⠀⠸⣿⢄⠣⢄⡀⠀⢶⣀⣀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⢥⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⢩⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢻⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⢒⡤⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠲⢀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣂⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⣴⢰⡆⠛⠀⠈⠓⣿⢺
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⡙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⡀⣀⡰⠿⠁⠀⠀⠀⠀⠀⢻⠀⣷⣄⣀⢀⢸⣏⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠐⢿⣏⢈⣿⣿⡇⠀⠀⠀⠀⠀⠐⢄⠀⠈⣿⡇⢉⣛⣛⡛⠟⠀⠀⠀⠀⠀⠀⢀⡀⢋⠀⢼⣧⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠐⠛⠙⠉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠑⠊⢛⡀⢸⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀⢘⠳⣄⠲⠸⠷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠰⠄⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡼⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⢄⠐⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⠀⢠⣄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠶⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⡇⠛⠀⠀⠛⢸⠁⠡⠀⠀⠀⠀⠀⠀⣠⡶⣿⣅⠈⠁⠚⠻⠀⠐⣄⠀⠀⠀⠀⠀⠀⠈⠠⡆⠀⠀⠂⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣅⠈⢻⠟⠀⣨⠷⠂⠀⠀⠀⠀⠀⠘⣿⣇⠳⠈⠂⠀⢂⡀⠀⢸⣿⠂⠀⠀⠀⠀⢠⡇⠀⢿⣄⠲⠶⡦⣭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢿⣾⣷⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠁⠈⠳⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠲⠺⣇⠘⡟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣲⣥⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡀⠀⠀⠀⠀⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡇⠙⢀⡘⠃⣧⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠛⠛⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠤⣈⣡⠔⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢠⠀⢳⣰⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⢠⣄⠀⠀⢠⣤⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡇⠀⢸⠀⠈⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠘⠧⣼⠀⠈⠁⠀⠀⠈⠁⠀⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠧⠤⠿⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠛⠛⠀⠀⣰⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠙⠲⠶⠶⠶⠛⠁⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠻⡆⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠦⢤⣤⠤⠆⠀⢸⠀⠀⠀⢻⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⡋⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠘⠃⢰⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⡇⠰⠀⠀⠆⢸⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣰⣧⡀⠀⢀⣼⡀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⡘⢃⣠⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠈⠙⠛⠋⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠉⠉⠀⢀⠈⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢲⡆⠀⢸⠀⠈⠟⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣀⣸⣧⣀⣼⣀⣀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀⠀⡀⠀⠀⣀⡴⠶⠞⢟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠳⠄⡀⠀⠀⠀⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠈⢻⣿⠟⢀⠐⠈⠀⠀⠀⠐⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣼⣵⢀⠈⠻⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠓⠆⢸⠋⠀⠀⠀⣠⣄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡙⠳⣆⠘⡿⠀⠦⡀⠸⡄
⠀⠀⠀⠀⢠⡇⡐⠉⠀⠀⢠⠇⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣥⣀⠀⠠⠈⡄⠀⠘⠢⣷
⠀⠀⠀⠀⣸⠇⣿⣾⡆⠀⡧⢀⡖⢋⣙⣶⣿⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢰⣿⣏⣉⠛⠳⠘⣥⣦⣤⡀⠂⡆
⠀⠀⠀⠀⣿⠀⠛⠋⢀⣼⣷⣿⣾⣿⡿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠙⠶⣿⣿⢻⣿⣷⣾⣇⣻⠉⠻⠟⠄⡇
⠀⠀⠀⠀⠈⠛⠓⠤⢿⣿⣿⣟⣿⠿⣷⡿⠟⠋⠀⠀⠀⠀⢀⣠⣴⣤⣶⣤⡀⠀⠀⠀⠀⠈⢻⣿⢏⣿⣿⡶⢻⡗⠤⠾⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣻⣶⠟⠀⠀⠀⠀⠀⡴⢟⣭⢶⣿⡗⣩⡿⣧⠀⠀⠀⠀⠀⠙⣿⣿⡿⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣇⠹⣿⠏⠀⠀⠀⠀⠀⣸⣡⣿⣿⡟⣿⣿⣿⣷⣸⣆⠀⠀⠀⠀⠀⠈⢿⡅⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⣿⠀⠉⠀⠀⠀⠀⠀⠀⢻⡟⠿⠿⣱⣿⣿⣛⡿⢻⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣹⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣿⣿⡿⣋⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠹⢋⠛⠟⢹⣿⡿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣿⣏⢄⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠄⠀⠤⠤⠒⠁⠊⠁







⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣯⣽⣩⣿⣭⣭⣹⣏⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣯⣭⣭⣭⣽⣿⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠖⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣀⣀⣀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⣿⣿⣿⣿⣷⡄⠀⢱⡜⠒⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡞⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠜⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡀⠀⢀⠜
⠀⠀⠀⣇⠀⠀⠙⠒⠦⠤⣤⣀⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣷⠀⠙⠿⣿⣿⣿⠿⠓⠒⠒⠔⠚⠚⠁
⠀⠀⠀⠈⠓⠦⣀⣀⠀⢰⣿⣿⣿⣿⣿⣿⣯⠙⠻⠿⠿⠿⠋⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠙⠛⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠔⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⡠⠊⡨⠋⠒⠒⠂⠤⠒⠒⡆⠀⠀⡔⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢠⠊⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣷⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠘⢤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢘⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⢠⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⠿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠇⠙⢸⣿⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣦⣴⣦⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠈⠁⣀⣀⠀⢀⠉⠉⠛⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⢠⣿⣦⠀⠀⡰⠑⢉⠀⠀⠘⠻⢃⠠⡏⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠄⠠⠄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠸⠟⠿⠀⠀⠈⠳⠎⠀⠀⠀⠠⠶⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠰⠀⠀⠯⠀⠂⠉⠤⠆⠀⠀⣠⡿⣗⣤⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠄⠀⠀⠀⠀⢯⠰⠀⠈⠀⠀⠠⢳⠡⢬⡜⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠁⢡⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠧⣰⣄⠀⠈⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢫⡟⢩⣿⠀⠀⢀⣄⠀⣈⠩⡇
⠀⠀⠠⠄⠀⠀⠀⠉⠛⢧⡼⣯⠈⠀⠀⠁⠛⠈⠀⠀⠀⠐⠂⠀⠀⠀⠻⠋⠝⠛⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⣀⠀⣤⡀
⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⢿⣿⠀⠀⠀⠀⠀⠂⢀⣀⠀⠙⠁⠀⠀⢀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠈⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠙⠀⠀⠀⠀⠀⠐⠦⡭⣷⠁⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠈⠁
⠀⠰⠷⢠⣤⣠⡀⠀⠀⠀⣀⣀⠀⠀⣾⡄⣀⣤⡄⠀⠀⠀⣤⣤⣀⠀⠈⠈⠀⠀⣠⢤⣀
⠀⠀⠀⢸⣿⡟⠃⠀⡿⢇⡘⣼⠀⠀⣽⡏⢿⡇⠀⠀⠈⠝⠛⠛⠃⠀⠀⠀⠀⠘⠛⠒⠋⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠞⠙⠁⠀⠈⠿⣽⣿⠟⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⢻⠀⢀⠀⠀⠀⠇⣼⣰⢆⣧⡰⠀⠈⠹⣛⠏

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠡⡄⠀⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⠁⠀⠀⠈⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠃⠀⠛⠁
⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡤⠲⠆⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⡀⣒
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣴⡞⠀⠀⠀⠀⠀⡄⣴⡏⠀⠀⠀⠀⠀⠤⠂⢀⣀⣶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠇⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠈⡙⡏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⠃⠀⠟⣋⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡖⠀⠀⠀⢠⡜⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⣃⠀⠀⠀⠸⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡿⠀⠀⠀⢶⡇⣿⡖⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⠀⠀⠄⠃⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠹⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⡡⡄⠀⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠃⠀⠛⠁
⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠺⠆⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⡀⣒
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⡞⠀⠀⠀⠀⠀⡄⣴⡇⠀⠀⠀⠀⠀⠔⠂⢀⣀⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⣋⡉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⢉⡴⠛⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡋⣉⣉⡛⠻⠷⣶⣤⣄⣀⠀⠀⠀⣠⣴⡶⠿⠿⠿⢶⣦⣴⡾⠟⠉⠀⢠⡟⠁⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠉⠉⠳⢦⣀⠈⠉⠛⣻⣿⠿⠻⣅⠀⠀⠀⠀⣸⠁⠉⠛⠂⠀⢠⣟⣤⣄⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣙⣷⣄⠀⠉⠀⢀⡄⠘⣆⠀⠀⠀⡟⠀⢶⣄⠀⠀⠛⣽⠋⠁⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠘⠛⢿⣍⠀⠀⣠⠟⡔⢲⣸⡄⠀⠀⣧⣆⣹⡟⠷⠀⠀⠡⣄⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⢀⡀⠀⠀⠉⠀⠛⠛⣹⠃⠀⠀⠘⢯⡉⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡿⠁⠀⠀⠀⠀⢀⡴⠃⣴⣒⣲⣦⠀⠙⢦⡀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣠⠏⠀⠀⠘⠻⡿⠋⠀⠀⠀⠙⢦⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣀⠀⠀⠀⣇⠀⠐⢦⣀⡴⠛⠦⡤⠏⠀⠀⣼⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣬⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠳⣦⠀⠀⠀⠀⠀⠀⠐⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢸⡇⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⢻⡌⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡅⠀⠀⢘⢧⡀⠀⠀⠀⠀⣰⣋⠀⠀⠈⡇⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠘⣇⠀⠀⠸⣆⠙⠀⠀⠀⠘⢡⡏⠀⠀⢰⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡹⣦⠀⠀⠙⣦⡀⠀⠀⢀⡾⠁⠀⢀⡾⣀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⠈⢷⡀⠀⠨⣝⢷⡞⣫⠀⠀⢠⡞⠁⠈⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠾⠿⣦⣤⣿⣾⢷⣿⣤⣴⡿⠷⠶⠶⠶⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⣿⢾⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡩⠀⡠⠀⠀⠀⠀⠀⠀⠐⠒⠄⢱⡀⠈⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⡄⡇⠈⣠⣤⣄⠀⠀⠀⠀⣾⣷⣦⣸⢁⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⠹⡞⢻⣿⣿⠀⠀⠀⠐⠿⣿⠃⡎⠘⡇⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠃⠀⡇⠀⡼⠁⠀⢾⣿⡷⠀⠈⠳⣷⡀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠆⡸⠳⢄⠀⠀⠀⠀⠈⠀⠀⠀⠰⠃⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡏⠰⠒⠂⢈⡁⠤⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢈⡅⠀⠀⠁⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⡀⠀⠳⠞⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⣆⡀⠀⢀⡄⠀⠀⢸⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⠀⠀⠀⢩⠙⠶⠋⡝⠀⠀⢸⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⡇⠀⠀⠸⡆⠀⢀⡇⠀⠀⢸⢁⣾⠛⠉⣉⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠷⣄⣧⠀⠀⠀⢷⠀⢸⠁⠀⠀⣾⠞⠓⠲⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢰⠀⠀⢀⠟⠀⠀⠀⠘⣧⡏⠀⠀⠀⡈⢢⣰⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢦⣼⣄⣠⠤⠞⠳⠤⢧⣠⠧⠼⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⡶⠤⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣶⡼⣿⠷⡇⣤⢴⣷⢀⡄⠄⣾⣿⠓⠂⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡟⣋⡉⢠⡯⢇⠀⠿⣴⢼⣿⡿⠸⡯⠿⢫⣼⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠍⠃⠀⠆⢠⠁⣄⣾⣷⢭⡟⠀⣴⡿⢂⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣑⠢⠄⢳⣿⡟⢾⢹⡆⠝⡑⠚⠟⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⠛⠛⣥⣌⣷⣉⣹⡆⠀⢸⢡⡏⣠⠴⠖⡶⢶⠿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⠉⣻⣿⣤⣷⠀⠀⢾⣷⣟⣷⣾⣿⣟⠂⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⢀⣽⠯⢿⠀⣀⣽⣿⣿⣟⠻⣿⣋⣙⣯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣤⠀⠀⠀⠀⠀⠉⡿⠛⠙⠙⣿⠶⣤⣭⣽⣿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⡀⠀⠀⠀⠐⠶⠄⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⡷⢦⣄⣀⡀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣦⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠀⢰⠋⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢻⠟⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣺⣿⢻⣿⣾⣿⣿⣟⢿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⡿⢾⢿⣏⣹⣿⢿⠿⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠶⣶⠶⠞⠿⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⡀⣠⠶⠌⠀⠐⠤⡀⠀⠀⠀⢀⠠⠔⠒⢲⣤⣄⡀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣷⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢰⣿⠅⠀⠀⢀⣤⢶⣶⣤⡀⠀⠀⢠⣴⠶⣶⣦⣄⠀⠀⣹⣷⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠘⣿⣤⣀⡔⢿⣿⣾⣿⣿⠧⠤⠠⠼⠿⠿⣿⣿⡟⢳⣠⣿⠿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⡟⠉⠀⢸⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠹⢖⠀⠀⢠⠆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⢰⡇⠀⠀⠁⠀⠀⢀⣴⣶⠾⠛⣷⣦⡀⠀⠀⠀⠁⢠⡏⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠈⢻⡗⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠹⡆⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠈⠻⢿⡿⠛⠁⠀⠀⠀⠀⠀⠠⡇⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣾⣿⣄⠀⠀⠀⠀⠀⠀⢀⡔⢣⡀⠀⠀⠀⠀⠀⠀⢀⣇⡀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠹⢄⣘⣦⡤⠔⠓⠁⠀⠀⠙⠑⠶⣄⣀⣜⣠⠞⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠲⠦⠦⣄⣤⠤⠖⠚⠁

⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣦⣔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣿⣶⣶⣶⣦⣄⣀⣀⢀⡀⠀⠹⣿⣿⣿⣿⣿⣭⣓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣷⠆⠀⠈⠉⠿⣿⣿⣿⣿⣿⣧⣤⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣼⣿⠟⣿⣿⣿⡟⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦⣤⣈⡉⢁⡀⠼⠿⠿⠀⠘⣿⣿⣿⠀⠀⠀⠈⣿⠿⠛⠻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠈⠉⠙⠛⠻⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠋⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣵⣮⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⠂⠀⠀⠀⠀⢨⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠼⠾⠿⠿⢿⢿⠿⠿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣠⣄⡄⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⠀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣼⣿⣿⡿⣿⣇⢬⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠁⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡠⢀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⡀⠀⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠠⠂⠀⠀⢂⠀⠀⢡
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡠⠁⠀⠀⠈⢢⠀⠈⢇⠀⠀⠀⠀⢘⡀⠀⠘⠃⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢇
⠀⠀⠀⠀⡻⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠂⠀⠈⣄⡠⠐⠂⠉⠁⠀⠀⠠⠈⠁⠈⠈⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢆
⠀⠀⠀⡰⠁⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠣⡀
⠀⢀⠜⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⢢⡀
⢠⠎⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⠀⠀⠱
⡆⠀⠀⠀⠀⣰⡧⠚⠓⠶⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡤⠀⠀⠀⠀⢀⠔⠊⠁⠀⠱⡀
⢣⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠲⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣄⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠘⠢⠄⠤⠊
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢀⣠⢾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⣿⣿⣷⡙⣶⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⠻⠁⣄⣸⣿⣿⣷⠀⠠⠔⠒⠂⠀⠓⠒⠂⠀⠘⠿⣾⣿⣿⡿⢁⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠱⠜⠿⠟⢋⠄⠀⠀⣴⡖⣿⣟⣷⡆⠀⠀⠀⠂⠈⠉⠛⠁⠉⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠒⣄⠀⠀⠀⠀⠀⠀⣰⣧⡀⠀⠀⠀⠀⠀⣠⠞⠒⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠳⣦⣤⣴⡶⠛⠛⡿⠛⠛⣶⣶⣶⠟⠁⠀⠀⠀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠈⠻⣟⡁⠀⠀⠀⠀⠀⣍⠿⠁⠀⠀⢀⣠⠔⡡⠊⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠒⢄⠈⠱⢄⡀⢀⣀⠔⠁⢠⠴⠓⢊⡩⠐⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠙⠦⢄⣀⡀⢀⡤⠒⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⣀⡀⠀⠸⡆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡼⠀⢀⢀⣀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠁⠀⠀⠀⠉⠠⡄⣧⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⡇⡵⠋⠀⠀⢉⠓⢤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⡆⠀⠢⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢸⢸⡀⠠⠂⠀⠶⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣈⣀⣀⣠⡤⣟⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⢸⢤⣧⡀⠂⠔⠀⠂⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠦⠄⣀⠸⠄⠤⠜⠉⠉⠉⠉⠳⠄⢠⡀⠀⠀⣀⣀⠜⠀⠀⠉⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐
⠀⠀⠀⠀⠠⠀⠈⠁⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠂⠀⠀⡀⠀⠀⠐⠤⠄⠀⠀⣦⡔⠀⠄⠀⠀⠄⠀⢤⡾
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠿⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠆⠀⠀⠐
⠀⠀⠀⠀⠈⠠⠠⠈⢠⠠⠘⠊⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠂⠀⢀⠀⠀⠀⠀⠈⠧⠀⠀⠂⡐⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠁⠒⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠁⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠄⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠂⠄⠀⠄⠂
⠀⠀⢀⠰⣀⠌⠀⠀⠀⠀⣀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠈
⠀⠀⠀⠀⡁⠤⠀⣀⡀⠤⠀⠀⠀⠀⠀⠠⣀⠁⠐⠀⠀⠐⠂⠀⣀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡄⠈⣛⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠩⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠬⠉⠧⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠀⣀⠀⠐⠁⠀⠀⠀⠀⠐⢄⠀⠂⠑⠀⡀⠀⠀⠀⠀⣇⡀⠀⣀⣀⣀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠣⠦⡉⠀⢉⢴⠜⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠈⡀⣀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠔⠀⠀⠁⠀⠁⡀⠢⡀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⡄⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠲⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠈⠀⠉⢀⠘⡟⢀⠈⠀⠊⠀⠀⠀⠀⠀⢀⠄⠉⣄⠉⢠⠀⠀⠀⠀⠀⢀⠀⢠⠀⠰⠆⠀⡄⠀⡀⠀⠀⠀⢷⠀⠁⣀⠈⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠟⠒⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠃⠀⠈⠀⠀⠀⠀⠀⣧⡀⢘⠀⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠤⠄⠀⠀⠂⠀⠀⠀⠀⢈⠀⠀⠀⡈⠀⠠
⠀⠀⠀⠀⠀⢠⡀⠀⢠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠺⠆⠀⠠⠟⠂
⠀⠀⠆⡀⢀⡀⠀⣛⡀⢀⡀⢀⠰⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢴⠀⠐⡄
⠀⠀⠀⠀⠀⠁⠂⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⡈⠀⠄⠀⠀⠀⠀⠀⠀⠑⠄⠈⠅⠀⠐⠀⠀⠀⠀⠀⠸⠤⣀⡘⣀⣤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣲⣄⣠⣤⡄⣀⣀⣀⣀⣀⣀⣀⣠⡤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣦⢉⣭⣿⣿⣿⣿⣿⣿⣮⣻⣗⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⡀⣬⣭⣓⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣯⢿⣿⣷⢹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⢇⡔⢨⡳⣤⣿⣿⣿⣿⣿⣇⣠⠚⠀⣀⢹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⣿⣜⠿⠿⠧⣿⣿⣿⣿⣿⣿⣿⣁⣿⣶⡿⢂⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⡇⣤⣠⣴⣿⣿⢹⡏⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢻⡟⣿⣿⡿⠋⣿⣿⣿⣿⢿⣿⣷⣿⣿⣿⣿⣿⢰⣧⠘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠁⠈⢧⡘⠉⠀⢠⣿⣿⣿⡏⠈⠁⠈⠙⠟⠁⠀⢩⣾⣿⠀⠘⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠛⠉⠀⠀⠀⠈⢇⡀⢰⣿⣿⣿⣿⣷⡄⠀⡆⠀⠠⡀⣰⣿⣿⡿⠀⠀⠘⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⣭⡙⣛⣻⣿⠀⠀⢑⣴⢃⣴⣿⣿⣿⡇⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⣿⣿⣿⡿⠋⠀⠀⣸⠟⠋⣸⣿⢻⣿⣇⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢶⣤⣄⠀⠀⠀⣷⣦⡽⠭⣤⡤⡶⠟⠁⠀⠀⣿⠁⣿⣿⣿⠀⠀⠀⢠⠖⣿⠋⢙⡿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⢹⣦⣼⣇⣸⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⡇⠀⠀⢻⣤⠿⠳⢿⣤⠼⣧
⠀⠀⠀⠀⣤⣤⣤⣬⣧⣬⣿⣥⣤⣬⣿⣧⣤⣤⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣶⣿⣿⣿⣧⣤⣤⣾⣧⣤⣤⣬⣧⣴⣧⣤⣤⣤
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⣿⡔⣶⢠⠂⣼⢳⠀⣶⣠⡗⡆⣴⢰⢠⡖⡆⡴⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠓⠛⠛⠒⠃⠘⠊⠚⠙⠈⠓⠛⠛⠚⠈⠛⠓⠛



⡿⢿⠿⢿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⠤⠂⠀⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠈⡆⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣳⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⡀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⣾⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⢿⣿⡆⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⠜⠈⢿⡀⠀⠀⠀⠀⡞
⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⡸⠀⠑⠨⠿⠿⠟⠀⠀⢀⡤⠔⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸
⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡞⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠉⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡠⠊⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⡠⢴⠋⠀⠀⠀⠀⠀⠘⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠒⠒⠒⢄⡀⠀⠀⠀⣀⠄⠊⠉⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⡆⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢠⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⠎⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢇⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠇⠀⠀⠀⠀⠀⢀⠃⠈⡇⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠁⠀⠀⠀⠀⠀⠀⣸⣀⡴⠂⠀⠀⠀⠀⠀⠀⡸⠀⡔⠁⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣸⠀⢰⠀⠀⠀⣠⠁⢨⠀⠀⠀⠀⠀⠀⠀⢀⡗⠚⡄⠀⠀⠀⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠁⠀⠈⠣⠀⢄⣀⣀⠤⠠⠞⠀⠀⠀⠁⠈⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠈⠁⠒⠦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠽⠀⠘⠉⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡷⠀⠀⠀⠀⠀⠀⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢬⠟⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣼⢹⡞⠁⠂⠀⡀⣤⠀⣀⢀⡄⢀⠐⠉⠳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⠆⠀⠘⠀⠀⠀⠀⠀⠈⠀⢴⠇⠈⠀⠀⠀⠀⠁⢋⢄⠀⠀⠀⣴⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⠠⠄⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠃⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢉⠙⠇⠀⠀⣴⡿⣿⣷⣦⣀⡄⠐⠠⣤⠀⢀⣴⣾⣿⣦⣄⣀⣀⠶⢏⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡾⠿⠤⣼⠷⠿⢿⣷⣿⣽⣿⠟⠀⠀⠀⠀⠰⣿⣿⣯⣿⣿⠟⠛⠉⠡⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠃⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⢀⣀⣠⡀⠀⠉⠩⠋⠉⠁⠀⠀⠀⠀⠐⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⠓⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡆⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⣸⣿⣿⣿⣿⡇⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢠⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣬⣿⣿⣿⣿⣿⣿⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣅⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡙⠋⠉⠘⠋⠉⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⡄⢀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢙⣉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣤⡛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡄⠠⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠛⢻⣯⡸⣡⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡬⢃⣁⣸⣄⡉⢢⣀⠀⠄⠀⠀⢀⡀⢀⠀⠀⠀⢠⢠⠀⡧⠠⠶⠊⠉⠑⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠁⢈⠀⣩⠙⠚⠋⢙⠥⠄⠀⠠⡴⢭⡇⣼⣤⠷⠀⠀⠌⠉⢁⡀⠠⠀⠀⠀⣁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢁⡄⠀⠀⠉⠁⠀⠐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢳⠀⠀⠀⠀⠙⢏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⣤⣤⠁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⢸⡆⠀⠀⠀⢾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⠠⠀⠀⠀⠠⣟⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⢐⠒⠃⠀⠀⠀⠛⠼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⡰⠉⠙⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠂⠀⠀⠀⠀⠀⠁⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⡿⢿⠿⠿⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡿⣿⣿⣿⢿⠿⠿⠿⣿

⠀⢀⣴⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⣿⣿⣿⣿⣿⣿⣇⠀⣀⣀⣀⣠⡿⠁⠀⠀⠀⠀⢠⡄⠛⢠⣤⡌⠉⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇
⠀⠘⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠃⠀⠈⣿⠁⠀⠀⠀⠀⠀⠈⠙⠛⠳⣦⣤⣤⣶⣶⣶⣿⣿⣿⠟⠇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢤⠀⠉⢠⡞⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢹⣿⢿⣿⠋⠈⢿⣇⠻⣧⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠈⠁⠀⠀⠀⠀⠀⢀⣼⡿⢛⣿⡟⠉⠛⠛⣿⢿⣿
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⣸⡇⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⢹⣇⠀⠀⠀⠀⣿⠘⣏
⠀⠀⠀⠀⠰⠿⢠⣿⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠀⠙⠃⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⢠⡐⣀⡆⣆⠂⡇⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠙⠛⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⢠⡿⠀⠀⢀⣽⣿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⠀⠘⠛⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⡴⠀⠐⠖⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢣⠴⠐⠄⠇⠀⡇⠂⠘⠐⠰⠰⠤⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠⡄⠀⠀⣠⠦⣄⠀⠀⠀⢀⣔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⠆⠀⢠⣾⣀⡇⠀⠀⣿⣄⣹⣦⣤⠀⠾⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢴⠄⢺⣿⣿⡇⠀⠀⢸⣿⣟⡿⠁⢠⠄⢸⠁
⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸⠀⢀⣄⣍⣽⣿⠇⠀⠀⢸⣿⡏⠈⣋⠀⢀⣸
⠀⠀⠀⠀⠀⠸⢿⣿⠋⠢⡀⠀⣰⣿⣿⢿⡿⣿⣿⡄⠀⠀⠀⠉⠁⢁⠀⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢡⣾⣿⣿⣧⡀⠀⣼⣿⡇⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⣿⣿⠿⢿⣿⣿⠿⢇⠀⠀⠄⠠⡐⠑⠤⣄⣀⠅⢠⡋⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⠀⠀⠤⠼⠀⠐⠂⠒⠀⠀⠀⠀⢄⣠⠇⠈⠉