Straightforward Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⣠⠆⠀⢀⣴⣿⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢻⣿⣧⠀⣙⠧⢰⣿⣿⠏⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣹⣧⠀⠉⠛⢋⣿⣿⣶⣤⡀⢀⣿⣿⡆⢀⠀⣿⣿⡿⠠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⣠⡿⠀⠀⠀⠀⠹⣿⣿⣿⣇⠫⣼⣿⣿⠈⠁⢻⣿⣵⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠧⣾⣿⣿⠀⠀⢸⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⣿⠃⠀⠀⢸⠃⠀⠠⠀⠀⢶⡗
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠈⠂⢴⠄⢏⠀⠠⣀⠸⠀⠀⠄⠁
⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡀⠀⠀⢶⣄⠀⠘⢇⠀⣹⠂⠐⠀⠀⠀⠀⠀⠒⠀⠠⣀
⠀⠀⠀⠀⠀⠀⣈⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣦⣀⣿⡆⠀⠈⢾⡇⠀⠀⣀⠀⣤⠾⠶⠂
⠀⠀⠀⠀⠐⠀⠸⣿⣷⣾⡇⢀⠀⢷⠀⢀⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⢸⡇⢀⠔⠋⠁
⠀⠀⠀⠰⣏⠡⠐⢬⣿⣿⠇⠈⠀⣈⠠⠟⠋⠀⠠⡀⠀⠛⠛⠉⠀⠀⠀⠀⣀⡀⠈⢣⡀⠶⣼⠇⠁⠀⣾⡆
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⢦⠀⠈⢹⣆⣳⠂⠀⠂⠈⢠⡄⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠁⢶⡇⠀⠀⠘⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠹⢿⣿⡷⢀⠀⠰⠀⠈⠀⠤⢄⣠⣘⣳⣤⣄⠀⠱⠀⣼⡇⠀⠀⠀⠀⢀⠀⣠
⠀⠀⠀⠀⠉⠈⠛⠀⠰⣦⡀⠘⠐⠆⠈⣿⠑⠊⠈⠀⠀⠀⡄⠀⠀⠈⠉⠙⠀⠙⠢⡀⢠⡿⠁⠀⣠⣤⠞⣩⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡆⠀⢸⣼⠃⠀⠠⠔⠂⠉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢀⡜⠃⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⠀⠈⠇⢀⠐⠀⠀⠄⠀⠀⠀⠀⣠⣶⡶⠆⠀⠀⠀⠀⢸⣇⡄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⢘⠗⠀⠀⠀⠀⠀⢀⣤⠀⠁⡴⠇⠘⢇⠀⠀⣨⠿⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⣷⡀⠘⡇⠸⠀⠀⠀⠀⠀⢀⣮⠠⠀⠂⠀⠀⠀⠻⣠⠞⠁⢀
⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣄⡀⠁⠀⡿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⣸⣿⡿⠟⠉⠀⠉⢢⡀⣷⠀⢀⣠⢶⡂⠔⢢⣄⠀⠀⠀⠀⢠⡟⠁⣤⠔⠚⠂
⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⢀⣄⡈⠻⣄⢈⠃⠈⠻⢶⣿⣿⡇⠀⠀⣤⠟⠛⠂⠄⠰⣤⣀⠀⢄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⡙⣾⡇⠀⠀⣀⣀⠀⠉⢀⡾⠁⠀⠀⠀⠀⠀⠐⠛⢷⣎⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠙⣇⠀⠋⠉⠉⠀⣿⠏⠁⠀⠀⠀⠀⠀⢀⣤⣤⡈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⢀⣾⡃⠀⢀⣀⣀⡀⠀⢠⠟⠋⠉⠉⠀⠘⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⣼⠏⠉⠀⠀⣿⣿⣿⣷⣥⠀⠀⠀⢤⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠿⠛⠛⠁⠢⡀⠀⠙⣿⠏⠀⠀⠀⠀⢿⣟⣹⣿⣷⡔⠈⠁⠀⠂⠄⠀⠀⠙⣿⣷
⠀⠀⠀⠀⠀⠀⡀⠀⢤⣴⣶⣶⣶⣤⢤⡀⠀⠈⠢⣀⣮⣤⣶⣶⣦⣄⣠⡿⣉⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠉⠛⠿⢿⣿⡀⠀⣰⣿⣿⣿⣿⡿⢋⣽⠋⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠂⠀⠀⠀⠉⢲⣿⣿⡿⠟⢋⣴⠟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⣀⡴⠋⠀⢈⠷⣦⡀⠀⠀⠀⠀⣀⡀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣦⣀⠀⠀⠀⠀⠀⠤⠋⠀⠀⠀⣿⡆⢈⣿⣄⠀⠀⠀⣽⣿⠗⠂⠁⠀⠀⠠⠀⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠒⢼⡿⠛⠉⠉⠉⠳⣄⠀⠀⢰⡦⠄⢰⣶⣦⡄⠀⢨⣸⣿⠀⠀⠀⠉⠉⠶⢊⡀⢡⢒⠀⣎⠀⢀
⠀⠀⠀⠀⠀⢈⡳⠈⠀⠀⠀⠀⠀⠀⠀⠘⢄⣡⣬⠀⠀⠀⠀⠀⠀⠐⣾⣿⡇⠀⠀⠀⠀⠀⠡⠈⣉⠛⣛⠷⠁
⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠾⠂⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠠⠀⠠⠈⠁⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠸⣧⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠰⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡗⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⡤⠀⢤⣀⠀⣿⢀⡄⠓⢾⣵⢲⣤⣽⣿⡆⠀⠀⠀⠀⠀⠀⡄⣶
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠈⣷⠛⢈⠇⠀⠀⠉⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⣸⣧⡆⠀⠀⠀⠀⠀⠀⠀⣿⣶⠇⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡄
⠀⠀⠀⠀⠀⢰⣿⡏⡙⠻⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⣿⢡⣶⡌⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⢁⠻⣇⢨⡐⣿⠘⢟⣡⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡏⠙⠆⣿⢨⣦⣽⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣈⡇⢸⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⡋⡍⢷⣍⣹⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠛⠿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⡏⣤⣱⣜⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠰⣦⣄⡀⢰⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⡹⢧⣝⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢠⡟⠀⠉⠻⠿⠀⠀⠀⠀⢣⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣍⡻⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠠⡟⠻⣶⣄⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡷⢭⣻⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠀⠀⠸⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣇⣨⡿⢷⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠛⠁⠀⠀⠀⠀⢻⣿⣿⣿⣾⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⣧⡀⢻⣿⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⣟⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠀⢿⣇⠀⠀⢹⣷⠀⠹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣀⣀⠀⠘⣿⡄⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⡀⠹⣿⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⢠⣀⢆⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⡿⢿⢿⣶⢤⣄⣀⠀⠀⠀⠀⣀⣀⠤⢴⣖⣿⠿⠿⠿⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⠿⠿⠿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠿⠿⠿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠆⠀⠀⠀⠀⠀⠈⠙⠛⢿⣦⣄⠀⠀⠀⢀⣀⣤⣤⣀⣀⣤⣤⣀⡀⠀⠀⠀⣠⣶⡿⠛⠋⠁⠀⠀⠀⠀⠀⠰⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠙⠻⣷⣶⣿⣿⣛⣉⣉⣛⣛⣉⣉⣛⣻⣿⣶⣾⠟⠋⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢀⣾⣿⣿⣿⣿⡛⠲⠀⢀⣠⣤⣾⣿⡿⠿⢛⣋⣽⣿⣿⣯⣙⡛⠿⢿⣿⣷⣦⣄⡀⠀⠔⢛⣿⣿⣿⣿⣷⡀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣿⣿⣿⠟⠃⠀⠀⣲⣿⣿⣿⣉⣤⣴⣾⡿⠿⢛⣿⣿⡛⠿⢿⣷⣦⣬⣉⣿⣿⣿⣗⠀⠀⠘⠻⣿⣿⣿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠹⣿⣿⠀⠀⠀⣨⣽⠟⢋⣵⣿⠟⢉⣀⣤⣶⣿⣿⣿⣿⣶⣤⣀⡉⠻⣿⣮⡙⠻⣯⣅⠀⠀⠀⣿⣿⠏⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠙⠿⠀⢀⣴⡟⠁⠀⣸⣿⣡⣾⡿⢛⣩⡿⢻⣿⣿⡟⢿⣍⡛⢿⣷⣌⣿⣇⠀⠈⢻⣦⡀⠀⠿⠋⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⣠⣿⣿⣇⠀⣘⡿⡿⢻⢣⠞⣿⣵⣾⢟⣿⣿⡻⣶⣬⣿⠳⡝⣟⢿⢿⣃⠀⣸⣿⣿⣄⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣰⡿⢟⣿⣿⡿⣿⡁⠇⠻⣤⣿⢹⡿⣣⣾⣿⣿⣷⣜⢿⡏⣿⣤⠟⠼⢈⣿⢿⣿⣿⡛⢿⣆⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠟⠀⣴⡏⠀⣾⡿⠋⢠⣿⠳⣤⡶⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠦⣤⠞⣿⡄⠙⢿⣷⠀⢹⣦⠀⠻⣷⣄⣀⡀
⠀⠀⠀⠀⠀⣿⣟⠛⠋⠁⢠⣾⡿⠀⢰⣿⡇⠀⣿⢹⠷⣦⠰⣧⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣼⠆⣴⠾⡏⣿⠀⢸⣿⡆⠀⢿⣷⡄⠈⠙⠛⣻⣿
⠀⠀⠀⠀⠀⠉⣻⣿⠃⠀⠀⣿⡇⠀⢸⣿⠁⢀⣿⢸⡷⢮⣻⣶⣦⡀⣩⣿⣿⣿⣿⣿⣿⣍⠀⣴⣶⣟⡱⢾⡇⣿⡀⠈⣿⡇⠀⢸⣿⠀⠀⠸⣿⣟⠉
⠀⠀⠀⠀⢀⣾⣟⣁⡀⠀⢠⡿⠀⢀⣾⣿⠀⢸⣿⣤⡙⠛⣻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⠛⢋⣤⣿⡇⠀⣿⣷⡀⠀⢿⡄⠀⢀⣈⣻⣷
⠀⠀⠀⠀⠀⢻⣿⡟⠀⠐⣏⣀⠀⠘⣿⣿⠀⠀⠉⠻⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠟⠉⠀⠀⣿⣿⠃⠀⣈⣹⠂⠀⢻⣿⡟
⠀⠀⠀⠀⠀⢸⣿⣤⡀⠀⠈⣿⣆⠀⣼⠷⣤⠀⢾⣷⡶⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⢶⣾⡷⠀⣤⠾⣧⠀⣰⣿⠁⠀⢀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀⢸⣿⡀⢀⣠⣤⡄⠀⠉⠃⢿⣈⠻⠿⣿⣷⣝⠻⣾⣿⠟⣫⣾⣿⠿⠛⣁⡿⠘⠉⠀⢠⣦⣄⡀⢀⣿⡇⠀⠀⢸⣿⠉
⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣈⡉⠛⠶⠶⠿⢿⣷⡍⢩⣾⡿⠿⠶⠶⠛⢉⣁⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⢻⣿⣟⣩⠭⠈⠛⠛⢛⣿⠟⠁⠈⠻⣿⡛⠛⠛⠁⢭⣍⣻⣿⡟⠻⠿⠿⠋⠁⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠰⣿⣧⣦⣤⡀⠀⠀⠀⠀⠀⠀⠠⠿⢿⣿⣧⠀⠀⠀⠀⣽⣤⣤⣤⣤⣤⣬⣯⠀⠀⠀⠀⣼⣿⣿⠿⠄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣼⣿⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠿⣷⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣋⣁⢀⡀⣈⣙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣾⠿⠋⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⣀⣠⣴⣶⠿⢿⣶⣄⠀⠀⢶⡿⣿⣿⣿⣿⣿⣿⢿⡶⠀⠀⣠⣶⡿⠿⣶⣦⣄⣀⣼⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠉⠀⠀⠀⠈⢻⣷⡀⠀⠀⠁⠛⠉⠉⠛⠈⠀⠀⢀⣾⡟⠁⠀⠀⠀⠉⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⡀⠀⠀⠀⠀⢀⣀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣷⣾⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣆⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣦⣴⣴⣿⢏⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣁⣀⣠⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⡿⠀⠛⠀⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣇⣤⣦⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣟⢯⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⡀⠀⡑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⢢⠀⠀⠀⡶⠓⢲⢴⠚⠳⣆
⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢟⠒⠋⠈⠓⠚⢹
⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠘⢦⠀⠀⠑⠂⠀⡁⠐⠁
⠀⠀⠀⠀⠀⡈⢦⠦⡀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠑⠤⠄⠀⠀⢳⠠⣄
⠀⠀⠀⠀⠘⡄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠉⠒⢢
⠀⠀⠀⠀⠀⠈⠓⠤⢵⣀⣀⣀⢠⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⢇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣇
⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣃⣀⣀⣙⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠄⠂⠡⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣄⣡⠴⠃⠐⠻⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⢙⣤⡀
⠀⠀⠀⠚⠁⠐⢄⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⡀⠉⠱⢦⣀
⢀⡶⢸⣿⣶⣴⣾⡷⡀⠀⢠⣆⠸⣷⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠘⠚⠳⢦⣈⢷⡀
⣼⢣⣷⣤⢿⣿⣿⣿⡇⠀⠈⠛⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡾⠀⢼⠇⢠⡟⠀⢄⠛⡆⠈⣷⠀⢻
⡇⣿⡈⣧⣛⣿⣧⠌⢸⠀⠀⠀⠀⠀⣀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣤⢷⣄⡈⠃⠀⢠⡿⠄⢈
⡇⠈⠙⠾⠉⠋⠑⠒⠀⠀⠀⠀⡠⠈⡀⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠁⢈⡉⠖⠉⠃⢱⣈⣿
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢙⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠘⠓⠂⠂⠀⠐⠀⠀⠀⠀⠀⠀⠉⠀⡸
⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠈⠙⠓⠒⠒⢰⠊⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠈⠙⠶⢤⣤⣀⣀⣀⣄⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠔⠁⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣠⠀⠘⣆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⠔⠁⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣀⠔⠁⠀⠀⠀⠰⡇⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠳⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⢹⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣄⠸⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⢹⡄⠒⠐⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐
⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠀⠀⠀⠂⠈⠈⠀⠠⠁⡀⠀⠀⠤⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠈⠂⠀⠀⠀⠠⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠅⠘⠦⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠚⠚⠀⣂⣀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠰⣾⣿⢛⠁⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠡⠀⠠⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⡀⠠⠀⡂⠀⠈
⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠁⠀⠀⢀⡔⠉⠀⢀⠀⠀⠀⢄⠀⠀⠀⠀⣀⠀⠀⠠
⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⠀⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣾⡏⠁⠀⠀⠀⠀⢀⣄⠱⡄
⠀⠀⠀⠈⠁⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠉⠹⠿⢿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⠿⠛⣳⣒⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⣀⣨⣁⣏⢽⠃⠀⠀⠀⠠⠖⠋⠁⣠⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⣀⡰⠀⠀⢠⣄⣤⣴⡲⠒⠀⢀⡈⣑⡤⠀⠴⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢥⣽⠤⢤⣤⣤⣤⡾⡧⣀⢀⣉⣉⣵⡗⠀⠖⠞⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠠⠼⣟⠦⠄⣤⡐⣒⣺⡷⠀⣀⣥⣤⣾⣉⠀⡙⡛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⢼⣿⠀⠀⢤⣬⡤⠼⡿⠀⠀⡤⢴⣾⣍⠈⣉⣹⣿⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢀⡠⠤⣀⠒⢒⠲⠲⠖⠛⠲⠚⠛⠦⠤⠤⠤⠤⢼⡟⠀⠠⢶⢾⣯⣄⠀⣉⣣⢿⡋⢉⣭⡇
⠀⠀⠀⠀⠀⠸⠳⠶⣯⣷⣬⠍⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠖⠒⠚⠛⠓⠲⡟⣿⠷⣇⠀⣡⣤⢿⣅⣸⢿⡇⣔⠂⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣒⠒⠒⢤⡀⢉⠡⡤⠔⢞⣪⣽⣿⡇⢀⣦⣿⡧⠼⢿⣷⣛⠀⠼⠷⢿⡄
⠀⠀⠀⠀⠀⢰⣤⠤⣤⣤⣼⡀⡀⠀⠀⠀⠀⠀⢸⣟⠊⠙⠛⠛⠒⠩⣭⣲⢾⡿⢥⡾⣵⢾⣧⣤⣼⠷⣗⡊⠉⢉⢻⡖⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠙⠳⠄⣀⠀⠀⠀⢀⢸⣇⠁⠠⠤⠀⠀⠀⡏⠀⠀⠄⠀⠀⢀⣺⡆⠀⠐⠘⠦⣀⣩⣭⡽⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠠⠤⠿⠿⣶⡴⣄⣀⣀⡇⣂⣤⣤⣶⣿⡽⠿⠭⠤⠤⠉⠉⠉⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠛⠛⠛⠛⠛⠄⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⣆
⠀⠀⠀⠀⠀⣠⣤⢼⡷⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⢾⡿⠶⠶⣤
⠀⠀⠀⠀⠀⢻⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣇⠀⣿⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠉⣻⠛⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⠼⠏⢿⣄⡀
⠀⠀⠀⢀⣠⡶⣛⡭⠖⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣑⠈⠙⠷⣄
⠀⢀⣴⠟⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣉⠻⢦⡀⠈⢷⡄
⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⣀⣠⣾⣋⣉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠹⣦⠀⢻
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡤⠤⣤⣍⣉⣉⡉⠉⣿⠲⢤⣉⠙⠛⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠘
⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡞⣠⡤⠤⢤⡀⢈⡏⢰⡏⠀⢠⠞⢁⣼⣋⠛⠛⠛⠛⣻⠇⠀⠀⠀⢸⣏⣿
⣿⠘⠁⠀⠀⢀⣤⣀⠀⠀⠀⣴⢃⡞⣼⣥⢀⡴⣄⢹⡼⢡⡟⢀⡴⢃⣴⠟⠁⠉⠉⣹⠂⢠⡟⠀⠀⠀⢀⣤⡉⠁
⣿⠀⠀⠀⠀⢿⣁⢙⡷⠒⠚⠛⠛⠓⠟⠚⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛⠷⠶⢶⡶⠛⢁⣽⠆
⣿⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠞⢻⡅
⣿⠀⠀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣼⠋⢉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⣿⠀⠀⡿⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣷⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⢸⡇⢸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⢸⣇⠈⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡤⣿⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⣿⠀⠈⠉⣹⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⢠
⣿⠀⣠⡾⢋⣴⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣷⣌⠳⣼
⣿⠀⠻⠶⣿⣇⣠⡾⠿⢿⣓⣶⠶⣶⠶⠶⠶⢶⡶⠶⠶⢶⣶⠶⠶⡶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⣾⢧⣀⣹⠟⣴⢿
⢺⠀⠀⠀⠀⠈⠉⢛⣷⣶⣤⣁⣰⠏⠀⣀⡀⢸⡗⢚⣉⣭⣤⣶⣾⡃⣶⣾⣻⣟⣻⣿⣆⣀⣙⣧⡈⠓⠟⣣⡾⠁⣼
⢸⡄⠀⠀⠀⠀⢀⣾⡏⠀⡶⠏⣻⣾⡿⡛⠛⢻⡟⠛⠛⣿⢿⣿⡿⣶⢿⣯⡷⡞⣷⣞⣋⣿⡉⢹⣿⣦⡾⠋⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠸⣿⢧⣽⣿⢻⣛⠿⣄⢻⡄⢸⣟⣛⣿⣻⣟⣟⣿⣙⣿⣿⣹⣽⣿⣉⠉⣽⣿⣯⠟⠀⠀⠀⠀⠀⣿
⠘⣧⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣭⣧⣽⠦⠶⠛⠁⠉⢹⣿⡿⣿⢿⣿⣿⣟⣿⣥⣤⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠙⢧⡀⠀⠐⠶⠶⠶⠶⠾⢿⠿⠿⢿⣤⣤⣤⣤⣤⣼⣿⣿⣿⣯⣭⣭⣥⣤⣭⣿⣭⣤⣤⡴⠶⠶⠖⠂⠀⠀⣼⠃
⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⡂⠠⠽⣾⡀⣞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢒⠢⠅⠠⠄⠀⠀⣀⣉⣀⣨⣼⡏⠥⣥⢾⣂⣾⠧
⠀⠀⠀⠀⠠⠐⠄⠀⠂⠀⠁⠀⠀⢀⠀⠀⢀⠀⠀⠀⠊⠉⠉⣄⡶⠼⠮⠧⠵⠻⡍⢙⣏⠏⠀⠀⣀⠀⠀⢀⠼⠗
⠀⠀⠀⣀⣀⡀⠀⠀⠀⡀⢠⣴⣴⠒⠬⣡⠀⢠⠔⠂⡀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⣘⣆
⠀⠀⠤⡈⠉⠁⠄⢀⠸⠤⠞⠹⣆⠀⠯⣇⡀⠈⡿⣿⣇⠈⠈⠄⠀⠤⠑⠠⠂⠀⠕⣀⡁⢙⠢⣀⡴⠀⢲⠶⣤⠔⠒⠉⠁
⠀⠀⠀⠈⠒⠀⡀⠀⠡⡀⠈⢉⣉⠓⡚⢛⠀⠩⠭⣿⠛⢃⣠⡄⠈⡓⠄⢈⠱⢁⠀⠀⠈⢠⡄⣠⡉⣫⣩⠍⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢈⡡⢤⡵⠀⠀⡜⠤⢀⣶⡶⣾⢧⡀⠈⠀⣈⠀⠉⠁⢉⡀⣀⣀⣀⡆⡠⠒⠠⣆⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⡓⠋⠉⠀⠙⣷⣼⠟⠛⠛⠛⠉⠀⠉⠉⠉⠈⠀⠀⠰⠋⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢀⠠⠖⠖⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠈⠉⠉⠉⠉⠉⠁⠠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡖⠐⠒⠢⠤⠄⠀⣀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠖⠲⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠓⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠙⠢⢄⣀⣀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⠀⠀⠀⠀⠀⠀⠻⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠐⡟⠉⠋⠀⠈⠑⠢⣄⠀⠀⠀⣠⠜⢻⠰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠉⠁⢸⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠇⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⡀⠠⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢠⡀⢠⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡌⠀⢸⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡸⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⡇⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⡎⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠀⠀⡀⢾⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢐⣇⢀⡤⠀⠒⠂⢉⡧⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠉⡶⠶⠁⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠆⠀⢀⡤⠚⠉⠀⠀⠀⣀⠰⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢀⡸⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠛⣄⠀⢀⣀⠠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⡜⠁⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢰⠁⢀⠾⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⡆⣀⡜⠀⠀⠀⠀⠀⠀⠸⡆⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣤⠋⠀⣉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠓⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠸⠂⢀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠸⣄⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠎⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⣠⠜⢧⡀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠠⠔⠒⠈⠣⣄⡠⠷⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠫⡄⠀⠀⠀⠠⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀
⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢺
⠀⠀⠈⢦⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣀⠠⠟
⠀⠀⠀⠀⠱⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⣀⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠂⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣀⡀⠤⠤⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣒⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⢀⡀⢀⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⠀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢀⣉⣍⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠨⢉⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢘⠆⠀⠀⠆⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠀⣀⠒⠈⢌⡐⠂⠤⢀⣀⠠⣤⠼⠉⠠⠶⠏⣤⣀⡀⢐⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠉⠅⢘⡂⠸⠁⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⣤⣠⠀⠐⢊⠓⠟⠇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠂⠀⠐⠢⠖⠚⡇⠀⠀⠀⠀⠀⠀⢀⠂⣅⡉⠉⢙⠃⠀⠀⠐⠛⠛⠉⠲⠦⠤⠀⡠⠀⠀⠀⢲⡀
⠀⠀⠀⠀⠀⠖⠒⠒⠠⠴⠀⡄⠸⠂⠀⠀⠀⠰⠤⠜⢃⣀⡀⠄⠤⣄⢰⢒⣋⡕⣒⠷⠶⣣⣅⣒⡦⠤⡁⠀⠉⠓⢈⡉⢄⠔⢒⠉⠉⡅
⠀⠀⠀⠀⠀⠃⠤⠀⠠⠼⠁⡅⠰⠦⣀⣀⣀⣀⣀⡠⢞⠈⠉⢈⠢⣿⠸⠀⠒⠨⠍⠛⠁⠀⠬⣁⡈⠉⠀⠍⠐⠽⢒⠉⢉⠩⢀⠀⠀⡇⡀⣠⢀
⠀⠀⠀⠀⠐⠣⠤⢤⡗⠟⠋⠭⣝⠄⠀⠀⠀⠀⠀⢀⡼⢄⠀⠀⡥⣴⠶⢄⠤⣠⣤⣀⣤⣄⣤⣄⡀⠀⠀⢀⣤⠤⠶⠎⣒⣩⡅⠖⠓⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣐⣀⣠⣆⣀⠀⠀⠀⣙⣰⠞⠓⠲⠒⢚⢭⢆⢲⠂⠀⠀⠀⠀⠈⠙⠙⠻⠽⠀⡠⠤⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⢪⡁⠒⠀⠐⡒⠂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠐⠒⠊⠉

⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠾⠉⠋⠁⠈⠻⠇
⠀⠀⠀⠀⢤⠀⠐⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠤
⠀⠀⠠⠄⠀⠐⠀⠀⠂⠁⠀⠀⠂
⠀⠀⠀⠀⠸⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠂⠀⣰⡀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣠⠏
⠀⠀⠠⠀⠀⠙⠓⠚⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⢀⡠⠀⠀⠀⠀⠂⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠤⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠐⠋⠀⠐⣇⠁
⠀⠀⠀⠀⠀⢀⣮⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠲⠆⠀⠀⠀⠀⢀⠀⡃⢸⡿⢧⡆
⠀⠀⠄⠂⠀⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣹
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡀⠀⣱⠄⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣈⣁⣠⠴⠖⠒⠒⠤⠠⠤⠖⠒⠒⠐⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⣾⣶⣦⣶⡖⠚⠛⠛⠛⢻⣿⣿⣶⣦⣶⣤⣴⣶⣦⣴⣶⣶⣶⣾⡿⠿⠿⠿⠿⠿⢿⣾⣧⣴⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⠒⠂⠒⠒⡖⠒⠲⠶⣶⠶⠶⠤⠀⠀⣀⣤⡴⣶⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠀⢦⣄⠀⠀⢀⡀⠉⠓⠋⠀⠀⠀⠛⠟⠀⠀⠴⣦⠀⠁
⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⣠⠞⠀⢀⠠⣤⣄⣀⣠⣄⡏⣉⣶⠀⠀⠀⠀⣀⣁⣀⠀⠀⠀⠨⠁⠀⣀⠁⢠⡀
⠀⠀⢀⡴⠋⠀⡀⠀⠀⣀⡤⣄⠀⢀⡾⠗⣠⣤⢭⢥⣼⡟⢫⣤⣤⠀⣉⢸⣤⠽⢯⣽⣷⠆⢀⣤⣞⢉⣬⣜⣤
⠀⣠⠟⠁⠀⠠⢝⠀⢸⣿⠺⡥⣴⡈⢉⢁⣱⠾⠛⠢⠚⠛⣒⠶⠶⠟⠀⠀⠈⠉⢑⠂⣤⣶⣿⢛⣵⣿⠟⢘⡿⢷⡄
⡠⠇⠀⠀⠀⣴⠋⠀⠀⣀⣽⣿⠣⠈⠀⣽⣷⠾⠓⠀⠀⠀⡉⢀⣰⠀⠄⠀⢀⣠⣀⠀⠩⠭⡡⣾⣾⡁⠀⠻⠷⣬⣷
⠷⣄⣀⠀⢸⢿⢳⣄⢀⣦⣹⠟⠀⠀⢀⣠⣤⠤⣤⡤⠤⢤⣤⣈⡙⠿⣷⣀⣜⠛⠋⠁⣀⣜⣻⣭⣟⣁⠀⢤⣥⣼⠻⠗⡀
⡇⢠⣿⣵⣾⣿⠿⣷⡿⠋⠁⠀⢠⡾⠋⠁⠀⠀⠀⠀⢀⣀⠀⠉⠙⠳⣄⠈⠙⢧⣦⡘⠊⢻⣟⠛⠓⠈⠀⠈⠉⠉⣀⡾⡇
⡇⠨⣹⡄⢠⣱⠊⠉⠁⠀⠀⠀⠈⢷⣄⠀⠀⢠⡴⠛⠛⠛⢛⠓⣦⠄⠙⢷⡀⠀⠻⠋⠐⣯⣩⡿⠇⠀⢀⣴⣾⡛⣿⠿⠃
⢙⠀⠀⡞⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣝⠂⠐⢣⡞⡅⠀⠀⢀⠸⢻⣷⣆⣸⠇⠀⠀⣿⢦⢾⣿⠀⠀⢠⣼⢟⣟⠟⣁
⠘⡆⠉⠂⠶⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡆⠀⠞⠀⠙⣓⢒⣉⣠⣄⣹⣿⣿⡆⠀⢈⣤⣍⠂⠁⠀⠠⣀⣵⣾⢁⠎⠘
⠀⠀⠀⣀⣀⡂⡀⠺⠖⠠⠄⠀⠈⠀⣩⣽⣦⠀⠰⣾⡿⣯⡉⠁⠈⠙⢷⣟⠛⠿⠛⢋⡹⣶⣠⣾⠞⣁⠌⣽⣿⢷⣶⡆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠐⠾⣿⡿⠋⠀⣶⠻⣷⠸⠇⠀⠀⠀⣸⠏⣀⡶⣶⣿⣿⣿⣇⠀⠈⠛⠁⠀⠁⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠳⡟⣦⠀⠀⠀⠀⠀⠀⣿⣼⢫⡇⠈⢁⠹⣿⣿⣷⡜⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⢻⣇⠀⠐⠁⢸⣿⣌⣹⣧⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠆⠀⠀⠀⠀⠀⣿⠀⣩⠿⠀⠀⠈⠛⢻⣿⣻⣦⡀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠞⢱⣶⡄⠀⠀⣿⠉⡄⠀⠀⠀⠀⠀⠘⠻⠿⠄⠿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠉⡇⠀⠀⣿⢸⡃⠀⠀⠐⠃⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⡇⠀⠀⢻⡈⠁⠀⣠⠄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⣼⠇⠀⠀⣰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡿⠞⢂⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢸⣷⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⢀⡀
⠀⠠⢠⠀⠀⠀⠀⠀⠒⢂⡐⠀⠀⠈⠋⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠉⠛⠂⠀⠂⡁⠀⠨⠀⠀⢀⠀⠀⠀⣶⠀⠀⣴⣾⣿⠃
⠀⠀⣆⠀⠀⠚⠂⠀⠈⠻⣧⣀⡄⠀⠀⠀⣀⠀⠀⢀⣖⣀⣀⣰⣤⠀⠘⣿⠛⠀⠀⠀⠀⢰⣷⣶⣿⣇⡀⠀⠀⠀⣼⠀⠀⣽⣿⣿⡃
⠀⠀⢻⣼⣶⣶⣿⣭⣿⣿⣿⣿⣽⠀⠀⠀⠸⠿⠿⠿⠿⠟⠛⠛⠛⠀⠘⠛⠳⠞⠃⠀⠀⠈⠀⠃⠀⠹⣇⠀⠀⠀⡟⠀⠀⡿⣿⣿⠁
⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠘⣧⠀⠐⣿⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢦⡀⠀⠀⠀⡔⠂⠀⠀⠀⡞⠈⠃⠀⠀⠀⠀⠀⠀⠀⡛⠶⣬⡁⠀⢿⡆⠀⠾⠀⠀⣿⢾⠿
⠀⢠⣤⣤⣤⣤⣴⣞⠻⠿⠛⢋⣡⣦⣥⣤⡀⠀⠘⠀⠀⠀⣦⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠓⠶⠚⠁⠀⢸⡇⠀⠀⠀⠀⢀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⠚⠛⠉⠉⠙⣏⠳⡄⠀⠀⠀⠢⣄⣀⣀⣀⣀⣠⡴⠟⠀⠀⠀⠀⠈⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣇⡀⠀⡗⠀⠀⠀⠀⠰⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⣧⠀⠀⠀⠀⠀⣿⡴⠃⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠐⣨⡀⣾⡆⣿⡇⣿
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠹⡄⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠨⠍⠽⠆⠲⠆⠿⠇⠿⠇⠿⠇⠿⠃⠿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢧⣀⡀⢀⣨⣿⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⠻⠟⠉⣯⠳⡄⠀⠀⠁⠀⠀⠀⠀⠈⣡⠀⠀⠙⠍⠉⠉⠁⠁⠀⠀⠈⠂
⠀⠀⣠⣤⠤⠤⣤⠐⣆⠀⠀⠄⠀⠠⡆⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠿⠆⠀⣾⡏⠀⠀⣧⠰⠀⠨⠀⠈
⠀⠀⣆⠀⠀⢀⠀⢁⡧⢀⠂⠀⠀⠀⠇⠀⠀⢀⣄⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠹⣧⣠⣤⣟⠆⠀⠀⠀⠠⠤⠠
⠀⠀⡹⠀⠀⠘⠢⠸⡧⠘⠀⠀⠀⠀⢰⠀⠀⣿⣅⣉⠿⠀⢀⣴⣏⣁⣉⠉⠀⠠⠙⠛⠛⠛⠛⠛⠉⠉⠉⠋⠉⠉⠉⠍⠉⠉⠉⠉⠄
⠀⠰⠀⣀⣀⣀⡀⢨⣇⡰⢰⣰⣦⡶⣸⠀⢠⡦⠋⠛⣿⡄⠐⢿⡗⠒⠓
⠀⢈⡀⢭⣤⣤⣤⣼⣯⡥⠤⠬⣥⣤⣭⠀⠀⠉⠛⠛⠉⠀⠀⠀⠙⠛⠛⠁⠀⠀⠄⠀⠀⠀⠐⣢⡄⠀⠀⠀⠉⠁
⠀⠀⠉⠙⠛⠛⠉⠹⠏⠉⠒⠶⠾⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡄⣀⣉⣁⢀⣙⣷⣴⡄⠀⠀⢠⣤⣤⣤⣤⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⡙⠛⠛⠋⢭⡇⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⡇⠀⠀⢺⣭⣭⣽⣿⣿⣿⡇
⠀⠀⠀⠀⣄⣀⣐⣛⠛⠋⠉⢛⣃⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⠋⠀⠀⣾⣭⣭⣭⣽⣾⣶⡀
⠀⢰⣶⣶⣿⢿⣿⣿⢲⣶⣶⢼⣿⣿⡟⣿⣶⣶⡆⠀⠀⠸⢰⠀⠀⠀⢸⡇⠀⢈⣿⣿⣿⣿⣿⣟⣛⣿⣶⠀⠀⢹⣿⣿⣶⣿⣿⣿⡇
⠀⢸⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣯⣭⣽⡏⠀⠀⣽⠶⢿⣿⣿⣿⣿⡄
⠀⢸⣿⣿⡏⢸⣿⣿⢸⣿⣿⠀⣿⣿⡇⣿⣿⣿⡇⠀⠈⠐⠀⠜⠹⠍⣺⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⡇⠀⠀⠸⠛⠛⠛⠛⠛⠛⠃
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠷⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠻⣶⡄
⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡟
⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡶⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣠⡿⠁
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⡈⠇⠀⣠⢟⡻⣿⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⠃
⠘⠛⠛⢿⣷⣦⣤⣀⡀⠀⣠⡴⢻⣧⣾⡇⠀⠀⢠⠟⢻⡿⡇⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠘⣿⣇
⢀⣠⣤⣤⣿⣿⣦⣉⣹⡿⠷⣤⡀⣿⣿⣤⣄⣀⡏⣴⣿⡁⠀⠀⠀⠈⢿⣦⣤⣶⣾⡿⠿⢶⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠻⢿⣿⡋⠛⠛⢿⡻⣦⣬⡿⠉⣽⣛⣛⣛⠛⠛⠂⠀⠾⢋⡵⠋⠁⠀⠀⢠⡇⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⢷⣄⣀⢀⣠⣿⣿⢿⣿⣟⡛⠛⠛⠲⠾⣧⣄⡀⠀⣠⡿⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⣩⣿⣿⠿⠁⠈⠁⠀⠉⠛⠻⢶⣾⣤⣭⣥⣶⠿⠋⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠛⢻⣿⠷⣤⣶⣤⣤⣤⣤⣴⣶⡾⠟⠉⠙⠿⣧⣄⠀⠀⠀⠀⠀⢀⣠⣴⡾⠇
⠀⠀⢴⣦⡀⠀⣀⣤⣾⡿⠋⠘⢛⣹⣿⣤⣾⡿⣍⠙⢿⣌⠙⢷⣤⣤⣤⣤⣤⣤⣥⣴⣶⣶⡾⠿⠟⠋⠁
⠀⠀⠈⢳⣌⠻⣍⣈⣻⣿⣿⡟⠉⠀⠀⠀⠙⠻⢶⣤⣤⣿⣷⡄⠈⠛⢯⣍⠉⢉⣵⣿
⠀⠀⢠⡟⣠⠞⠛⠋⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣦⣤⣀⡀⢈⣿⠟⢿⠁
⠀⠀⣿⠞⠁⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠈⠉⠛⠻⢿⣄⢬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⣶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠙⢦⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⣍⠛⠛⣿⣿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣽⣆⣰⡟⠀⠙⠻⢿⣶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡏⢹⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣿⠀⣷⠸⣷⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣰⡾⠋⠉⠉⠉⠉⢉⣛⣁⣀⣏⣀⣀⣀⣀⣀⣀⡀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣼⣿⣴⣶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢠⣶⡆
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⢠⣿⣟⠀⠀⠀⠀⠀⣸⣿⡀
⠀⠀⠀⠀⢼⣿⣿⣤⡀⠀⠀⠀⢀⡾⣿⣿⠶⠂⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⣹⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⢠⢿⣿⡇
⠀⠀⠀⠀⡸⣿⣿⡆⠉⠃⠀⢀⠞⠀⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣏⠙⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⢠⠃⢼⣿⡛⣄
⠀⠀⠀⠀⢀⣿⠻⣷⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⢸⡿⣿⡀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⣾⠿⣧
⠀⠀⠀⢠⡞⠁⠀⣿⠀⠀⠀⠀⢀⡾⠁⠀⣷⠀⠀⠀⢀⣴⠟⠀⣿⠀⠀⠀⢠⡟⠁⢸⣇⠀⠀⠀⢀⣤⠾⣿⠀⠀⠀⢠⡾⠃⠀⢻⡄
⠀⠀⢠⣟⠀⠀⠀⠸⣧⣀⠀⠠⣾⠁⠀⠀⠸⣦⡀⠠⣿⡁⠀⠀⢹⣆⡀⠀⣾⠀⠀⠀⢹⣄⠀⠘⡟⠁⠀⣯⡀⠀⢠⣞⠀⠀⠀⠈⢳⣄⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠉⠉⠉⠉⠛⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⡄⢤⡄⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡷⢂⣨⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⡄⠠⣀⣠⣶⣄⡀⠀⢰⣿⣿⣿⣿⡿⢟⡱⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣾⣠⠤⠀⠉⣤⣶⣿⡿⠛⢺⡇⠀⣿⠿⣿⠟⢥⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡯⠐⣿⢋⣹⣿⣿⣿⣿⣿⢆⣼⢻⣿⣿⣿⣿⣿⣿⡟⣣⣴⣿⡿⠟⠉⠀⠀⢠⡇⠀⣿⡄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⡿⡇⢼⢣⣾⡟⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⢀⠀⣿⣀⢀⣈⣵⣾⢿⣿⣿⣿⡷⠆⠄⠀⡾⠿⢉⣿⡿⠿⣿⣿⡟⠹⢷⡾⠃⠀⠀⠀⠀⡼⠁⠘⡇
⠀⠀⠀⠶⠶⠿⠿⠛⠻⡟⠛⣿⣿⣷⣾⣿⣷⣿⠟⠰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣦⡌⣷⣾⠞⠁⠀⠀⣠⠜⠁⠀⠀⢀
⠀⠀⢀⣠⣤⣴⠶⠶⠚⢻⠉⠙⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣯⠛⠶⠿⠛⠉⠀⠀⠀⠀⢈
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠳⡀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣿⣿⠟⠻⠟⠻⣿⣿⣿⡟⢻⠂⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⢿⡍⣶⣿⣷⣾⣶⣿⣧⣬⣿⡟⣠⣿⣦⣿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣼⣿⣻⣿⣶⣶⣽⣿⣿⣿⣿⣿⡿⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣯⡉⠻⣿⣏⣴⡿⢋⣼⣿⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠉⠉⠀⣸⣿⣇⠀⠀⠉⠉⠉⠉⠋⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⢀⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣿⣥⣶⣶⣶⣿⡿⢿⣿⣿⣄⡀⠀⡄
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣥⢿⣿⠿⣿⣿⣦⡀⠀⠁
⣻⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠀⠈⠿⣿⣿⣦⡀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢡⣿⣿⣿⣿⡿⢻⣿⣿⣰⣿⡟⠀⠀⠀⠙⢿⣿⣿⣦⡀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣿⣿⣿⡿⢱⢸⣿⣿⢻⢻⡇⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣜⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⡀
⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠴⢶⣶⡦⠄⢻⡄⢻⣧⣿⣷⠀⠸⣿⣿⣃⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣥⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣷⣦⡎⠱⠈⢿⣿⣿⣯⠺⣿⣟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣄⡁⠐⠂⠀⠀⠀⠀⢀⠀⣠⣿
⣿⣇⠀⠀⣀⣿⣿⣿⣟⣛⣿⣿⣇⣼⣿⣀⣤⡐⢠⣿⣿⣿⡆⢿⣿⣿⠋⣀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣶⣦⣤⣷⣶⣿⡿⠛
⣿⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣤⠋⢿⣿⣷⢼⣿⣯⣄⣈⡑⠂⢀⠀⠀⠀⠈⠀⠚⠁⠀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣋⣵⣶⣿⣿⣿⠺⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⢆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣯⠓
⣿⣿⣿⣿⣿⡿⣿⡝⢹⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡯⢭⠛⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠙⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢠⣤⡶⠶⠶⠶⠶⠖⠛⠛⠒⢀⠀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠛⢧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡤⠤⠤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣾⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣿⣿⡇⠀⡀⠤⠀⠀⢀⣐⡐⢐⣿⣿⡏⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠤⢤⣿⣇⣸⣟⣀⣠⣾⣟⣛⣿⣾⣿⡀⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⣿⡇⠹⢿⣿⡿⠋⠉⣩⡿⠉⣿⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣿⡶⠖⠂⠀⢶⠒⢦⡌⠰⠸⢿⡆⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⡴⢤⡸⣆⠀⠈⠑⠒⠆⣻⡀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠒⢿⡇⠐⣷⠀⠈⠘⠷⣦⣀⠀⠀⠙⣧⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣘⣳⡀⠀⠁⢉⣬⣷⣶⣦⡙⠆⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠋⡉⢵⣀⠀⠀⠙⢿⣿⡻⣧⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠿⣷⣄⠀⠀⠉⠛⢴⠗⠀⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⣶⣆⠀⠀⠙⠣⢤⠀⠀⠀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠠⠟⠟⠻⠿⠄⠀⠀⠘⣧⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠐⢄⣠⣼⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣉⣙⣫⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠲⠴⣮⣁⡀⠁⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠉⠉⠈⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣼⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⣚⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠉⠉⠁⠀⠐⠛⠻⠿⠿⠿⠿⠏

⣿⣿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⢀⠀⢠⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡆⠀⠀⠀⢀⠀⠀⠀⠈⠀⢀⠂
⠀⠈⠀⠀⣤⣤⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠛⠃⠀⠘⠂⠀⠀⠀⠈⠁⠀⠀⢒⣀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⢡⡍⠀⠀⣾⡍⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠘⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣀⣀⠀⠀⠠⣼⣧⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠁⠐⠀⢀⣀⣤⠀⠀⣤⣤⡤⠶⠖⠓⠀⠀⠛⠉⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣤⡄⠶⠶⠀⠈⠁⠀⠹⠀⠀⢸⡟⠋⠀⠀⠀⠀⠀⠄
⠀⠷⠿⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⢠⠍⠀⠀⠉⠁⠀⣆⣤⣥⣤⠀⠀⠀⢻⡄⠀⠈⠁⠈⠄⠒⠀⠀⠃
⠀⠀⠀⠀⠀⢰⣆⠀⠀⠰⣄⡀⠀⢸⠆⠀⠰⠀⠀⠀⠉⢀⡤⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠘⠁⠀⠀⠐⢀⡀⠒⠀⠀⠀⠉⠁⠀⢰⡆
⠀⠄⠤⠀⠀⠀⠀⢰⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠈⠀⠀⠠⠀⠀⢸⡇⢽⠀⠀⠀⠀⠰⠂⠟⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠉⠓
⠀⠀⠂⡄⠀⠃⢀⠸⠇⢽⡄⠀⠀⡀⠀⠀⠷⠷⠶⢶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠟⠀⠀⠙⠲⠆
⠀⠀⠂⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠂⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢊⣠⣴⣾⠥⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⠃⠴⣦⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠉⠤⠀⠀⠀⠀⠀⠠⡔⢄⠀⢀⡴⠛⠉⠢⣀⣀⣠⣤⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡴⠀⠀⠀⣀⠈⠀⠙⠾⢤⣤⠶⢚⣻⣉⣀⣤⣤⣷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⡴⠒⠒⠂⢀⡀⠀⠀⣠⠁⠀⠀⠀⠀⢂⠁⠀⠲⠿⠿⠿⢃⣴⠶⠎⠑⠙⡏⠉⣽⠁⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠁⠀⠀⠀⠀⠀⠉⢫⣀⠉⢁⠠⠀⠀⠘⠛⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⢰⣇⠶⠃⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠊⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠤⠔⠚⠁⠀⠀⠈⠐⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠀⠀⢀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣎⠉⢉⣀⣠⣼⢄⠀⠀⣿⠐⠉⠉⠙⠛⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠔⠊⢀⠴⠋⠛⠝⣡⠞⠉⠉⠈⠀⢢⡤⠤⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⢠⣞⣁⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠈⣷⠀⢨
⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⣀⡜⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢉⣡⡜⠡⠄⠒⠒⠀⠀⠂⠀⠒⠂⢤⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠤⣀⣀⣀⣀⣀⣠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠇⠀⠀⢠⠤⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⠀⡰⠃⠀⠀⠀⢀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢛⠉⠉⠁⠀⠀⠈⠉⢋⠉⠠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⢈⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠤⠬⢍⣉⡙⠛⠻⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣬⣉⡛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠴⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⠉⠀⠀⡾⠀⠀⠈⢈⣀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⠀⢠⠔⠂⠀⠄⠀⠀⠀⡀⠀⢸⠀⡀⠈⠀⠤⠤⠄⠐⠒⠒⠒⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣿⣿⣿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⢀⣨⣥⡶⠾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣀⣤⡾⠟⠉⠁⠀⠀⠘⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣃⣴⡾⠛⠁⠀⢀⣀⣤⣴⣶⠶⠶⠿⢷⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠵⠾⢛⣁⣤⣴⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⠶⠿⠛⠋⠉⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⢠⣴⣿⡟⠿⢿⣿⣿⣷⡄⠀⠀⠀⠀⣠⣤⣄⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⢋⡦⢺⣴⣿⣿⣿⣧⠀⠀⠀⠘⣿⣿⣿⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⣉⢈⡉⢿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⠟⣿⠸⢃⣾⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⡀⠘⠛⠛⠀⠀⠀⠀⠈⢿⣿⣿⣶⣤⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⢁⣀⣤⣴⣶⠾⠿⠟⠛⠛⠛⠻⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣶⡶⠶⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠒⠒⠒⠒⠒⠂⠄⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣤⣠⣾⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⣿⣿⣿⣿⣤⣀⡀⠀⠀⣀⣀⢀⣤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣿⣿⣇⣾⣿⣿⣿⣶⡞⡉⠀⠋⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢀⠐⠁
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠸⠏⢘⣿⣿⣿⣿⠟⠛⢿⣅⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⠘⠿⣏⢻⣷⣶⣦⠝⠻⠃⠂⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣰⡤⠀⠀⠀⠀⠀⠈⣉⣀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⢀⠦⠼⡥⠬⠿⣶⣖⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡄⠀⠀⠠⠄⠀⠀⠄⠈⠂⠀⡐⠀⠀⠀⢀⠀⠐⠠⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠠⠄⠠⠀⡀⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠤⠤⠤⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⡀⡈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠂⠙⠦⠛⠳⣦⣤⣶⣿⣿⣏⠹⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠄⠀⢾⣿⣿⣿⣿⣿⣿⣿⣷⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠒⠈⠻⣿⠿⣿⣿⣿⣿⣿⠟⢺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠀⠀⠀⠰⣿⠗⣀⣤⣹⣿⢿⣿⠆⡀⠁⠀⠀⣀⣴⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠁⠈⠁⠀⠀⢀⡀⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠤⢤⣠⣴⠚⠻⣆⣀⠀⠀⠀⠀⢹⡿⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⣀⠀⠀⢀⠀⠀⢀⣴⣿⠏⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠒⠂⠀⠐⠠⠂⠀⠀⠀⠐⠀⠄⠀⠀⠠⠀⠈⠋⢁⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣸⠁⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠦⣄⡀⠀⠀⣤⣀⡌
⢀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠠⠀⢠⠃⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⢳⡾⡴⣻⠉⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⡀⢠⠞⠒⠂⠀⠀⠐⠊⣒⣤⣤⣤⠤⠤⠤⠤⠤⠤⠴⠦⠴⠶⢾⠶⠖⠒⠒⠒⠿⣅⡷⠃⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀
⠀⠤⠤⢀⡤⢎⠀⠐⠈⠁⡰⠃⠀⢀⣠⡤⠖⠚⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣼⠀⠀⠀⠀⠀⢀⡞⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠑⠁⠀⠀⠀⢸⢁⡴⠊⠉⠀⠀⢀⣠⠤⠤⢶⡶⠖⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⡟⠉⠉⠉⠉⠉⠛⢶⢤⣀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠎⠀⠀⢀⡴⠚⠉⠀⠀⠀⠆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢣⡀⠉⠓⠦⣄⡀⠈⠉⠒⢤⣀⡀
⠀⠀⠀⠀⠀⡠⠀⢐⠞⠙⢦⣀⡴⠋⠈⠢⡀⠀⠀⢰⠀⠈⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠉⠑⠲⢤⣀⠀⠉⢙⠒⠦
⠀⠤⠖⠂⠈⢀⡴⠋⠀⢀⡴⠋⠀⠀⠀⠀⠈⠢⡀⠆⠀⠀⠲⠀⠀⠀⠀⠀⠀⢀⠀⡄⠼⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠈⠙⠲⢮⣀
⠀⠀⠀⠀⣠⡞⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⢂⠀⠀⠀⠀⠀⣸⠊⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⡾⠻⣄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠲⡀⠐⡀⠀⠀⡠⠊⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀
⢀⣴⠟⠁⠀⠹⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣡⡠⠊⠀⠀⡆⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⠤⣄⣀
⠟⠁⠀⠀⢀⡴⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠂⠐⠂⠓⠂⠀⠠⠄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠉⠙⢲⠦⢄
⠀⠀⢀⡴⠋⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⣠⠁
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠇⠀⠀⠀⡐
⠞⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⢱⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠘⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠠⠄⠙⠓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠄⠀⠤⠂⠀⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢦⣀⣀⠀⠀⠀⠀⠀⣀⠤⠘⠳⣄⠀⠀⠀⠀⠀⣀⡤⠐⡚⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⠴⠂⠉⠀⠀⠀⠀⠀⢙⣦⣄⡂⠈⠀⢀⠜⠀⠀⠐⡄
⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣾⣿⣶⣶⣶⣶⣶⣶⣿⣷⣾⣾⣿⣷⣶⣾⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠰⠶⠀⠀⠀⠀⠰⠶⠂⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢠⣄⠀⠀⡀⠀⠀⣠⡀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠈⠛⠿⠟⠛⠿⠿⠋⠀⠀⣼⡟⠀⣶⣦⣾⣦⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠐⠿⠀⠀⠀⣠⣾⠏⠀⠀⢻⡇⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣦⠈⠛⠷⣦⣤⣤⣤⡶⠿⠋⢡⣴⣶⠆⣸⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⡿⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⠏⣁⣈⠙⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣿⣆⣉⠛⠳⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣄⠙⠋⣠⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠁⠀⠀⠀⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠈⠛⠿⠿⣿⣿⠿⠿⠛⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣁⢠⢢⢤⡾⠧⡒⠂⡀⠀⠀⢀⡜⠁⠀⠀⠀⣁⠀⠀⠀⢀⠂⣤⡤⠍⠀⠀⠀⠀⠀⠤⠤
⠀⠀⢀⡐⢋⡀⠀⠀⠀⠀⠀⠉⢀⠙⠚⠼⣧⠉⠨⠀⠔⠂⠀⠐⠀⠀⠀⠊⠀⠀⠐⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠉⠁⠠⡇⠀⠀⠀⠀⠀⠈⠰⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠘⡃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠠⡄
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⢀⡄⠛⠉⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠤⠀⠁⣂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠷⠾⠁
⠀⠀⠀⠀⠀⠀⠿⠀⠰⠛⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠒⠢⠀⣀⠀⠀⢀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠔⠁⠀⠨⡀⣴⡁⡙⠀⠘⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠃⠀⠀⢀⡈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠒⠀⡀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠰⠀⠰⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣤⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢀⠜⠈⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡮⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⠔⠁⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠌⠀⠀⢄⡀⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢩⠀⡆⢨⠙⣆⠀⠀⠀⠀⠀⠀⠰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠤⢭⣉⡃⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣘⠀⠤⢘⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣠⣶⣿⣿⣿⣷⣦⣴⣾⣶⣴⣶⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⣀⠤⢄⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⠃⠀⠀⢳⠀⠀⠀⢰⠇⠀⠈⢣⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣌⠁⠀⡾⠀⠀⠀⠸⡎⠁⢀⡜⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠑⠈⠀⠀⠈⠉⢦⡈⠒⠋⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣶⠄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣶⣾⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠉⠉⢈⡻⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠈⠛⠿⢶⣶⣤⣤⣤⣠⣤⣤⣤⡶⠞⢿⣇⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠋⠉⢹⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣄⠀⣹⠆
⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⡴⠚⠋⠛⠓⣶⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣞⠉⢳⡀
⠀⠀⠀⠀⠀⣰⠟⠀⣴⠏⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢳⡀⠙⠳⢤⣀
⠀⠀⠀⣠⠴⠋⢠⡞⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⠳⠦⣄⠉⠛⠶⣄⣀⣀
⠀⣰⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠉⠳⠦⡀⠀⠈⠙⢦⣄
⣶⡋⢀⣴⣄⢰⡏⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢷⡀⢀⣤⣄⣈
⠈⠛⠋⠁⠉⠋⠁⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠃⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⡾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⠶⣦⣤⣄⠀⠀⠀⠀⠀⠹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠠⠀⡈⢿⣆⠀⠀⡀⠄⢀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠻⠷⣦⣄⣸⣿⣶⣀⣠⡶⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠀⠀⣠⡾⠉⠛⠁⠻⠟⠻⣦⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠛⠉⠁⣀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣯⣀⣀⣤⡴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣾⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣿⣿⣿⡿⠿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⢻⡟⠛⠷⣦⡀⠀⠀⠀⣠⡾⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⠂⠀⢀⡀⠀⠀⠟⠻⣦⠀⠀⣿⡁⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⢸⣇⣀⣀⠀⢀⣻⡆⠀⠘⢷⣤⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⠀⠀⠈⠛⠛⠛⠀⠙⣻⡇⠀⢀⣴⠾⠿⠿⢶⣄⠀⠀⠀⢠⣴⡶⠶⠿⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⠀⠀⠀⠀⠀⠀⣤⣰⡟⠀⢰⡟⠁⠀⠀⠀⢀⢹⣟⠛⠿⢿⡇⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣰⣆⣀⣤⡾⠋⠀⠀⢸⡇⠀⠀⠀⠀⠛⠛⠛⠿⠶⠾⢿⣤⡀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⣷⠀⠐⠻⠷⠶⠶⣦⣤⣤⣤⣀⣼⡇⠀⣀⣀⣠⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠘⣿⠀⠉⠹⠿⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⣦⣄⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⢀⣴⠟⠀⠀⣈⣽⠿⣦⣄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⢀⣠⡾⠛⠁⠀⠈⣿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⣀⣠⣴⠟⠋⠀⠀⠀⠀⠀⢸⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠁⢠⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣴⡶⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢳⠀⠀⠀⢀⣀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⡳⠒⠊⠉⢀⠎⠀⢡⠀⠀⠀⢀⣀⠤⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠕⠒⢦⡀⠀⠀⡜⢁⠤⠒⣤⣏⠀⠀⠀⡵⠒⠉⠁⠀⡰⠁⠘⡄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡠⠤⡙⢲⡎⠀⢸⠀⡰⠁⡜⠀⠀⡜⢀⢤⡀⠀⡴⠁⠀⠀⠘⣄⣀⠤⠔⠚⠉⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢧⠀⡧⠃⠘⠒⢋⡜⠀⢀⠑⢦⣎⠴⠋⢀⠇⡼⠁⡎⠉⡇⡰⠁⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢀⡠⠔⢁⡜⠁⣀⣀⣀⠞⠯⢇⡿⣁⠎⡤⡀⣠⢋⡜⠀⠰⣇⠀⡙⠉⢱⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠘⠤⢤⠞⠀⡞⠁⢠⢯⠀⡔⠉⢠⠿⡐⠦⠺⢴⡟⠹⡄⠀⠈⡛⠲⠒⠁⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢠⠒⠲⡄⠀⣠⠋⠀⡜⠁⡰⠃⢸⠀⠹⣤⣋⠜⠁⠀⢀⠞⡠⠴⠁⠀⡼⠁⠀⠀⠀⡰⢫⠃
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⣀⠞⠀⠘⣅⡴⠳⡀⠀⠳⡴⠁⠀⠻⠤⣶⢧⡀⠀⠀⢀⠎⠀⢳⠀⠀⡼⢁⠤⠒⠤⠚⢁⠏
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡇⠀⠀⢀⠞⠁⠀⠑⣄⣼⠇⠀⠀⠀⡰⠁⠰⢅⠀⢀⠞⠀⡴⠋⢀⡼⠁⠘⠒⠲⠚⢉⠏
⠀⠀⠀⢠⠞⢣⡀⠀⣠⠤⣹⠀⣰⠋⠀⠀⠀⢀⠟⠉⠀⠀⠀⡰⠁⠀⠀⠈⣇⠎⠀⠀⠧⠚⡽⠹⡀⠀⢀⠀⢀⠎
⠀⠀⠀⠹⡄⠀⠙⡆⠈⠲⢋⡶⠛⠉⠒⠤⣤⣏⡀⠀⠀⠀⣼⠕⠒⠒⢤⣾⡟⠀⠀⠀⠀⡰⠁⠀⠉⠉⠉⢱⡎
⠀⠀⠀⠀⠹⡄⠀⡇⠀⢠⢞⣀⣀⠀⠀⣠⠃⠀⠉⠳⠤⡼⢃⠔⠦⠼⢁⠞⠙⠶⠋⡗⡰⢁⣠⣀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠘⢆⠱⣤⠟⠉⢀⣈⠵⠒⡇⠀⠀⠀⢀⡞⣜⠁⢀⡤⢴⣮⠀⠀⠀⣰⣱⢡⠎⠀⠀⣓⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠶⠧⠒⠋⠁⠀⠀⠀⠸⡀⠀⢀⡞⠓⣮⣉⡁⣀⠞⠈⡆⠀⢠⣿⢃⡈⢦⡀⠠⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢠⠏⣸⡠⠴⠒⠉⠀⢆⠀⠹⡤⢣⠃⣇⠙⠒⠃⠀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠈⡆⠀⢠⠃⠀⣈⣙⠢⣄⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠏⠀⠀⠓⠒⠃⢳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⠙⠻⠿⠿⠿⠟⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⠿⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⠀⣿⡇⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⠆⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠻⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⡀⢀⣀⣀⠠⣶⡿⠉⠉⠀⢠⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣴⣾⠛⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠿⠿⠂⢀⣀⣀⣀⡀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠛⠋⠈⠙⠻⣦⣤⠀⠀⠀⣤⣤⡴⠛⠋⠀⠀⠀⠀⠈⢻⣿⠿⢿⣶⣦⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⠉⠉⠉⠉⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⣿⠇⠀⣿⣤⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢴⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⣿⡇⠀⣿⠟⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠉⠀⠀⠈⡇⠀⢠⣿
⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠛⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿
⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠸⣿
⠀⠀⠠⣾⣿⣿⣇⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⣷⡆
⠀⠀⠀⠉⠁⠙⡿⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠙⢇
⠀⠀⠀⠀⠀⢰⣿⠀⠀⣠⣤⡾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⢀⣤⣤⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡖⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠘⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠙⣥⡀⠀⠀⠀⢀⣶⡆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠘⠟⠁⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣿⠀⠙⠿⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠛⣄⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠘⠿⣆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡄⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢠⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⢀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡿⠋⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠿⠋⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠉⠁
⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⠿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠛⠋
⣀⣀⣉⣉⣉⣈⣹⣿⣿⣿⣿⣋⣁⣠⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣮⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⠋⠁⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣠⣄⠀⠀⠀⢈⣍⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠻⠟⡀⠀⠀⢸⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠘⠇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠘⠓⠛⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢶⣶⠒⢚⡿⢿⡛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢯⣹⢟⡭⠖⠛⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⠀⣾⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⡇⠀⡏⠀⠀⠀⠀⢤⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠁⢸⡅⠀⡇⠀⠀⠀⠀⢸⠙⢦⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠛⠁⢀⡤⢾⡇⠠⡇⠀⠀⠀⠀⢸⡆⠈⢧⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢈⡽⠶⠚⠉⠀⢸⡇⠀⡇⠀⠀⠀⠀⢸⡇⠀⠘⢧⣠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢀⣸⡇⠀⠀⢠⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⠉⠉⠉⠉⠉⢹⠇⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⡶⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡞⠁⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡼⠙⢦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⡀⣰⠃⠀⠀⠳⢴⡎⠙⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠉⠀⠀⠀⠀⠀⣹⢶⠞⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣺⣁⣼⠁⠀⠀⠀⠀⠀⠀⡿⠂⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⣀⣉⣉⣹⠀⠀⠀⠀⠀⠀⠀⢧⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⢀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠲⡄
⠀⠀⠀⠀⠀⠀⢀⣜⢁⣴⣦⣿⣷⠀⠀⠀⠈⠻⣿⣿⠿⠿⠿⣿⡿⠿⢿⣿⣧⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣴⠉⠉⠛⠿⣶⣭⡉⠀⠀⢀⡤⢚⠭⡅⠀⠀⣀⠭⢭⡓⠀⠀⠉⠳⣄⢸⠅
⠀⠀⠀⠀⠀⣿⣶⣦⢀⣾⣿⡟⠀⠀⡠⠋⢰⢁⣤⡇⠀⡔⢁⣄⢠⠇⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⣼⣿⡟⢿⣿⣿⠏⠀⠀⡴⠁⡀⠉⡾⠿⠀⢸⣀⣿⡿⠃⠀⠀⠀⠀⠀⢼⣿⣿⠖⠒⢦
⠀⠀⠀⠘⣽⣿⢧⣿⣿⠏⠀⠀⢰⠃⠚⡁⠀⠓⠄⠀⠀⠁⠀⠀⠀⠀⣠⢄⠀⠀⠀⠙⠁⠮⡀⢸
⠀⠀⠀⣰⣍⡉⡿⢿⡃⠀⠀⠀⢸⠀⠀⠐⠠⣀⠀⠀⠀⠀⢀⣀⠤⠊⣡⡎⠁⠀⠀⠀⠀⣨⡴⠋
⠀⠀⢠⠷⠦⣸⡀⡰⡇⠀⠀⠀⠘⣇⠀⠀⠀⠈⢫⣍⣉⣩⣤⣤⣶⣿⠟⠀⠀⠀⠀⢀⣼⣁
⠀⠀⢸⢷⣄⡼⠁⢼⡀⠀⠀⠀⣀⠼⠣⡀⠀⠐⠫⣉⣛⣛⣿⡿⠟⠁⠀⠀⠀⠀⣠⠊⠀⠈⠉⠓⠦⣄⡀
⠀⢰⢫⣷⡿⣷⡴⠃⢨⠛⠛⠉⠁⠀⠀⣿⢷⣤⣀⠀⠈⠉⠀⠀⠀⠀⢀⣠⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⢰⣿⣿⡟⠀⠙⢦⠔⠁⠀⠀⠀⠀⠀⠀⣿⢼⣧⣈⡉⠓⠒⠒⠒⠒⠋⢉⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦
⠈⠛⠋⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⢀⣀⣿⣤⣷⣿⣽⣿⣿⣿⣿⣿⣿⡯⣇⣸⣧⠀⠀⡴⠒⠒⠒⠶⠶⠤⣤⣄⠃⣠⠷⢤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁⠸⣇⣷⣺⣿⢻⣿⣿⣛⣻⣿⡿⣽⣿⣙⣶⣾⠇⠀⠀⠀⠀⠀⠀⡸⢉⠉⠁⠀⢀⡇⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⠀⠀⠀⠀⠀⠀⠀⣳⣾⡇⢀⣤⠎⢠⡶⠃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣯⣽⣿⣭⣯⣿⢷⣿⣿⣿⢧⡀⠀⠀⠀⠀⢠⣎⡀⠳⠟⠉⢀⡠⠚⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⢿⢻⣟⣻⣿⡾⣿⣿⣿⣻⣭⣿⣿⡷⠻⣄⠀⠀⠀⢸⣼⡿⣆⠀⢰⡿⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⣿⣿⣯⣿⣿⣮⣭⣿⣽⣽⣽⣿⣟⣲⠿⣮⣷⣽⡄⠀⠀⠸⣯⣻⢿⡖⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣟⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣞⣟⣿⡄⠀⠀⠈⠙⠾⣧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣯⣭⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣥⣧⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠂⠤⠤⠭⣥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠒⠿⠿⠿⣽⡀⠀⠀⠀⠀⢰⠂⠤⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠆⠀⢤⢿⣄⠉⠙⡛⢉⣉⣿⣦⣤⠀⠀⢰⠀⢩⣭⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣾⡃⠐⡞⠻⠄⠉⣟⣋⣛⣭⢿⣾⡷⡄⠀⠼⡂⠰⠶⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⣐⣿⣏⠀⣛⣻⡓⠀⠸⠶⠶⠶⢿⣋⠐⠂⢰⡖⣹⣟⠙⣛⣩⠀⢀
⠀⠀⠀⠀⠀⡀⠀⢀⡗⠰⣶⢶⠧⠤⢯⣽⣏⠐⠐⠖⠲⠖⣻⣽⠛⠒⢚⣛⣽⣟⡋⣹⡍⢸⣟⢐⣒⣿
⠀⠀⠀⠀⠈⠅⢰⣿⡟⠶⣯⡁⠒⠤⠤⠽⣮⠉⠛⠻⠟⠟⣿⣮⣉⣈⣹⣭⣵⣷⡶⠷⠧⢤⣗⢠⣾⣾⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⣄⡈⡙⣛⣙⣯⣙⣛⣒⣒⣛⣻⠗⠆⠠⢼⣟⣉⣉⡀⣈⣛⣛⣿⣭⣿⣿⡿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡉⡙⢛⢛⣷⡄⠉⣍⣉⣏⣍⣏⡓⠈⢻⣯⣭⣭⢬⣤⣭⣭⣬⣭⣍⡤⠔⠲⣦⡀
⠀⠀⠀⠀⠀⠀⢠⡂⠐⠂⠒⠐⣄⠈⠉⠉⠳⠄⣉⣑⣛⣛⣏⣛⡟⠋⠛⣛⣿⠷⠦⠤⡦⠴⢾⠘⠦⠭⠽⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠨⢭⣿⣭⠿⠃⠀⠀⠘⠤⠠⣼⣬⣧⡿⣏⠽⣯⡭⠭⡭⠛⠝⠉⠉⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠁⢏⡀⢒⢒⣒⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⢀⣠⣿⣤⡀
⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣻⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⠍⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣆⠀⠀⠀⠀⡾⣾⣿⣿⣯
⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠺⢸⡿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠃⢻⣿⣿⠛
⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⢸⡇⢿⡇⠀⠀⠀⠀⠀⢸⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡃
⠀⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⡀⠀⠀⠀⠀⠀⣠⣿⣿⡄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄
⠀⠀⠀⠀⢸⣿⣿⠙⠲⠄⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⠀⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠘⢿⣿⡿⠟⠷
⠀⠀⠀⠀⣼⠟⠈⢿⡄⠀⠀⠀⠀⢠⡿⠁⠙⣿⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣴⣿⠟⣿⠀⠀⠀⠀⠀⠀⣿⡿⣷⡀
⠀⠀⠀⣸⠏⠀⠀⠈⠻⣤⣤⠀⢠⡿⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⢠⡟⠁⠀⢻⡀⠀⠀⠀⠀⣰⡿⠀⠙⣷⡀
⠀⠀⠀⠛⠓⠀⠀⠀⠀⠉⠀⠀⠘⠳⠂⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠀⠀⠛⠓⠀⠀⠈⠉⠁⠀⠀⠐⠛⠁⠀⠈⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡤⠤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠻⠷⠶⠦⣤⡄⠀⠀⠀⠀⠀⠉⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⡏⠙⠛⢿⣿⠶⠶⠦⠀⠀⠀⠀⠙⣷⠒⠶⢠⣤⣀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⣄⠁⠀⠀⠀⠀⠙⠛⠶⠤⢀⣀⣀⠀⠈⢳⡀⠀⠀⠈⠙⢷⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠛⠀⠀⠀⠀⢀⡄⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠘⠇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡄⠀⠀⡠⠀⠐⠒⠀⠀⢠⡄⠆⠀⠀⢠⡄⠀⠐⠒⠂⠀⠀⠀⠀⠀⠈⣿⣀
⠀⠀⠀⠀⠀⠀⢠⡞⠉⢹⡏⠀⠈⠃⠀⠰⢶⣶⠄⠈⠀⠀⠀⠀⠀⠀⠀⠒⣾⡶⠀⠀⠀⠀⠀⠈⣿⠉⠓⣄
⠀⠀⠀⠀⠀⠀⢾⠀⠀⠸⡇⠀⠀⠀⠀⠀⠴⠿⠁⠀⠀⠀⠂⠀⠀⠈⠁⠔⠻⠟⠁⠀⠀⠀⠀⠀⡇⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠈⠇⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂⠀⠀⠀⠀⠀⠀⢀⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢶⡿⣧⠉⠘⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⡿⠁⠉⠉⠁⠈⣰⡆⠋⠀⠀⠉⠁⣠⣾⢳⠏⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠈⢃⣾⠀⠀⠀⠚⠁⠙⠄⠀⠀⠀⠊⣿⣹⠇⠀⠀⠀⠀⠀⣰⠏⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⡟⠀⠀⠸⠃⣦⠀⠀⠀⡆⠀⠀⠀⠀⣠⢞⡷⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢰⡇⠀⠀⠀⠻⡈⢧⣀⡀⠁⠀⣀⣠⡞⣡⠞⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⠁⠀⠀⠀⠀⠙⢦⡉⠛⠒⠚⣉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣄⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣇⣸⠉⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠠⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢠⣾⠑⠲⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠠⠙⠷⠶⠀⠸⠁
⠀⠀⠀⠀⢠⣿⠦⠛⠋⢻⣦⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⢠⣞⣁⡶⢸⠀⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠉⠙⠿⣧⣼⣯⣸⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⢦⣤⣤⡀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⢿⠃⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠷⠶⣶⣄⡈⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣘⣻⣷⣦⣴⣟⠀⠀⠀⠀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠿⠛⠇⠀⠀⠀⠀⠀⠀⠉⠛⠒⠷⠒⢊⣉⣉⡉⠉⢉⠙⣿⣿⣇⣶⣼⠟⠁⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⢠⣦⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠛⠛⠛⠛⠛⣛⣛⣉⣙⣿⣻⣿⣴⣶⢾⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠘⡏⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠘⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡾⢿⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⢸⠁⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠤⠤⠤⠤⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇⠀⠀⠐⠒⠒⠂⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣄⣠⣤⣤⣄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣧⡴⠆⣈⣋⣀⠴⣤⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⣉⣉⠉⣉⣉⣻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠗⠊⠉⠉⠀⠐⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⢴⣶⣶⣶⡤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⣤⣶⡡⠔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢈⣴⡿⡄⢠⣾⢟⣼⣿⣀⡤⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠴⠾⠟⣡⣾⠁⣿⣿⠿⠟⠛⢩⢰⣟⡀⣀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡀⣠⠞⢀⣤⣸⣿⠀⠈⠓⡂⠤⠿⣿⣿⣶⣏⣥
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣴⣤⣧⠈⣟⢸⡾⣿⠏⡝⠁⠀⠀⠀⠀⠀⢙⠻⡅⠙⢿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣶⣾⡟⠁⢿⣤⣾⣿⣿⣭⢹⣶⣤⡀⠀⠀⢀⣀⢨⠀⠘⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠜⣿⣛⣭⣖⣯⣽⣇⢿⣿⣿⣶⡄⣾⠋⠸⠃⠀⠀⠀⣡⣀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡞⣷⣍⡻⣾⣿⣿⣿⡇⠹⠀⣎⠀⠠⠀⠈⠋⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣜⢿⣿⣿⡿⡿⣷⡇⠀⠸⣿⡢⣴⣶⣶⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣮⣿⣷⣽⢿⣿⡆⠀⠀⡀⠀⠉⠻⣿⣿⣯⣉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣍⡻⣿⡟⣷⠒⠈⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣧⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢀⠀⠈⢉⡽⢯⣍⣛⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⠟⠶⠶⠟⠉⠁⠉⢀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠒⠶⠶⠶⣶⠶⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣦⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣍⢉⡿⠿⠟⠓⣦⡀⠀⠀⠈⠉⠉⢁⣀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣉⣛⣛⣁⣀⣤⣴⣿⣷⠈⠉⠛⠛⠛⠛⠋⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣉⣉⣉⣉⣉⣍⠉⣿⣿⠀⠒⠶⠶⠶⠾⠃⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⣉⣉⣉⣭⡄⠀⣿⣷⠐⠲⠶⠶⠶⠶⠟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠠⢤⣤⣬⣤⠄⠀⣿⡇⠐⠶⢦⣤⣴⣶⠶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠠⠤⣤⣤⣤⠄⠀⣿⣇⠀⣤⣄⣀⣀⣠⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢤⣤⣤⣤⠤⠀⣿⣿⠀⠀⠈⠉⢉⣉⣁⣠⣿⡧⠶⠖⠂⠠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠠⣤⣤⣤⣤⣦⣀⣿⡿⠶⠶⠾⣿⣉⡉⠁⠀⠂⣂⢤⣒⠠⠀⣤⠌⣙⠻⠶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣠⡤⠤⠶⠲⣾⣋⡉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣥⣄⡀⠈⠙⠛⠋⠐⠠⢕⡀⣄⣭⣙⠛⠿⠷⣶⣤⣄
⠀⠀⠀⡼⢻⢛⣋⣯⡥⢦⣴⣲⣮⣽⣵⢿⣛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣤⣀⠀⠂⣀⡽⠶⠮⠾⢀⣀⣠⡤⠄⢩⡄
⠀⡄⠐⠤⡀⠀⠘⢬⡙⣿⣎⡧⢀⠀⠈⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣯⡤⠶⠖⢚⣋⣩⠭⠶⢒⣋⣹⡇
⠲⡇⠀⠀⠈⠒⠄⠀⠉⠉⠙⠲⢤⠟⡒⠲⠦⡄⠀⠠⠔⢒⣈⡉⠒⠄⠀⠀⣀⣀⣤⠴⠶⠚⠋⠉⠁⢸⠀⠀⠉⠩⠤⠒⠚⢉⣁⣀⣿⡇
⠀⡇⠙⠶⣄⠀⠀⠈⠳⢤⣀⠀⠀⢦⡙⢷⢆⣹⣇⡤⠚⠉⣀⣠⣤⡶⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣠⠤⠖⠚⠋⠉⢁⣸⣿⡇
⠀⣿⠲⣄⡈⠛⢦⣀⠀⠀⠈⠓⠦⣄⠉⠛⠛⣉⣤⣶⠾⠛⠛⠉⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣁⣠⣤⡴⠶⠞⠛⣋⣹⣿⠇
⠀⣿⠦⣀⠙⠦⣄⠉⠳⢦⡀⠀⠀⠀⠁⣶⣛⣭⠥⠒⢊⣉⣤⠤⠒⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢉⣀⣠⣤⠶⣞⠛⠋⣹⣿⣷⣤
⠀⠈⣄⡈⠳⢤⡈⠑⠤⠀⠉⠳⢄⡀⠀⣿⡴⠶⠚⣛⣩⡥⠶⠚⠋⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠭⢭⣒⣮⣭⣶⣶⣿⡿⠟⠋⠉
⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠉⢲⣿⡶⠾⠛⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣿⣿⡿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣴⣶⠿⠛⠀⢹⣀⣠⣤⣶⣾⣿⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠀⠀⠀⣿⡖⠚⠩⠛⣋⡥⢀⣠⣤⣶⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠸⣿⣧⠶⢞⣫⣵⡾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣯⡴⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠤⠄⠄⣠⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠁⠀⠀⠀⠉⠲⢂
⠀⠀⠀⠀⢀⣀⠴⠊⠀⠀⠀⠀⠀⣰⠁⠀⠈⢦⣀⠀⠀⠀⠀⠀⡠⠚⢅⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢱⠀⠀⢉⡆⠀⡤⠘⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⡤⠼⣄⣀⣀⠀⠀⠀⠀⠀⢀⢠⠄⠀⢤⠔⠏⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡀⢙⠦⣀⠀⠀⠀⠀⡇
⠀⢠⣞⠁⠀⡧⠀⠈⠁⠀⠉⡉⠉⠁⠜⠀⠀⠀⠀⡤⡀⠀⠀⠙⠛⠋⠒⠂⠉⠈⣍⠀⠀⠚⠳⣄⠀⢠⠃
⠀⢀⠃⣀⣀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠇⠀⢀⠀⡠⠁⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⡨⣧⠋⠢⡀
⠀⠀⠀⠸⠊⠣⡀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡫⢛⠁⠀⠀⠀⣠⠀⠡⡀⠐⠆⠂⠀⠀⠀⠀⠀⣩⡕⠙⡄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠈⣓⢤⣤⣀⣠⡤⣤⠒⠙⠢⣼⠻⠀⡰⡴⠀⠀⠀⡠⠰⣶⣤⣤⡤⠐⡶⠮⣖⡓⡄⠘⠢⠔⠁
⠀⠀⠀⠀⠀⠀⡰⠁⠀⡷⠀⣠⠒⠦⡙⢍⠈⠚⣶⠏⠀⠀⠀⠀⠀⠁⠀⡿⠀⠀⠀⠀⡇⠀⠈⡂⣹⠆⢠⡄
⠀⠀⠀⠀⠀⠀⡇⡤⠚⠀⠀⡇⠀⠀⠠⡀⠙⡄⠈⢆⠀⠀⠀⠀⠀⡆⣞⠁⠀⠀⠀⠀⡘⠶⡈⠡⠸⠈⣤⠃
⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠑⠤⡀⠀⠀⣠⡶⠐⠈⠄⠀⠀⠀⠀⠈⣻⠀⠀⠀⠀⠀⠀⡐⠀⠘⠈⠈⢹
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⠉⠉⣠⠃⠀⢀⠃⠀⠀⠀⠀⠀⠳⡤⠤⢤⣤⣤⣀⠀⢀⠃⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠑⠂⠤⣤⣀⣀⣀⣀⡠⣶⡻⣑⠒⡁⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⠀⠀⠸⡵⡋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⡟⢀⠇⢐⠉⠙⢮⡀⠀⠀⡀⠀⠀⠀⠀⡠⠉⠀⢹⡄⠊⡠⠉⠑⠠⡀
⠀⠀⠀⠀⠀⡠⡴⠣⣌⡢⠤⡼⠳⣮⠔⠉⡄⠀⠀⢱⠀⠁⠀⡰⠖⠆⠺⠱⢄⣀⡆⠘⡯⠀⠀⠀⠀⢸
⠀⠀⠀⠠⡎⠀⠑⠄⠈⠁⠀⡄⠀⠘⡓⠊⠀⠀⢀⡜⠀⠀⢘⠀⠀⠀⠀⠀⠀⢰⠀⠀⡆⠀⠁⠀⢠⠋⠀⠲⠄⠂
⠀⠀⠀⠀⢣⡀⢀⢀⠀⢀⡰⠀⠀⠀⠙⠢⠤⠒⠉⠀⠀⠀⠈⠢⢄⡀⠀⠀⢀⠎⠀⠀⠈⠢⠤⠔⠁⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣟⣿⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠘⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢨⠗⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠎⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⠂⣀⠄⠀⠀⡀
⠀⠀⠀⡌⠁⠀⠀⡄⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⠜⠋⠀⠐⠀⠀⠁
⠀⠀⠀⠀⡀⠄⠊⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠄⠀⠄⠌⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠲⣍⠳
⢀⠊⢉⠉⢳⡀⡤⡄⠀⠀⠀⢠⠊⠁⢉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠊⠁⠔
⠸⣀⣈⠤⠈⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⢊⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠄
⠀⠀⠀⠀⠖⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⢀⣄⠀⠀⡀
⠀⠀⠀⠀⢄⠀⠀⠀⠀⢼⢀⠀⠀⠐⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠉⠂⠀⠰
⢠⠂⠛⢦⠀⠉⠀⠀⠀⠈⠀⠉⠒⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠻⣄⣠⡾⡁⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⠀⠀⠐⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠙⣷⠀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⡽⠃⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠊

⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠈⢲⠂⠀⠀⠀⠀⠀⠁⢽⠀⠀⣀⠄⡰⠃⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⢠⠇⠀⠀⠁⠀⢀⡼⠋⠀⠀⠀⢀⠿⣦⡀
⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⣀⣑⣄⣠⠤⠴⠶⠖⠛⣏⠀⠀⠀⠀⠐⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⡟⠀⠀⠀⠀⣠⡾⠁⠀⠀⢀⠔⠣⠀⠈⢻
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⣶⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⡀⠀⠀⠀⠌⢀⠞⠁⠠⠀⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⡠⠋⠀⠀⢀⠔⠁
⠀⠀⠀⢀⡽⠆⠀⠀⠀⣀⣤⠶⠛⡁⠀⠈⢳⡀⠀⠀⠀⢀⣀⣤⠴⠶⠛⠋⠉⢯⠉⠉⠛⠓⠦⣾⣄⣀⠀⠀⢠⠞⠀⠀⠀⢀⣼⢃⣀⡠⠠⠮⠀⠚⠒⠈⠉
⠀⠀⠀⢸⠀⢀⡤⠖⠛⠁⠀⠀⠀⠈⠂⠄⡀⠹⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠗⠂⠀⠀⠈⠸⡇⠉⡙⣶⣏⠀⠀⠀⢠⡞⠁⠓⢄
⠀⣀⡤⢾⠋⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⡸⠠⣀⠀⠀⢀⡿⢈⡼⠃⠈⠙⢦⣴⠏⠂⠀⠀⠂⡑⠦⡀
⠊⠁⠀⠘⣆⣸⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⣿⠀⠀⠀⡈⠁⠒⠤⣤⡠⢀⣠⡁⠀⠀⠉⠒⠾⣤⣾⡀⠀⠀⣠⡾⠉⠓⠦⣄⣀⣀⣀⣐⣁⣀⡀⣀⣀⣀⣠⠴
⠛⠓⠶⠦⣞⠉⠀⠀⠀⣀⡠⠄⠒⠂⠈⠉⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠙⡆⠀⠈⡄⠀⠀⣰⡾⠋⠀⠙⢳⣴⣏⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⠉⠙⢍⠉
⠀⠀⠀⠀⠈⠛⢱⠤⠞⠁⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⠐⠻⣄⣠⡾⠋⠀⠀⠀⣠⣾⡁⠉⠛⠶⣤⣀⠀⠀⠀⠀⡿⠀⠀⡠⠊⠑⢆
⠀⠀⠂⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣴⠟⢧⡀⠀⠀⢀⣼⠋⠀⠹⡄⠀⠀⠈⠙⠳⢦⣄⣸⠃⠀⠀⠇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣀⣯⣀⣀⣀⣀⣠⣤⡴⠶⠟⠋⠀⠀⠀⠙⢆⣰⠟⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⢻⠷⠶⢶⣤⣤⣬
⣀⣀⣤⣤⣤⣾⠶⠶⠶⠶⢶⣄⠀⠀⠀⠀⢉⣟⠉⢹⠉⠉⠉⠁⠀⢀⣀⠠⠢⠐⢄⠀⠀⣠⡾⠛⠄⠤⠤⠤⠤⣸⡀⠀⠀⠀⠀⣰⠇⢀⠀⠀⡘⠀⠀⠀⠀⠀⢨
⠉⠁⠀⠀⠀⣧⠀⠀⠀⠀⢀⡿⠒⠛⣏⠉⠉⠁⠀⢸⡂⠁⠈⠉⠁⠀⠀⠀⠀⠀⠈⢱⣴⠋⠀⠀⠀⠀⠀⠀⠀⣸⠉⠲⢄⡀⢸⠇⠀⠀⠀⠠⠁⠀⠐⠀⠀⠀⡎
⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣼⡇⠀⠀⠸⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠒⠀⠀⠀⠀⣠⠟⠉⠣⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣹⠳⣄⡀⠀⠀⠸⠀⠀⠀⠀⠀⡬⠙
⠀⠀⠀⢀⣀⡨⡧⠶⠒⠋⣿⠀⠀⠠⠀⢷⠀⢈⣀⣈⣇⣀⣀⣀⣀⣤⣤⣤⣤⠾⠋⠀⠀⠀⠘⢆⠀⠀⠀⠀⣼⡀⠀⠀⢠⠁⠀⠀⠙⠦⣀⡇⠠⠀⠀⠀⡜⠁
⠒⠚⠉⢩⡇⢀⣻⣤⣤⡶⢿⠶⠶⠛⠛⠛⡟⠋⠙⠉⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⡼⠁⠀⠁⠲⠇⡀⠀⠀⠀⠀⡌⠛⢦⣀⢀⡜⠁
⠀⠀⠀⠀⢹⡟⠙⡀⠀⠀⠈⠳⡄⠀⠀⠀⢸⡀⠀⠀⢻⠀⠅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣁⡀⠀⠀⠀⠀⠀⠑⠢⢄⡜⠁⠀⠀⠈⠻⣄
⣀⣀⣀⣀⣾⡁⠀⠇⠀⠀⠀⠀⠙⢆⠀⠀⠀⢷⠴⠶⠺⠒⠒⠚⠚⢛⡟⠲⢤⣄⡀⠀⠀⠀⠀⠐⠀⡼⠃⠀⠉⠒⠤⢄⠀⠀⠀⢠⠎⠉⠢⢄⠀⠀⠀⠈⢣⡀
⠉⠀⠀⣼⠋⠛⢶⣄⠀⠀⠀⠀⠀⠈⣳⡤⠖⠚⣆⠀⠀⠀⢀⠀⢀⡞⠀⠠⠀⠀⠉⠓⠦⣄⡀⠀⡼⠁⠀⡄⢀⡀⠀⠀⡘⠉⠉⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠉⠲
⠀⠀⣼⠃⠀⠀⠀⠙⢷⣄⠀⢀⡴⠊⠁⠻⣄⠀⢹⡀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡿⠳⢤⣄⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠑⢄⡀
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠹⣶⠋⠀⠀⠀⠀⠈⢧⡀⣇⠀⠀⠀⢸⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠈⠙⠳⠦⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂
⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠱⣿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠐⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠾⠛
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠲⠶⢦⣤⣼⣀⣀⣀⣀⣹⣤⣤⣤⣤⣤⣤⡤⣴⠷⠶⠶⠶⠞⠾⠛⠛⠻⣟⠛⠛⠋⠉⠉⠙⠻⣭⣍
⠉⠉⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⢉⣿⠉⠀⡀⠀⠀⠀⣠⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠛⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⣔⣌⢣⣀⣎⣻⣆⠀⠛⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⢐⡀⢃
⠀⠀⠀⠀⠀⠉⠋⠛⠙⠀⠉⠀⠀⠀⠛⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠉⡀⠀⠀⢀⣴⢟⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢰⠀⠀⢀⠰⠒⠐⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠃⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⡐⠀⠀⠀⡀⠉⢠⣶⣛⠉
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠉⠀⠃⠀⠀⠀⠀⢀⣤⡿⠃⠀⠉⠐⠐⠒⢲⠒⠒⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⣠⣤⣤⣄⣤⡴⠶⢟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠷⠾⠿⠛⠻⠶⠾⠿⠛⠁⠜⠤⠖⠂⠀⠁⠀⣶⠀⠀⠀⠀⠀⠀⠀⢀⣁⠴⠒⠚⠛⠉
⠾⠀⠂⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣤⣤⣶⣶⣶⣶⣶⠾⠟⠁⠀⡀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣆⡀⠀⠂⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤
⠉⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠈⠀⠀⠀⠀⢀⣀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠂⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠉
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣀⣤⠀⠀⠐⠄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠻⣻⣿⠿⡿⠶⠶⠶⠐⠦⠤⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣾⣿⡞⠻⡀⠀⠀⣠⡀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡐⣷⠀⣰⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣉⣛⣷⣿⣿⣿⣿⡧⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢋⣽⣿⣿⣿⣷⡆⢶⣏⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⢶⣿⣿⣿⣿⠟⣼⠀⠈⠻⠧⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⢀⣸⣰⣇⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⣰⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣷⣿⣿⠇⠀⢻⣿⣿⣹⣇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⠀⠀⠛⢻⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠀⠰⣼⡇⣿⢻⣿⡆⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠽⢿⣿⣿⣿⠛⠳⣶⣦⣤⣤⣄⣀⠀⠀⠀⢀⣀⡴⣿⣷⣿⣾⡿⠃⠀⠀⠀⠀⠀⢺⡄
⠀⠀⠀⢀⣠⣤⣭⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡵⠞⠋⢹⣿⣗⠸⠏⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠸⠿⣿⣿⠛⠓⠛⠻⠿⠿⢿⣿⡋⠥⠖⠒⠻⢿⣿⣿⢋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠠⠿⠿⣿⣿⣿⣳⣶⣶⣤⣌⣀⣀⠀⠐⠊⠁⣾⣿⣿⣤⡖⠿⢷⡶⠈⢠⣤⠴⠚⠉
⠀⠀⠀⢰⣶⣦⣤⣠⣀⣈⠉⠉⠛⠛⠿⢿⣯⠤⣖⣋⣽⡿⠿⢿⣿⣿⣿⣿⣟⢸⠟⠃
⠀⠀⠀⠈⠛⠛⠳⠾⢿⣿⣿⣷⣶⣦⣤⠖⠃⣉⡡⠤⠒⠁⠀⠀⣄⣀⠀⢰⣗⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠒⠉⠀⠀⠀⠀⠀⠀⠀⢍⣿⠀⣸⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⣳⣂⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣴⠦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣀⣀⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣦⣴⣾⣿⣿⣿⣶⣴⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣤⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠻⣿⣿⣿⣿⡟
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⢸⣿⣿⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣴⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢷⡀⠀⣿⡏
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣆⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣼⡇⠀⢛⡛⣷⡀
⠀⠀⠀⢀⣼⠿⠿⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠏⠀⠀⠈⠁⣸⡇
⠀⠀⢀⣿⠁⠶⠶⠆⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛
⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠘⠻⢦⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠃⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡿⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⣶⠟⠋⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠉⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠁⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣠⡾⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢻⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠘⠻⣦⣀⠀⠀⣀⣀⣀⣤⣶⠶⢶
⠀⣀⣀⣀⣀⣀⣠⣴⠟⠁⠀⠀⠀⣠⣶⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠁⠀⠀⢈
⣾⠏⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⡾⠋⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢷⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢿
⢻⣦⣀⣀⣀⣀⣀⡀⠀⠀⠰⣿⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⠛⣿⠆⠀⠀⣾⣿⣯⣥⣤⡿
⠀⠸⣿⡉⢉⣩⡿⣿⡄⠀⠀⢻⡆⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣄⠀⢀⣿⠁⠀⠉⠁
⠀⠀⠈⠛⠛⠉⠀⠈⠻⣶⡶⠟⠁⠀⠀⢻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠇⠀⠀⠀⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠻⢶⣄⡈⠻⣦⡀⠀⠀⠀⣠⣴⠿⢷⡄⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠋⠁⠀⠀⠀⠉⠛⢷⣾⠿⣦⣴⠞⠋⠁⠀⠈⢿⣆⢀⣴⡞⣫⣝⣿⡿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠉⢻⣦⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠈⢿⣆⠀⠀⠀⠀⠀⣿⣟⡵⣫⡿⠛⠁⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⢳⠀⠀⢹⠟⣹⠟⣺⣿⣉⠀⠀⠀⠀⠀⠀⠙⢷⡄⢀⣴⣾⡿⣫⡾⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢣⡀⠈⠛⠛⢶⡋⠈⠻⣧⠀⠀⠀⠀⠀⠀⠈⢻⡟⣡⢮⣾⠋⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣉⣉⣉⣉⣉⣉⣉⣉⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣵⡟⠁⠀⢀⣤⡾⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⠉⣉⠉⡉⢉⡉⢉⣉⣉⣉⠀⠀⡀⣀⠀⣀⣀⣀⠈⣻⣷⣶⡿⠛⣁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢛⡛⢿⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡡⠒⠁⠀⠀⠀⠈⢻⡝
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠙⠻⢷⣄⡀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠛⠓⠾⣯⠔⣋⠀⠐⠂⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠐⡠⢀⡾⠋⠀⠀⠀⢀⢀⡀⠀⠑⢍⠛⠳⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠝⠃⠐⠆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠃⢡⠏⠀⠀⠀⠀⠀⠈⠑⠈⠢⣀⠈⢆⠜⠁⢀⠀⣀⠀⡀⠠⠐⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡾⠀⡘⠀⠀⠈⠀⠀⠀⢀⣀⠤⠤⠐⠒⠈⠉⠉⠉⠙⢳⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⠀⢠⠁⠀⠀⣀⡤⠔⠊⠉⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⣸⢀⣴⠞⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢾⠉⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠛⠲⢶⣟⠋⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠷⠦⣀⣀⣀⡤⠚⠁⠐⠀⠀⢀⠈⠁⠀⠈⠓⢦⣀⣠⣤⣬⡓
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣤⣤⣤⢤⡖⢹⡄⠀⡜⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⣴⣿⣿⡁⣹⣿⡶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⢋⡠⠒⠢⣀⣀⠀⠀⠐⠒⠀⠀⣀⡿⢿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⡄⠀⠀⠀⠀⢸⣤⠤⠤⠌⢁⣈⡏⠀⣀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣿⢦⡀⠀⠀⢸⡁⣠⠖⢁⣠⠄⣱⣦⣩⡏⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⢠⠇⣽⢛⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠛⠳⢦⡘⣇⢹⠈⠻⣦⠀⠢⠍⠁⠀⠀⠁⢰⢿⠈⢦⣄⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⢀⡞⢠⠇⡼⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢣⡾⠋⠉⠙⢶⡄⢻⣿⠈⡇⠀⠈⢷⡀⠢⠤⣠⡤⠴⠃⠈⠓⠦⣌⠙⢦⡀⠀⠀⠀⢠⡟⠀⢻⠋⠀⠁⠜⢡⣾
⠀⠀⠀⠀⢀⣤⣄⣤⠴⣋⡴⠋⠀⠀⠀⠀⠀⢻⣄⠏⢸⠃⠀⠀⠈⣷⠀⠀⡏⠀⠀⠀⠀⠀⠀⠸⣇⣀⡇⠀⠀⠀⢸⡇⠀⠀⠃⠀⠀⠐⢁⡟
⠀⠀⠀⠀⠈⠛⠒⠒⠛⠉⠀⠀⠀⠀⣀⣠⡤⠺⣧⡠⣿⠀⢀⡤⠖⢿⠀⠀⣟⡛⠒⠒⠄⠀⠀⢠⢟⣉⢳⠀⠀⠀⢸⡇⠀⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠺⠭⢣⡿⠀⣿⡴⠋⠀⠀⠙⠖⡖⠛⢄⠀⠒⢆⠀⠀⣾⡘⠸⠛⠀⠀⢀⡟⠀⢰⠶⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠘⠳⠞⣹⠃⣸⣿⡄⠀⠉⠉⠺⡄⢆⠀⡈⠀⠀⠈⢄⠀⠈⠃⠈⠀⠀⢀⡞⠀⣴⠇
⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠈⠉⠛⠲⢤⡾⠁⢾⠟⣹⠁⠀⡴⠂⠀⠈⠉⠉⠀⠀⢂⠀⡈⢦⠀⠀⡼⢻⢀⡞⠀⣸⠃
⠀⠀⣴⠋⢀⠄⠀⠒⠀⠐⠀⠤⣄⣀⣀⣀⠠⠔⠁⢠⠏⠀⠘⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇⠈⠌⠳⣴⢃⣾⠋⠜⣰⠃
⠀⣼⠃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠓⠊⠀⢚⡡⠞⣹⠃
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢨⡇⠀⠀⠀⠀⠀⠋⢀⡖⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠚⠦⠤⠤⠄⠀⠀⣀⣀⣤⡤⠤⣤⠤⠤⠶⠞⠁
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⣆⡀⠀⢀⣀⡠⠴⠒⠋⠉⠀⠀⠀⠀⠙⡄
⠸⡆⠀⠀⠀⠀⠀⢀⣴⠞⠋⣹⠀⢾⠋⠛⠒⠒⠚⢋⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠙⢀⡀⢀⣀⠴⠋⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⣒⣒⣶⣶⣶⡦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢊⣡⣴⡎⢉⣉⣿⠶⠶⠾⠷⠦⢽⣯⣻⣆
⠀⠀⠀⠀⠀⠀⣯⠀⠸⣿⣿⡿⠛⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠈⢙⠳⡄
⠀⠀⠀⠀⠀⣟⠌⢧⠀⠹⣿⣇⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⢦
⠀⠀⠀⢀⣴⠙⡜⣌⢧⠀⠹⣿⣆⠀⠀⠀⠀⠁⠀⠀⣴⣿⣻⣽⣿⣷⣦⡀⠱⣄
⠀⠀⠀⢨⡏⢆⠸⡜⡌⢧⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⢿⣿⡹⣜⣿⡿⢾⣿⣦⠈⢦
⠀⠀⠀⢼⢿⡈⢆⠹⡜⡌⢧⠀⠘⣿⣦⠀⠀⠀⠀⢀⣀⠽⢟⣛⣫⣭⣭⣭⡽⢓⣲⡷⣄⡀
⠀⠀⠀⢸⣯⣷⡘⣆⠱⡜⡌⢧⠀⠘⣿⣧⢀⡤⢚⠥⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡢⡀
⠀⠀⠀⠀⢣⡹⣷⡘⢆⠹⡘⣎⢦⠀⢘⠟⣡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⢳⡹⣷⡘⣆⠹⡜⡎⢧⢋⡞⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣠⣄⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠳⡙⡽⡌⢆⠙⣼⢃⢮⠀⠘⣿⣧⠀⠀⠀⠀⠀⣀⣤⡀⣾⣿⣧⠹⣿⣷⡿⣿⣎⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡜⣝⢎⢦⢃⡟⡌⢧⠀⠘⣿⣧⠀⠀⠀⢺⣿⣿⣷⡝⠿⣿⣷⣼⣿⣵⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢎⡾⣼⠹⡘⡌⢆⠀⠈⢿⣷⣶⣾⣿⣿⡿⣟⣫⣵⣿⠿⠛⠛⠉⠉⣁⣀⣀⣀⣄⣈⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣗⣯⣇⢱⡹⡈⢇⠀⠈⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⣀⣠⣴⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⢳⢱⠈⢆⠀⠈⢿⡿⠟⠉⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢻⣿⡄⢣⢣⠈⣆⠀⠀⢀⡤⣶⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⢿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢫⣿⡀⢿⢦⠈⠶⠊⢓⣪⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⣷⡀⠉⠳⠤⢒⣭⣯⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡃⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠹⣧⣀⣤⣞⣿⣿⢟⣽⡟⡿⠁⢸⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡽⢵⣷⣿⣿⢯⣿⣿⣿⣿⣄⠘⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⣾⣿⣟⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠏⠛⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠁⠀⠐⠀⠀⠀⠐⠘⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢰⢶⡄⠀⠀⠀⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⡓⠀⠀⠀⠀⠀⠀⠀⠀⡐⡐⠆
⠀⠀⠀⠀⠠⠐⠐⢃⠀⠀⠀⠀⠀⠀⠀⢤⡟⠐⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠑⠆⡀⠀⠀⠀⠀⠀⠐⢈⣤⡆⠀⢀⡆
⠀⠀⠀⠀⠀⢠⢨⡟⠆⠀⠀⠀⠀⠒⣲⠁⣹⠁⠀⠀⠀⠀⠀⠀⠙⡉⣇⣀⠀⠀⠀⠀⠀⠀⢀⢾⠀⠈⠁⢌⠂⠀⠀⠀⠀⢈⠋⡆⢨⣐⠕
⠀⠀⠀⠀⠐⢲⠁⠘⠁⠀⠀⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⢦⣀⣋⠑⠑⠀⠀⠀⠠⠦⠕⢺⠀⣠⠀⠀⠚⠃⠀⠀⠀⠘⢾⠀⢠
⠀⠀⠀⠀⠀⢘⠐⠚⠀⠀⠀⠀⠀⠀⢀⠂⠸⠀⠀⠀⠀⠀⠀⠀⠘⢯⠝⠲⠄⠀⠀⠀⠀⠀⠀⠈⠇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠙⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢤⠀⠀⠀⠀⠀⠀⠀⢰⢀⣇⣐⠂⠷⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⡌⠑⡈⢄⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⠀⠈⠫⡂⠀⠀⠀⡰⢁⠴⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠑⠃⠃⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠰⠤⠀⠀⠀⠀⠀⠀⠐⠞⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⠅⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣿⠀⠀⠀⠀⠀⠀⢸⡁⡍⠀⠀⠀⠀⠀⠀⡎⢻⠟⠀⠀⠀⠀⠀⠀⠀⠞⢻
⠀⠀⢀⡀⠀⠑⠜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣿⣧⠀⠀⠀⠀⠀⠚⢻⠓⠄⠀⠀⠀⠀⠀⢉⠿⡀⠀⠀⠀⠀⠀⠀⠀⡑⠙⠄
⠀⠀⠀⠻⡂⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⠂⠟⠃⠀⠀⠀⠀⠐⡆⣛⢤⠂⠀⠀⠀⠀⠐⡿⣠⢧⠀⠀⠀⠀⢉⣅⠘⠇⠐⠤
⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠉⢂⠀⠀⠀⠀⠀⢠⡃⠘⢑⠂⠀⠀⠀⠀⠰⡅⡀⡀⠆⠀⠀⠀⠀⠁⢚⠀⡰
⠀⠀⠀⠀⠀⣹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢂⠀⠀⠀⠀⠐⠇⢰⠈⠀⠀⠀⠀⠀⠀⡗⢀⠂⠀⠀⠀⠀⠀⠀⠈⠘⢳⠁
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⡌⢂⠀⠀⠀⠀⠀⠀⠸⡀⠘
⠀⠀⠀⠀⠘⠀⢆⠐⡀⠀⠀⠯⡤⠮⠤⡴⠀⠀⠀⠉⠈⠫⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠙⡌⢆⠀⠀⠀⠀⠀⠀⢡⠀⢃
⠀⠀⠀⠀⡀⠐⠀⠣⣐⠄⠀⠠⣶⠔⢆⠧⠄⠀⠀⠀⣆⠀⢡⡄⠀⠀⠀⠀⡄⢸⠀⡀⠀⠀⠀⠀⠈⡠⠀⠈⡼⠂⠀⠀⠀⣠⢀⠂⠠⠀⡄
⠀⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠳⠾⠋⠉⠩⡔⠲⠀⣩⠍⣱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⣭⣥⠤⣀⠀⠀⠀⠈⠙⢀⣮⣥⣾⣻⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠂⠉⠁⠀⠀⠉⠙⠛⠶⠤⣀⣴⣿⣯⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠲⠋⡍⠛⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡟⠂⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⣪⠑⠊⠀⠀⠀⠱⢤⠀⢈⠑⣅⡨⢯⢟⣦⠠⣣⢡⣿⣿⣿⡛⢪⣦⣾⣿⣇
⠀⠀⠀⠀⠀⠀⣄⠒⢉⡴⠞⠅⢉⡁⠀⠀⠀⠀⠀⠀⠉⠉⠉⡠⢒⣽⣿⣿⡀⣱⣿⣾⣟⣀⣴⣟⣽⣯⢏⡾
⠀⠀⠀⠀⠀⢰⡿⣛⠲⠤⣌⣓⠠⣌⡀⠀⡠⠤⣤⡄⡠⣰⡭⣺⣿⣿⣿⡿⢀⣽⣟⠂⠀⢀⢹⡷⡿⣱⣏⡀
⠀⠀⠀⠀⠀⢘⡇⠈⢛⣒⢦⢭⣙⣶⣍⣉⠤⢞⣩⣔⣮⣷⣿⣿⣿⣿⣿⡝⠋⠁⠀⠀⣠⡼⢪⣿⣷⣯⣒⡚⠑⢶⠤⢄⣀
⠀⠀⠀⠀⠀⠘⠣⢄⡀⠠⢍⣋⠒⠮⢙⠿⠯⣗⣿⣟⣯⡿⣿⣿⠋⠓⠂⢀⣩⡿⣿⣪⣳⡼⢾⣿⡥⠴⠚⣇⣀⡂⡰⠔⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣦⣭⣛⠲⠬⣴⠒⣾⣿⡿⠟⠷⠂⠀⠀⠉⢁⢎⣾⣿⠧⡳⣡⡎⠁⠀⢠⠂⠉⠚⠵⢖⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡺⠗⠂⢉⣉⠒⠤⣼⠏⠽⠀⠉⠁⠀⠀⢀⢔⣵⣟⣽⣿⢀⡴⠃⢀⡠⠕⠁⠀⠀⠀⠐⠒⠈⠙⡏⢙⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢰⡎⠤⠸⠥⠀⢓⣀⠠⠬⢗⣒⠀⠀⡠⠔⣒⡖⢒⣵⡷⣳⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⣀⠘⡀⠈⢐⣡⠔⣫⡀
⠀⠀⠀⠀⠀⠀⢸⡯⠭⠍⢀⣒⣒⠒⠀⠉⠩⠍⠋⢉⡀⠐⠫⢒⠽⣣⣮⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⠯⢒⡩⢔⣫⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠭⠔⢒⣒⣒⣀⠭⠍⠭⠤⠶⠒⠀⠭⠽⠤⣾⣿⡿⡿⠿⣶⣖⠒⢲⣖⠢⢄⣀⡠⠄⢀⡢⢭⣒⣬⣴⣾⢿⣿⡯⢛⠯
⠀⠀⠀⠀⠀⠀⠀⠈⣟⢆⡳⣖⠶⡴⠤⢭⠭⡭⢩⠏⡭⡩⢭⠍⡽⣿⡫⡂⠀⠈⠙⣯⣒⠦⡭⣤⣖⠲⢽⣗⣿⣿⣿⡿⠿⢛⡉⢔⣚⣽
⠀⠀⠀⠀⠀⠀⠀⠨⡎⠁⠉⠊⠑⠦⣀⢁⠊⠐⠑⠠⠊⠔⠡⠢⢂⡜⣿⣾⡀⠀⠀⠀⠱⠍⢨⣿⣿⣾⡿⠿⢛⡩⢕⡂⢬⡰⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⠈⠙⡳⣖⠈⣉⡽⠖⢲⣶⣿⣿⣿⣿⡿⡶⠄⡀⠀⠀⢸⡿⠽⣔⣶⡯⠿⠛⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠘⡟⡙⠢⣴⢾⣿⣽⣿⣿⡷⠝⠋⠀⠀⠈⠐⠠⠜⠛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠈⠮⠀⣼⣿⣯⠿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠐⠀⠀⠄⡠⢀⠄⡠⢀⠀⢀⠀⡠⠀⠀⡀⢀⠄⡠⢀⠄⠀⠀⡠⢀⠄⠀⢀⠀⡠⢀⠀⡠⢀⢄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠊⢔⠄⡀⠄⡀⢀⠄⡠⠔⡁⢀⠅⠠⢊⠄⡨⢀⠀⣀⠄⠀⡠⡠⢊⠔⠡⢀⠔⡡⢊⠔⡡⢊⠔⡁⠨⠪⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠐⠁⠊⠐⠁⠐⠀⠊⠐⠡⠂⠄⠡⢂⠀⠡⠪⠈⠄⠁⠊⠐⠁⠈⠀⠁⠈⠀⠁⠈

⠀⠀⠀⠀⠀⠀⣀⠀⢤⣀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠒⠒⠒⠒⠲⠶⠤⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⣀⠀⠀⠀⠈⣁⠰⠖⠐⠚⠉⠉⠉⠈⠉⠀⠀⠒⠒⠒⠒⠀⠉⠛⣠⡶⠖⠛⠉⠉⠉⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣯⡥⠖⠀⡀⠀⠀⠀⣀⠰⠋⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠚⠛⠉⠉⡀⠋⣀⠴⠒⠶⠃⢀⡄⢊⡁⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠐⣠⣄⣀⣀⡤⣄⠾⠋⠁⠀⠀⢰⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡆⢸⡆⢀⠴⠂⠀⠀⢀⣠⠞⢀⣀⠀⠈⣉⣥⣆⣀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⣿⣄⢻⡾⠅⠈⣀⠤⠄⠀⠀⠀⠀⠀⣸⣴⣿⠿⢛⣿⣿⣿⣷⣥⣤⣴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣌⠹⣄⢈⠿⢏⠑⠆⣠⡟⡰⠲⡜⢶⡶⠋⠀⠘⣿⣿⣷⣉⣹⣯⣿⣿⡿⠿⢿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡈⢖⠉⠠⡀⠈⠳⣏⣾⡗⠀⠐⠉⡈⠁⠀⢀⣼⠂⠉⠛⠿⣿⠿⠟⠋⠀⠀⠈⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠣⡀⠉⣢⣴⠶⢶⣤⣥⠀⠲⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⡄⢀⣤⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠛⠉⠉⠉⠀⣸⠉⠉⠓⠛⠳⢶⣟⣈⠀⠲⠀⠀⢀⠀⠀⠀⠀⠀⠐⠺⡅
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠸⠃⠀⢠⠄⠐⠂⠐⠦⠄⠶⠄⠴⢾⣿⣶⣶⡶⠀⠲⠶⠶⣴⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⢶⠶⣦⠂⠄⠠⠄⠠
⠀⠒⠒⠒⠒⠦⠼⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⣀⠏⠉⠍⠉⠀⠀⠀⠀⠀⠀⠀⠸⢏⠀⠀⠀⠀⠀⠛⠂⠘⠃⠘⠳⠶⢶⡴⢶⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠈⠙⠉⠙⣏⠀⡀⠀⢱⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⢀⣀⣀⠴⣧⠀⠡⠀⠈⢡⡙⠲⣤⣦⣄⣀⡀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠤⠞⠀⠀⠀⠀⠀⢁⠀⠈⠉⠙⢛⣿⠛⠋⡃
⣀⣀⣀⣀⣠⡴⢦⣤⣀⣀⣀⣀⡀⠤⠛⠻⣿⣿⠀⠀⠀⠀⡀⠀⢆⠀⣆⠀⠀⠛⡿⠋⠀⠈⠣⠘⠛⢠⠶⠀⢀⣀⣀⣀⣀⡤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⠑⠂⠐⠃⠀⠈⠀⠘⢳⣖⠊⣀⠀⠠⠌⠀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠤⠤⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠄⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠀⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠸⠃⡐⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⢀⠄⠀⣠⠊⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣠⠃⠀⡠⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡖⠁⢀⠄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠤⠸⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠙

⠑⢄⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⣀⣀⣀⣱⡀
⠀⠀⠑⣄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠙⡄
⡠⠔⠊⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠈⠢⣄⢀⡀⠤⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⡇
⠀⠒⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⠤⠔⠎⠀⠀⠀⠙⠒⠢⢄⡀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠈⢫⠉⠁
⠈⠁⠀⠀⠀⣀⣀⠠⠄⠚⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠒⠂⠉⠉⠁⠁⠈⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠰⠀⠠⠤⠀⠀⠁
⢄⠀⠀⠀⠀⢀⠀⠀⠐⠒⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⠉
⣲⠄⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠶⠀⠁
⠀⠀⠀⠁⠂⠀⡀⠀⠀⠀⠀⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⠀⠀⢀⠘⡤⢤⣀⣀⡀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⣉⠉⠀⠂⠀⠉⡗⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡨⠥⠒⠛⢏⡰⢲⠤⠤⠄⣀⡀
⠀⠀⠀⠀⡤⠒⠚⡍⢆⠂⠈⠠⠭⠆⠂⡐⢀⠚⠚⡜⠀⢬⢳⠢⢄⡀⠀⣀⠤⠔⢊⠧⠀⣎⠁⠀⠀⠀⢠⢾⠁⣏⠔⠂⠉⠑⢎⢹
⠀⠀⠀⠀⡇⠀⠀⠘⡌⢣⣁⠁⢀⡈⡴⠵⣆⣀⣀⢐⡀⠸⠘⠀⠀⠈⡉⠀⠠⢄⣿⠀⢧⠢⡙⢄⠀⠀⡇⡘⢸⡃⢀⡤⠒⠒⠁⢸
⠀⠀⠀⠀⣧⠂⠐⠀⠈⢦⡙⢦⡀⢨⣁⣀⣁⠸⠛⡄⠀⡇⣇⠞⠉⠳⠠⢀⡇⠘⣅⣀⣽⠀⢷⠈⠢⠜⠀⢠⢸⠑⠋⠆⠁⠀⠰⠎
⠀⠀⠀⠀⠃⢱⡎⠀⠂⢢⠙⠢⣈⠒⢄⡀⢠⣁⣀⣠⡼⠰⡙⠀⠀⢠⠃⢺⢆⣀⢾⠉⠿⣤⣼⡥⠔⠒⠀⠉⠀⠉⠉⠀⠒⠒⠤⡇
⠀⠀⠀⠀⠀⡠⠀⠄⢲⠊⢀⠤⡈⠑⠦⣈⠑⠤⣀⡰⢡⢣⠁⢀⡠⣊⠤⢐⡒⠢⢄⠀⡠⠒⠁⠀⠀⣀⠠⠤⠤⡀⣤⠄⣀⡀⠀⡇
⠀⠀⠀⠀⢸⠐⣴⠂⠀⣀⠎⠀⠈⠒⢄⠀⠙⠢⡜⡱⠧⡘⠒⡩⡪⠒⠉⡊⠙⡕⢆⠉⠀⠀⢀⠔⡩⠒⠈⠑⡄⠃⢐⠠⠀⢀⡉⡇
⠀⠀⠀⠀⢸⢄⡁⠀⠪⣀⡀⠀⠀⠀⢈⠃⢀⠎⡔⠉⠢⡈⠻⡋⢈⠁⡡⠈⣎⡴⠁⠀⠀⢰⠁⠊⠀⠀⠀⠀⡄⡆⡌⣄⠃⠶⠾⠆
⠀⠀⠀⠀⢸⠢⢌⡑⠤⣀⠀⠑⠤⠤⠋⠀⡎⡜⠐⢀⠁⠌⢦⠘⢆⠻⢀⡠⠊⠀⠀⡠⠛⢆⠑⢕⠂⢄⠀⢀⣵⡱⠰⠒⢎⠀⢠
⠀⠀⠀⠀⢸⡎⠑⠪⠵⣦⡑⢄⡠⠄⠒⣾⠀⠑⠓⠒⠒⠒⠧⠵⠀⠑⠉⠀⠀⣠⠞⡔⠒⠢⡑⢄⡑⠤⣉⣪⣧⠃⠅⠀⠴⠀⢸
⠀⠀⠀⠀⠸⢸⠀⣠⣴⠗⠛⠄⢧⠀⣺⠀⢷⣀⣀⠦⠀⠀⠀⠀⠀⠀⣀⠀⣎⠁⡜⠀⠀⠀⠈⠲⡉⡒⠤⢀⣉⠒⠒⠠⠤⠤⢼
⠀⠀⠀⠀⠀⠈⡺⠋⠁⠀⢀⣼⢸⠫⣭⠀⠨⣦⣟⠀⣫⠉⢰⢒⢉⠕⢬⡳⡈⠢⡱⡀⠀⠀⠀⠀⡧⠁⡇⡆⡔⠛⠛⠭⡀⠀⢺
⠀⠀⠀⠀⠐⡋⠀⢀⡠⠊⠁⡸⢸⢀⣥⣽⡁⢹⡇⢀⣰⣂⡆⡌⠠⡀⠀⠑⢌⢦⡘⢮⣄⠀⠀⠀⠱⡀⡇⢿⠀⠀⣀⢤⣊⠤⢼
⠀⠀⠀⠀⠀⣧⠔⡁⠘⠀⢠⢃⡏⠛⣹⡉⠫⡫⡀⠉⠁⡜⡰⢠⠤⡘⠦⠤⠤⠃⠑⢄⠙⢷⡂⢄⡀⡸⠱⡘⢅⣩⢖⢅⡲⠭⠯
⠀⠀⠀⠀⠀⡕⠀⠀⠂⡠⢃⢮⣿⡰⠉⠑⣀⠈⠪⡒⠞⡰⡱⠁⠀⠈⠒⢦⢀⠘⠰⠀⡑⠦⣈⠒⠬⣁⠂⡝⢌⠱⣅⡏⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠰⢀⠔⡡⠃⠂⠀⢧⠤⠤⠄⡀⣡⢊⢜⠜⠀⠀⠀⠀⢰⠡⠈⠀⠀⠄⢀⡰⠜⠓⠢⠬⣑⣢⣀⠑⣌⢪⢢⠀⡇
⠀⠀⠀⠀⠀⡗⡠⣪⠎⠀⠘⠒⣒⠸⠦⠠⠤⣕⣡⠊⢸⡀⠀⠀⠀⠀⠘⠀⠠⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠘⠦⢇⣉⡇
⠀⠀⠀⠀⠀⢯⡼⠥⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠬⢉⣐⠢⠄⠔⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠉

⠁⢀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠚⠫⡶⣠⡄⣠⠔⠁⠀⠀⠁⠀⠀⠀⢀
⡀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢩⢖⣠⢄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣵⣟⡴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣄⣠⣀⣤⡤⠰⠒⠚⠋⠁⠀⠀⠀⠀⠉⠛⠿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠖⠒⠒⠒⠛⠒⠀⠀⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠉⠘⠋⠴⣆⣤⢀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠈⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠷⢖⣤⣀⡠⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠻⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠀⠀⠀⠀⠱⢆⡄⠀⠀⢀⣠⡄⠒⠉
⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣴⡄⠒⠉⠀⠀⠀⠄
⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠋⠀⠘⣷⠂⠀⡀
⠀⠀⢀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠊⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠰⠖⠉⠀⠀⠀⠀⠀⠀⠀⣿⢆⠀⠀⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠊⠜⠒⢤⡀⠀⠉⠀⠀⠀⠀⠀⣀⣤⠐⠊⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠐⠊⠁
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⡀⣀⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠔⠚⠙⠳⢄⠀⠀⡀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⢀⡤⠖⠂⠉⠁⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⣠⠜⠣⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡶⢞⡁⠀⠀⠀⠠⠀⠀⠀⣀
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠈⠋⠠⠖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠶⢤⣄⢀
⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠄
⠀⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠠⠤⣀⡀⠀⠀⠀⠘⠁⠀⠁⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠙⠳⣦⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠉⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⣦⣄⠀⠀⢀⡴⠉⠀⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠆⣀
⠀⠉⢻⣶⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣠⡾⠋⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡶⣦⣄⣀⠀⠀⠀⠀⠀⠀⡀
⠋⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠈⠉⠛⠳⢦⣤⣀⣀⠀⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠛⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⣩⠛⠛⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⣤⣄⣀⠀⠀⠀⡎⠀⠀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣄⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠙⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⢞⠄⣉⣽⠛⠷⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⡤⠒⠉⠐⢀⠞⠁⠀⢧⠀⠀⠀⠈⠉⠛⠷⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡠⠞⠉⠀⠀⠀⣰⠋⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣄⣀⠀⠀⢀⡠⠔⠉
⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣀⠔⠋⠀⠀⠀⠀⢀⠞⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⠿⠷⣤⣄⣀
⠀⠀⠀⠈⢉⠛⠻⢶⣌⡀⠀⠀⠀⡴⠁⣀⠐⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠈⠙
⢀⠀⡀⠄⠀⠀⠀⠀⠈⠙⠳⢦⣤⡧⠊⠀⠀⠀⠀⠀⢐⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⢉⠁⠂⠤⢄⣀⡀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢻⣀⣀⠤⠔⠚⠓⢲⣶⠿⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠈⢦⡀⠀⠀⠈⢹⠛⠙⠒⠀⠓⠂⠀⠀⠲⠚⠀⠓⠐⠂⠀⠛⠙⠁⠉⣄⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠁⠰⠦⢀
⠀⢀⡴⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣠⠞⠁
⣶⣧⣶⣶⣶⣶⣶⣶⣶⣴⣦⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣾⣷⣤⣶⣶⣶⣦⣶⣦⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⣻⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣽⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⣤⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠘⢾⠋⠀⠀⠀⠀⠀⠉⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢰⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⢀⣄⣀⣴⣾⣿⣎⣵⣾⣿⣷⣄⠀⠠⣄⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢻⣧⡀⠀⣿⡟
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⣿⠀⣿⣿⠇⣤⣿⠇
⠀⠀⠀⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⣿⣼⣿⣿⣾⣮⡟
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠈⠛⣽⣿⣿⣿⣿⣿⡿⢋⣙⡻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠟⣿⣿⠟⠁
⠀⠀⠀⠿⠇⠀⢿⣿⣿⣿⡇⠘⢿⣿⣿⣭⣙⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⢡⡿⠿⣦⢀⣃⣾⠛⢿⣄
⠀⠀⠀⢀⣀⣀⣀⡈⠹⣿⣧⠲⣄⣉⡉⠋⠉⡁⢠⣶⣿⣿⣷⣦⣄⢀⣴⣾⣿⣿⣿⢃⢸⡇⠀⠈⣿⣿⣿⣦⣾⣿⣓⣲⣶⣄⡀
⠀⢀⠔⠁⠀⠀⠀⠙⢦⡈⢿⣧⡽⠥⠉⠋⠁⠀⣿⠏⠀⠀⠉⠛⢿⣿⠟⠛⠛⠋⠻⢁⣶⣿⣦⠘⢿⠟⠋⣱⣿⣵⣿⢿⣿⣿⡇
⠀⡘⠀⠀⠀⠀⠀⠀⠈⢧⠈⢿⣿⣦⣄⡀⠀⠀⣿⠀⢀⣤⠒⠀⠂⣙⣦⣀⣐⣢⣴⣿⣿⡗⠀⢀⣶⣾⣿⣿⡿⠟⣡⣾⣿⠟
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣿⣿⣿⣿⡷⣦⣽⣷⠿⠿⢧⠀⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠛⠿⡿⣿⠿⠛⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⣿⣿⣸⣿⣿⣿⡔⣦⣘⣛⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠘⢿⣧⣹⣟⣻⣿⣶⣿⣿⣿⡿⠀⠀⠀⠀⣿⠟⣛⣿⣿⣿⣿⣋⠉⣀⣿⣧⣤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠘⢷⣄⠙⠿⢿⣿⠉⠙⠉⠉⠉⠀⠀⠀⠀⡰⠴⠋⢀⣽⢿⡟⢻⣿⠆⠋⠛⠻⣥⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣤⣙⠛⣷⣶⢷⠀⠀⠀⡀⠀⠀⠀⠀⢠⣷⠶⡾⠟⠁⠸⣇⣠⠋⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⣿⣿⣿⣿⡿⠋⠀⠈⢣⡀⠀⠻⣶⣤⣤⣤⣾⠗⠋⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⣀⣤⠤⠈⠛⠶⠦⠤⢬⣭⣿⡿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡀⠀⣉⠀⠀⠀⠀⠀⣀⣤⡉⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⠀⠀⠘⢿⣿⣷⣦⣤⠶⠶⠶⠶⣶⣦⣤⡐⢢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡶⠶⠶⢞⣻⣿⣿⣧⣤⡀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣶⣴⣿⡛⠁⠉⠐⠂⠠⠦⢦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣯⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣠⣄⣀⡉⠽⣿⣿⣿⣿⣿⣿⡿⠶⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠻⠿⣿⠿⠛⠿⠟⠁⠀⠀⠀⠀⠉⠉⠉⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠖⠒⠂⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢆⠈⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣰⡀⠹⡀
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢼⠀⢆⠀⢰⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢣⠘⠀⡇
⠀⠀⠀⠀⠀⢀⠁⡀⢀⠔⢀⠠⡄⢀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠛⠈⠒⠂⠛⢠⠉⢆⠀⠀⠀⠀⠀⠀⠀⢀⠐⡄
⠀⠀⠀⠀⠀⠀⠈⡦⠀⠈⠀⠀⠈⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠰⠆⠀⠀⠁⠀⠠⡀⠀⢀⡄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡤⠀⠀⢠⡄⠀⠸⠆⠐⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⡀⠚⣧⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⠊⠀⢰⡀⠠⢃
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠦⡤⠄⠲⢧⡀⠀⠀⠀⢀⡙⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⡠⠤⠺⠛⠭⠥⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣃⣝⠀⡀⠀⠀⠠⡀⠀⠀⠓⠊⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠁⠀⠰⠀⠀⠐⣄⡃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣀⠜⠀⠬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢄⢰⡉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠁⠰⠠⣀⠀⠀⠀⠀⠀⠀⡀⡔⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⠀⠀⠀⠈⠀⠀⠐⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡄⠰⠦⠄⠀⠀⠀⢠⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢠⡀⢄⡒
⠀⠀⠀⠀⠀⢠⠈⠉⠀⠀⠀⠀⠀⣇⠀⣀⠀⠀⠀⢤⠀⢀⠃⠀⡀⠀⠀⠀⠀⠀⠀⡐⠲⠰⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠈⠂⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⢀⠎⠀⠀⠀⠟⢠⠂⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢠⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢒⣒⡲⢤⠄⠀⢀⠀⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠏⠀⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢇⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢐⠄⣸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣸⠀⠀⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⢀⠃⠡⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⡇⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠄⠀⠀⠡⡀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣟⠳⢄⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠌⠀⠀⠀⠀⠱⡀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢿⠀⠀⠙⠢⣄⢸⠀⠀⢀
⠀⠀⣀⠠⠤⢄⡀⠀⢀⡴⠁⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⣎⠉⠀⠀⠈
⠀⠘⢃⠺⢦⣄⠙⠐⠧⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠈⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢸⠀⠀⠀⠀⡿⠀⠀⢀⠆
⠀⠀⠀⠑⠀⠑⠳⣄⠀⠀⠀⠑⢆⠈⠀⠀⠀⠀⠀⡠⠔⠚⠀⠀⠀⢠⣢⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠊⠀⠃⠉⡆⠀⠀⡼⠁⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠐⠀⡉⣂⡀⣠⠋⠀⠀⠀⠀⠀⠸⣠⣤⣂⣀⣡⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠙⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠆⢀⠀⠐⢊⡽⢿⣟⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠿⢤⣤⡾⠃⠉⠛⠁⢀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠙⠻⠶⢶⣶⣶⣶⡶⣶⡾⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠤⣤⣤⣤⣤⣤⡄⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣀⣀⡀⢉⣉⣁⣠⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣶⣷⡶⢤⣀⠀⠈⠉⠛⠛⠛⠛⠋⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⠾⢷⠾⠋⠈⢀⣠⣿⡆⠐⠶⠶⠶⠶⡶⠿⠀⢻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠙⠛⠶⠶⠾⠿⠿⠟⠻⣿⣿⠠⣤⣤⣤⣤⣤⡤⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠒⠲⠶⠶⠟⠃⠀⣿⣏⢀⣀⣀⣈⣁⣩⣤⠀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠘⠛⠛⠛⠛⠁⠀⣿⡟⢀⣀⣉⣉⣉⣉⣁⡀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⠛⠛⠛⠛⠁⢠⣿⡇⠀⠉⠙⠛⠛⠛⠉⠁⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠙⠛⠛⠛⠁⠀⣿⣇⠀⠛⠷⠶⠶⠶⠷⠂⣿⣧⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⣿⣿⠀⣀⣀⣠⣤⡴⠶⠖⠛⠛⠋⢉⠁⠀⠙⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠑⣒⣶⣾⡿⠷⠶⠛⠛⠋⠉⠙⠛⠶⣤⣄⣀⡠⠄⠘⠲⢭⣥⣨⡖⠒⠠⡉⠛⠻⠷⣶⣤⣄⣀
⠀⠀⠀⠀⣀⣀⣀⣤⠤⠶⠒⠚⠋⣉⠽⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣄⣀⠀⠀⠀⠈⠑⠲⣔⠲⠷⢦⠉⠙⠛⠻⠿⠶⠄
⢀⡀⠈⠉⠉⠁⢀⠀⣤⣙⡳⣤⠥⠖⠒⠛⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣀⡠⠔⠚⢛⣛⣋⣤⠤⠶⢒⣀⣠⣧
⠘⡇⠈⠑⢦⡀⠀⠳⢤⣼⣿⡾⠲⢤⣀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⠿⡷⠚⢛⣉⡩⠤⠶⠚⣋⡩⠥⢸⣿
⠙⣷⣄⠀⠀⠉⠳⢤⡀⠀⠈⠙⠓⣶⢫⣍⠛⢷⣦⡴⠖⢚⣩⠤⠄⠉⠂⠀⣀⣠⣤⠶⠖⠛⠋⠉⠀⠀⠀⣷⠀⠀⠀⠐⠒⠋⣉⣠⡤⠴⣿⡿
⠀⣗⠈⠛⢦⣄⠀⠀⠉⠳⢦⣀⠀⠘⢦⣉⣿⣦⣿⡥⠖⠋⣀⣤⣤⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡠⠴⠖⠛⠉⠁⣀⣠⣤⣿⡇
⠀⣿⠑⢦⣀⠈⠳⢦⡀⠀⠀⠈⠙⠦⣄⠈⠉⣉⣤⣴⠾⢟⡋⠉⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⡤⠶⠶⠟⠛⣉⣁⣬⣿⡇
⠀⢿⠲⣄⡈⠓⢤⡀⠙⠳⣄⡀⠀⠀⠀⢰⣟⣯⠵⠖⢚⣉⣤⡤⠖⢒⣁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣠⡤⠶⠞⣛⠋⢍⣘⣿⣿⣶
⠀⠀⢤⣀⠙⠦⣄⠉⠒⢄⠀⠙⠲⣄⡀⢸⣷⠶⠚⢛⣉⣭⠴⠖⠛⠉⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠍⣒⣺⣭⣵⣶⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣷⠶⠟⠛⠉⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⠿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣀⣤⣴⡶⠿⠋⠀⢹⣇⣠⣤⣴⣶⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⢸⣿⠖⠚⠩⠛⣉⡥⢀⣠⣤⣶⣾⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⢸⣿⣤⡴⢖⣫⣵⣾⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢾⣏⡴⠞⠛⠉⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡏⠙⠻⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⠁⠀⠀⠀⠑⠻⣿⣦⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡌⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣟⣟⡛⠿⣿⠭⠭⢭⠭⡭⠭⢿⠿⢻⣷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠋⠈⢱⠀⠀⠀⢀⣀⣀⣀⡃⠀⣀⣀⣀⡵⠀⠀⡸⢀⠃⠀⡘⠀⠀⠀⢙⠛⠻⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⠀⠀⠀⠉⢢⡀⡊⠀⠀⢸⠁⠉⠀⠀⠀⠀⠀⢸⠀⡸⢠⢋⡗⠂⠐⠢⠊⠀⠀⡰⠃⢩⠟⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⣉⡉⠑⡄⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠜⣀⡉⠁⢸⠀⠀⣠⠤⢄⠀⠀⠉⠦⠼⣍⠁⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠑⠒⠁⠀⡤⣀⠀⢠⠁⠀⠀⠀⠀⠀⣎⠁⣔⣁⠜⠀⡎⠀⡰⠁⠀⠀⡇⠀⠀⠀⠀⠈⢻⡏
⠀⠀⠀⠀⠀⠀⢰⡿⡏⢣⠀⠀⠀⠀⡜⠀⠈⢆⣸⠀⠀⠀⠀⠀⠀⠈⠓⡄⠀⠀⢠⠃⡠⠃⢀⣀⢀⣳⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⣼⣷⡀⠈⢣⡀⠀⡜⢡⡘⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⢸⠀⠙⠈⠗⠦⠀⠀⠀⠘⢬⠑⢤⡿
⠀⠀⠀⠀⠀⠀⠉⠻⣮⣗⣄⡈⠉⠀⠈⠁⠀⢰⣃⣑⢦⡠⠎⠉⠱⡄⠀⢘⠄⠀⡆⠀⠀⡠⠒⠒⡄⠀⢀⡤⠤⠂⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣶⢄⡀⠀⠀⢸⠧⠞⠀⠀⠀⠀⡜⠀⢠⠋⠀⢀⠃⠀⠀⢣⡀⠈⠦⠴⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⣢⣄⡆⠀⠀⠀⣀⣀⣀⣘⣤⣋⣀⣀⣸⠀⠀⠀⢀⡇⠀⡤⠒⢦⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠿⠿⢯⣵⣖⣧⢄⡀⠈⢉⡥⠤⠞⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣿⣦⡤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣉⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣾⣿⣿⣿⣶⣶⣄⣤⡀
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢻⣿⣶⣾⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠿⠛⠛⠛⠃⠀⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠘⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣄⠃⢴⣤⡤⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⢻⣿⡿⢟⡛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⠋⠀⠀⠀⠀⡆⠀⠀⣀⠈⠙⠛⠉⠀⠀⠀⠁⢰⡏⣹⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣑⣡⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠙⠛⠒⠲⠒⠒⠚⠃⠀⠀⠀⢀⣠⡾⠉⠉⠉⠛⠛⠛⠻⠟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀⣀⣀⣀⣠⣤⣴⠟⣋⡁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡍⢻⠉⠉⢀⡠⠛⣧⠍⣸⡛⠽⣟⢲⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣯⠀⠙⠒⠂⠉⣴⠊⣠⡖⠉⠛⣦⠈⣿⡚⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣰⣇⣴⠿⣤⣷⣶⠁⣠⣟⡀⠀⠀⠸⡇⢸⡇⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣤⣀⣰⡟⢰⠇⠀⠀⠀⢏⣉⠉⠒⠋⠈⠹⠀⠀⠀⢱⡞⡃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠇⠙⠺⣿⣿⣄⠇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣤⡀⠀⢸⣿⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠠⣦⣼⠗⢤⣤⣀⠈⠉⣿⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣀⠀⢈⣿⠀⢸⡿⢠⠏⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠀⠀⠀⠀⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠈⡃⠹⣸⠿⠋⢠⣆⠘⣅⡜⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣷⠀⠀⢸⡗⢻⡃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠸⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣿⠀⠀⠀⠁⣼⣡⠟
⠀⠀⠀⠀⠀⠀⠀⢿⣸⣇⣀⣀⠴⣦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡸⣄⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠛⢫⣤⠃⣽⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⡟⠁⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣋⠛⠶⢦⣤⣤⣤⣤⣤⣤⣤⣴⠶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠶⣾⣍⠀⢀⣈⣉⣁⣤⠛⢶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⣀⠁⠈⠉⠉⠷⠤⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡅⠈⠉⠁⠀⠀⣀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⡏⠀⠀⠀⠀⠀⠀⠉⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣸⠇⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⣠⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃⠀⠀⠀⡰⠋⠈⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣦⠀⢀⡇⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠉⢀⠻⣆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢈⡇⠸⣇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠘⡀⣠⠟⠁⠀⠙⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣄⡸⠀⠀⠀⠁⠟⠀⠀⠀⠀⢧⡀⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣦⣄⢸⠇⠀⠀⠀⠀⠘⢧⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⠻⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣞⣛⣿⣿⣿⣿⣿⣛⣒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡇⠀⠙⢦
⠀⠀⠀⣶⢶⡶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠙⣮⣽⡖⠛⠛⢛⣿⣛⠛⠿⢧⣷⡀⠀⠈⡇
⠀⠀⢀⣿⣿⣿⣿⣷⣿⣿⣹⠇⠀⠀⢀⠔⡫⠖⢆⠀⠀⢀⡤⠶⢮⠁⠀⠀⠈⠙⢦⣀⡇
⠀⠀⢸⢹⣿⣿⣿⣿⣿⣿⠏⠀⠀⡴⠃⢰⢁⣤⡜⠀⡰⠃⣠⡀⡼⠀⠀⠀⠀⠀⢸⣿⣧
⠀⢀⣾⣬⣉⡙⠻⢟⡿⡏⠀⢀⡞⠀⠀⠉⡾⠿⠁⠠⡇⣸⣿⡟⠁⠀⠀⠀⠀⠀⢼⣿⣿⠷⠒⠲⡄
⠀⢸⣉⡉⠛⠛⠻⠷⣾⠀⠀⡼⠀⠚⠁⠀⠣⠄⠀⠀⠉⠀⠀⠀⠁⠀⣤⣄⠀⠀⠀⠙⠋⢰⣃⠀⣿
⠀⠙⢾⠺⠽⣶⣶⣤⡏⠀⠀⣇⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⢁⡎⠁⠀⠀⠀⠀⠀⣊⡴⠃
⠀⠀⢸⡀⢀⡴⠚⠉⠀⠀⠀⢹⡀⠀⠀⠀⠉⢖⠒⠒⠒⢊⣉⣡⣴⣾⡟⠀⠀⠀⠀⠀⢠⠏⠁
⣴⢊⠛⡶⠚⢦⠀⠀⠀⠀⠀⠀⣳⡄⠀⠀⠀⣜⠛⠿⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⡴⠋⠙⠓⠦⣤⣀
⣏⣁⣉⣧⣠⢟⠆⠀⠀⠀⢀⡴⠁⢸⣶⣄⡀⠈⠉⠒⠒⠚⠋⠉⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⢞⣠⣀⣹⠀⠘⡦⢤⡤⠖⠋⠀⠀⠘⣿⣸⡟⠲⠦⣤⣀⣀⣀⣀⣤⠤⠶⣾⢫⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢈⠇⠀⡽⣶⡼⠁⢠⠀⠀⠀⠀⠀⠀⣿⠙⣿⣶⢤⣤⣄⣀⣀⣀⣠⣤⣴⡟⢳⡇⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⡰⠙⣆
⢸⠀⢠⠇⠙⠳⣴⡃⠀⠀⠀⠀⠀⢀⣿⣷⣿⣾⣿⣿⣾⣷⣶⣾⣿⣿⡿⣷⣾⢿⡀⢀⣿⠉⠉⠉⠉⠉⠙⠛⢲⠮⣤⠴⠋⠙⡶⢦⣀
⠸⠤⠞⠀⠀⠀⠀⠉⠓⠲⠶⠶⠚⠋⠙⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⡯⣿⣿⣿⣽⣻⡇⠀⠀⠀⠀⠀⠀⠀⡞⢠⡀⠀⠀⢀⠇⠀⣙⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⢾⣻⣿⣿⣿⣯⡷⣿⣷⣿⢿⣟⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣅⣀⡴⣾⣶⣿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣾⢷⣾⣿⣿⡿⠶⣿⣟⣻⣽⡶⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣾⡿⣿⣭⣾⣿⡿⢩⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⡿⣿⣿⣿⣿⣿⣟⣟⣛⣻⣯⣿⣿⣿⣷⢚⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⢿⣿⣿⡾⠟⡠⠊⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣿⣿⢽⣻⣿⣽⣽⣿⣿⣯⣽⣿⣛⣿⢿⣿⣿⢞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡿⠛⢉⡄⠊⠀⠀⠀⣸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⢿⢏⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣝⡻⡞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠑⢆⠀⣀⠔⢡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⣟⣋⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣙⣋⣩⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣉⣥⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠤⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠈⣧⠀⠀⠀⠀⠈⠑⢄⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠐⣿⣿⠂⠉⠙⠛⡇⠀⠀⠀⢿⠀⠀⢠⠀⠀⠀⠘⣧⠰⣤⡤⢀⣀⣀⡐⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠄⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⢹⡀⠀⣿⣿⡟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⠀⠀⠀⠀⠈⢄⠀⠀⠀⢨⠁⠀⠇⠀⠀⣠⣤⠄⠙⠚⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣶⡿⠀⠀⠛⠉⠐⢦⣆⣘⣠⡤⠶⠚⠓⠒⠒⠛⠥⡀⠄⠀⢹⣿⣧⡄⠖⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣼⠧⠀⢐⡤⠖⠋⠉⠋⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⢾⣆⠻⡟⠃⡓⠴⠤⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣶⣟⣒⡲⠊⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠹⣧⡁⡤⠃⣀⠠⠄⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣀⣀⡝⠁⠀⠀⣴⠿⣿⠻⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠹⣷⣾⣟⠠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠠⠀⢰⡇⢰⡟⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢹⣿⣿⠋⠭⠤⠰
⠀⠀⠀⠄⠀⠀⠀⠜⠧⠤⢀⠀⠤⠔⡄⠀⢻⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡍⣿⣷⡀⢠⠇
⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠐⠒⠊⠈⠀⠀⢸⡏⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⢹⡿⠉⣀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠂⠠⠄⠠⠀⠀⠉⠀⠀⠂⠀⣄⠈⣇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠃⠈⢀⣴⡷⠿⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠋⠤⡌⠀⠀⠀⠐⠀⠀⠀⠀⡜⠷⣾⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣸⣁⣠⢾⡏⢄⣙⡓⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠏⢀⣒⡏⠤⢉⣀⠀⠀⠀⠀⢹⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⣠⣾⣿⣿⣿⣯⣍⡲⢭⣵⣾⠟
⠀⠀⠀⠀⠀⠐⠀⠐⡚⢀⠒⠒⠒⠂⣨⣀⣀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⢰⣿⣿⠏⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠛⠻⠿⢿⣷⣶⡀⠀⠀⠀⠀⠈⠀⠟⠁⣴⡿⣩⠀⠀⠉⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⣠⣾⡿⡉⢥⣽⡲⣤⣶⣿⠏⢙⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⠻⣷⣕⠲⠞⣣⣷⠟⠃⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠐⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⡀⠀⣠⣶⠄⣰⣾⡿⢷⣦⣤⣴⣦⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢈⣦⣦⣀⣤⣩⣶⣶⣶⣶⣿⣷⠂
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣇⠈⢹⣿⣿⣿⠇⠀⠀⠈⠁⠀⠀⠠⠊⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠈⣿⣿⣿⣿⣿⡟⠛⣰⡿⠃⢸⡿⠟⢫⡄⠀⠀⣠⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣷⣤⣿⣿⡄⠀⠁⠀⠀⠀⣠⡀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣉⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣤⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⠉⢻⣿⠟⠻⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣶⣶⣦⣀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠛⠀⠀⣨⠉⢠⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣦⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⡛⠛⠀⠲⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡠⠘