Mermaid Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠤⠀⠀⠐⠋⠀⠀⠀⣠⣿⡃⠀⠀⠘⢿⡟⠿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠙⠿⠿⣦⣤⣠⡄⠀⠀⠤⠀⠰⠟⣿⣿⠃⠀⠀⣤⠾⠁⠀⠙⣿⠿⣿⣶⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⡇⠀⠀⠀⣀⣠⣾⣿⣿⠀⠀⠀⠁⠀⠀⠀⢠⡀⠀⠀⠹⣧⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠤⠀⠀⠀⠀⠀⠠⢤⠤⢶⣿⣅⠀⢠⣤⣿⡾⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⣿⣶⠏
⠀⠀⠀⠀⠀⠀⣀⢔⣻⣤⣤⠄⢀⣀⣴⠶⠾⠿⠿⠿⠶⢿⣿⡿⠀⢀⠀⠀⢀⣿⠏⠀⠀⠀⡀⠀⠀⠀⢀⣭⣿⣿⣴⣸⣿⢣⡶
⠀⠀⠀⠀⠀⠀⢁⣾⠛⢡⡴⠾⠟⠛⠁⠀⠀⠀⡀⠀⣴⣿⣿⣀⣾⣏⠀⠴⣿⡏⠀⠀⠀⢸⣿⣤⠀⣼⣿⡋⢀⣿⠏⣿⣿⠏⠁
⠀⠀⠀⠀⠀⢀⣿⣿⣶⡿⠤⠶⣤⣤⣶⣦⡤⠀⢁⣼⠿⢸⠟⠛⠘⣿⡀⣶⡿⠀⠀⠀⠀⠈⠛⠻⠀⢿⣿⡀⢸⣿⠰⣿⡋
⠀⠀⠀⠀⠀⠸⣿⣟⠀⠀⠀⡴⠛⠛⠋⠁⠀⣀⣿⣿⣆⢠⡀⠃⢠⡈⠁⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠻⣧⡀⢀⣴⠂⠀⠀⣠⠶⣶⠟⠁⠸⡏⣿⣷⠂⣼⣿⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡙⣿⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢻⣇⣰⡿⣾⣿⣶⣏⣠⣤⡞⢙⣿⣫⠞⠋⡁⠴⠉⣴⢞⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢣⠟⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢋⣵⡾⢋⡝⢂⣴⣉⣐⣥⣴⠓⠁⢀⡼⠃⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠠⠟⢉⡜⣡⣴⣿⡿⢋⣿⣿⠉⠀⠀⣠⣴⣶⡿⠟⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢶⣀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⢳⣆⣸⣿⣾⠿⠟⠁⠶⣬⣽⠿⣤⡰⢾⠯⠉⠛⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⡟⠳⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠃⠀⢀⣾⢂⣈⣡⠴⠊⣡⠆⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢠⣿⠿⠟⠛⠁⠀⠀⠟⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⢶⡆⢠⠄⣴⠆⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠘⠓⠲⡜⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢆⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡉⢉⣤⡈⣳⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡀⠞⡣⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠁⢿⣧⣼⡿⢀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡅⣷⡀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠟⢿⣿⣇⣸⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣤⣿⣅⠀⠀⠄⠀⠀⠀⠀⠑⠄⢸⣼⡿⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣛⠃⠀⠀⠙⠿⠻⣆⠀⠀⢀⠀⠀⢀⢀⣤⠿⠏⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢣⣤⣄⠈⢶⣤⡄⠀⠘⢿⣆⠀⠀⠚⠐⠛⠻⡈⠡⠀⠀⣾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡈⠓⠈⢏⣸⣇⡀⠀⠿⣷⣴⣀⢰⣶⠐⠁⠀⢀⡞⢹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⠿⠃⠀⠀⠈⡁⣾⣿⠦⠀⠛⠉⣨⠟⢀⠟⢀⠴⠟⠀⡟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠂⡿⠂⠀⠀⢰⣿⠀⣿⡟⣠⡆⠀⠘⠁⢠⣤⠒⢁⡴⣧⡿⣀⡀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣶⠃⠀⠀⠀⣸⣿⣴⣿⣷⡿⠀⠀⠀⠀⠀⠀⠀⢪⡵⠊⠚⠛⠁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⡇⠀⠸⣇⠻⣬⣛⣿⣿⢳⡄⣖⡀⣀⣡⠤⠛⣧⠦⢀⣻⣦⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⣼⣧⠀⡄⢸⣆⣩⣿⣿⣿⣿⡿⣿⣿⠛⢁⣠⠖⢁⣰⠯⠛⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⣦⢿⣄⣿⣿⣿⣿⠟⣡⣾⣿⣿⣶⣿⣧⡴⠞⠋⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢿⣷⡿⢸⣿⣼⣿⡟⠋⣼⣯⣿⣿⠟⠛⠋⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⣾⣿⣧⣿⣿⣿⡟⠁⣾⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣿⣿⣏⢷⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣏⣻⣿⣿⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠈⠁⣀⠈⢠⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣙⢿⣷⣦⡀⣠⡄⢘⠂⣀⣶⣌⣇⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢴⣦⣽⣧⣐⣫⣤⣌⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣛⣛⣛⣛⣋⣛⣛⣃⣈⣙⣛⣟⣛⡉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣯⣬⣭⣭⣭⣭⣭⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣍⣭⣭⣉⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⢀⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢾⣱⡎⠀⣡⡿⣿⠿⠛⠃⠀⢀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠿⠟⠿⠋⠀⠳⠋⢀⡤⠐⠒⣻⣿⣍⡃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢦⡤⠤⠤⠤⣦⣐⢩⡞⢠⣆⣿⣥⣴⣾⣿⣿⣟⠉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣟⣿⣶⣶⣶⣤⣌⠁⠂⠾⠿⠿⣿⣿⣿⣿⣛⡛⠋⠉⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡈⠁⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣸⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣣⣽⣿⣿⣿⣙⣷⠀⠀⠀⢀⡄⠀⠀⢠⣷⣦⠉⢿⡿⢿⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣈⣁⣦⣽⠵⣟⠿⣯⢿⡆⠀⠈⠉⠁⠀⠀⣼⡟⠿⢹⠟⣰⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⡟⠈⠻⡗⣊⠿⢷⣶⣾⡟⠀⠀⠀⠀⠀⢰⣯⣤⡴⡟⣤⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣦⡀⠓⣆⠿⠆⢀⣿⡉⠀⠀⠀⡠⠀⢰⣿⠿⠿⠳⠿⢟⡻⠁⠈⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠸⡇⢀⣷⣿⣿⡀⠀⠀⠀⢀⣤⣿⣟⢀⣠⣶⠈⠛⠁⠁⠀⠰⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠘⣿⣻⣿⣿⠟⠀⠀⣀⣣⣤⣾⣿⣿⣿⡈⣿⡩⠀⠿⠉⠉⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡯⠁⠀⣠⣬⣿⣿⣿⣿⣿⡿⠟⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡹⢿⣿⣿⡿⢄⣉⢴⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡘⣠⣿⣿⣿⠋⢀⣹⣿⣿⣿⠰⣿⣿⣿⣿⡙⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣯⣟⣹⡟⠀⠀⠀⠀⠀⠀⠐⢂⡄⠀⠠⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣟⢩⣯⣼⠟⡿⢿⣣⣴⣶⣦⠔⢛⣯⡦⠀⠀⠀⠀⡐⢡⣾⣿⣾⣧⣔⡘⣁⢤⡀
⠀⠀⠀⢅⠀⠀⠀⠀⣠⠀⣠⣿⣿⣿⣿⠿⢫⣷⣿⣿⣿⢿⣿⣼⣿⣧⠘⢀⠀⢰⢳⡞⠋⠜⠁⠀⠀⠀⢻⡇⠁
⠀⠀⠀⠀⠙⠓⠧⡤⠤⠚⣿⢿⣿⣿⣿⢶⣽⣿⣿⣿⠇⠀⠻⠿⢿⣿⣔⣞⣇⢸⣿⠀⣴⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⣹⣿⣿⣿⣯⣿⣿⣿⣿⡀⠀⠁⠠⢈⡿⣿⣿⣿⣾⣿⣷⣷
⠀⠀⠀⠀⠀⠀⢰⠞⣵⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠄⠻⠷⠯⢛⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢘⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠣⣀⠁⠀⢀⠀⠀⠀⠘⢾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡹⠈⠀⠛⠋⢹⣿⣿⣿⣿⣿⣿⣦⡄⠀⠈⠀⢀⡀⠀⠁⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠻⣿⣿⣮⣻⣿⣿⣿⡁⠀⠀⠉⠀⢸⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⡿⢋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣤⣀⠠⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⠶⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⡿⠿⠻⠷⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠿⠀⣀⠀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣀⡹⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⡆⠀⠀⠀⡄⠀⣦⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣿⣧⣼⡆⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣹⡆⠀⠀⠸⠛⠁⠐⢼⣆⢀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡌⡐⠀⡀⠐⠻⣉⣠⠀⠀⠐⢠⣇⣻⣴⣿⣿⣷⣦⡄⡀
⠀⠀⠀⠀⠀⠄⠠⢧⡀⡠⣰⣦⣈⣻⢷⣄⠀⠀⠙⢳⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⡾⠓⣣⣃⠰⣧⠿⣾⣏⣻⢿⣿⣿⣿⣦⣄⡀⠈⠁⠀⠀⠈⠘⠻⣿⣿⣦
⠀⠀⢙⡷⠚⠛⠸⣿⣿⣏⣿⣿⣿⢿⢿⣻⠿⠯⢭⡅⠀⠲⠀⠀⠀⠀⠀⠀⠻⣿⣗
⠀⠀⠰⣆⣀⣀⣤⣷⣯⣭⣼⣷⣭⣽⣿⡿⢳⣤⣾⡗⠂⡀⠀⢀⠀⡆⠀⠀⠀⢹⣿⣆⢠
⠀⠀⠀⠀⠉⣭⣭⣿⣿⣿⣿⠿⡉⠨⣍⠀⠉⠸⠅⠀⠀⠀⠀⠈⠀⠀⢀⠁⠀⠈⠿⣿⡄⠂⠀⠀⠀⠲⣿⣷⡶⠂
⠀⠀⠀⠀⠀⠈⣽⣿⣮⣿⣇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣻⣿⣄⡀⠀⠀⠻⣿⣬⠀⠀⠀⠈⠉⠉⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠟⠷⠏⠋⠐⠀⠀⠀⠈⠛⢿⣶⣤⣄⣠⣴⣶⣶⣦⡀⠀⠀⣢⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣒⣀⣿⡿⠿⠓⢢⣴⣶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠿⠟⠉⣯⣄⣀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡁⢠⣴⣿⣿⣿⣿⠃⣤⣼⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠛⠛⠛⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣉⣿⣉⣗⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣤⠸⠉⠁⠀⠙⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠻⠁⢸⠂⠀⠀⠘⣸⠜⡄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⠀⠀⠴⢲⡋⠁⠀⠈⠉⢹⠙⠀⠤⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢀⣿⢡⠐⠀⠄⠀⣾⣁⠀⣀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡅⠈⠀⠀⠀⢉⠙⣿⠓⢪⠒⠁⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠳⡀⠀⠀⠀⠀⢙⠯⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢔⡌⠇⠀⠀⠀⠈⠤⢂⡴⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠈⠀⠇⠀⠀⠀⠀⠀⣤⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠊⠳⠀⠀⠀⠀⠀⠀⠘⠒⠒⣀⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠀⠂⠈⠣⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣂⡠⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣖⣀⠀⠠⠄⡨⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠘⠁⠈⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣟⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠛⡱⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣁⣤⡾⠃⢠⡄⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣟⣫⣭⣿⣍⠶⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⠋⠹⣶⡤⠈⠁⠀⠈⠙⠻⣿⣿⣶⣿⣿⠃⠐⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠁⠘⣤⠁⠕⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣧⣤⣶⣿⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣫⡾⠁⠀⠀⢀⡄⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⠻⣾⣿⣯⣽⣯⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠂⠀⠉⢀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⠋⠁⠈⠙⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⠄⠀⣠⣴⣶⣿⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⢿⣿⣧⠀⠀⣀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡔⣼⣿⣯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠻⣿⣦⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁⠘⢿⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⢣⡀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣤⣭⣍⠙⢷⣬⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣵⣶⢹⡇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠷⣭⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣰⣿⠋⢸⣧⣴⣾⠟⠛⢛⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡦⣤⣤⣤⣤⣶⠿⠋⠀⣠⣾⡿⠁⢀⣼⣿⠟⢁⣠⣾⣿⡿⠛⠉⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⢿⡶⣤⣤⣀⣤⣤⣴⡾⠟⢉⣠⣾⡿⠋⣡⣴⣿⣿⠟⠋⠀⣠⡤⠤⣄⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡳⠯⣭⣭⣭⣥⠴⠾⠛⠋⣁⣴⣾⡿⠟⠉⠀⠀⠀⢸⡏⢰⣤⡿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⣤⣴⣶⠾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠿⣦⣬⣴⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⢉⡵⠋⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣶⢟⠁⠸⠇⢹⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣷⣾⣿⠷⣌⠁⠠⠄⠘⠿⣿⣿⣦⣀⣸⣿⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠁⠀⠄⡹⢻⠀⠀⠀⠀⠀⠙⠻⣿⣿⣟⣀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢟⡽⠃⠀⠀⢘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣟⣛⣳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠐⠊⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣦⣿⣿⠟⠉⠛⣷⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡅⠀⣠⣤⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⡇⠀⢀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⣾⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⠻⣿⣤⡈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠹⢯⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡣⣀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⢀⠀⠀⣠⣴⢶⣥⡈⠻⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢰⢿⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠘⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⢘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⢠⣾⠟⣷⢀⣠⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣀⡀⢀⣀⣀⣴⡿⠋⢀⣴⡿⠋⢀⣿⣿⠟⢁⣠⣾⣿⠿⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣮⣍⣙⣛⣉⣁⣠⣴⡿⠛⣀⣴⡿⠟⣁⣴⣿⡿⠟⠁⣀⣄⣀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⢯⣿⣛⣛⣫⣥⡴⠾⠛⣉⣴⣾⡿⠛⠉⠀⠀⣸⡏⣤⣸⡇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣤⣤⣴⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠘⢷⣬⣭⡾⠏

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢛⣩⢿⣿⣿⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⡿⠊⠙⠛⠋⠁⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⡃⠚⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⡔⠌⠁⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠋⠀⠀⠀⣤⣾⣷⡈⠃⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢯⡀⠀⠀⠀⣤⣾⣿⣿⣿⣷⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣉⡱⠃⠘⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢸⠟⢫⡅⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⣰⠃⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣃⣠⠄⠀⠘⢧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠚⣿⡟⢺⣷⠀⢾⣿⡄⠈⠙⠻⠿⠟⠋⠉⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠛⢋⡄⢸⠿⡀⣤⣴⠂⠀⡀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣸⣟⣇⡸⣆⣹⠿⠿⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠁⠂⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣦⣤⣿⠀⠀⡈⠀⣼⠧⣤⣄⠤⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⡧⢠⡄⢰⡧⠀⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⣴⡻⢿⣿⠿⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡉⠀⢀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⠝⠁⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠁⠀⣀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡿⠟⠋⠀⠀⢀⣾⣿⣆⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡹⠤⣤⠀⣾⣿⣿⣿⣿⣦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢖⠁⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣠⠎⠀⠘⠀⠀⣿⣿⣿⣿⣿⣿⣷⡖⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⣇⡠⢀⡀⠻⡄⠘⣿⣿⣿⣿⣿⣿⢇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣌⣿⠟⢸⡇⠘⠿⠆⠈⠉⠛⠛⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡋⣵⡆⢸⠱⣼⣿⣇⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠻⠷⠎⠱⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣤⣾⡄⠁⠈⢀⡶⢤⣄⠠⠀⠀⠀⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠠⠄⠾⠄⠈⠀⠀⠀⠀⠀⣿
⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣤⣤⣶⣶⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⢳⠀⢦⣄⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣶⣿⣿⠟⠻⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⡇⠀⠀⢸⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠁⠀⢀⣾⣿⣿⠟⠛⠛⢷
⠀⠀⠀⠀⠰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣠⣴⣿⣿⣿⣧⣤⣤⣄⡸
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠉⢿⣷
⠀⠀⠀⠀⠀⢾⣦⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁⠀⠀⢤⣄⣀⣠⣿⡿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⠻⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣶⢀⡿⠉⠻⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⡄⠙⠋⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣠⣿⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⣿⣿⣿⣷⡘⢷⣄⡀⠀⢀⣿⣿⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣷⡄⠙⠿⠿⠿⠿⠛⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⣤⡶⠄⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⢿⣿⣿⣷⠀⠘⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢿⣿⣯⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⢀⢢⡄⣤⣻⣾⣿⣹⡏
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠸⠿⠿⠿⠿⠾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⠛⠙⠃⠀⠀⠀⠀⠸⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡟
⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⢺⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠸⣿⡀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⡀⠀⢀⣶
⠀⠀⠀⡡⣄⠀⢀⡤⠀⠀⠀⠀⠀⣀⣠⠈⠀⣠⣤⣼⠂⠙⠃⠀⣰⡾⠁
⠀⠠⡎⢠⣾⡶⠟⠀⠀⠀⣠⣾⣿⣿⠃⠀⢀⡼⣿⡟⠉⣷⣦⡚⠉
⠀⢀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⢿⡇⠀⢰⣾⢁⣿⣅⣀⣠⣿⡇
⠀⠈⠀⣤⣤⣤⣤⣢⣾⣿⡿⠃⢼⠁⢠⠘⣿⢸⣿⡟⠉⠀⠉⠓⠺⠦⠀⠂
⠀⠀⠀⠀⠉⠓⠚⠻⠟⣿⠇⠀⢸⡆⢸⣿⢸⠀⣿⡄⠀⠈⠳⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠇⣸⡇⠸⠿⢠⡆⣿⣿⣄⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠀⣿⣿⡎⠀⢸⡇⣿⣿⢿⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⡿⠋⠀⠀⢸⣇⣿⠋⢘⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⠀⠀⠀⠀⢃⣼⠏⠀⣾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⣍⣠⡾⠟⣵⠀⠲⡘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⠀⠀⠀⢸⣧⣀⡛⠠⣶⡀⠀⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠈⣿⡆⠀⢸⡏⢈⣿⣧⣤⣏⢀⡛⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠉⢿⡿⢁⣿⠇⠀⠈⢻⣿⢷⣴⣟⠉⣿⠃⢠⡦⢶
⠀⠀⠀⠀⠀⠀⠆⣠⣾⣿⣿⣰⣧⠐⡞⢁⣾⡿⠀⠀⠀⠀⠙⣿⣯⣉⣿⠟⢠⣶⢀⣴⡇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⡾⢁⣴⡄⣀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⡃⣀⠚
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣋⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⡇⠀⠘⣿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣮⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣶⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠉⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣏⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⠀⡆⠙⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡘⣦⠘⢿⣿⣳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣌⢳⣄⠈⠻⣿⣯⣟⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⣿⣿⣿⣿⣧⡙⢷⣄⠹⣿⣿⣷⣦⡉⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⣿⣿⣿⣿⣿⣿⣷⡌⢻⣧⡘⣿⣿⣿⣿⣶⣄⡉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣽⣿⣿⣷⠈⠙⢿⣦⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⣿⣿⡿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣷⡄⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣴⣿⡿⠛⠁⢠⣿⠇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿⢹⣿⡄⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢋⡠⠞⡛⢋⣸⠇⠀⠀⢸⣿⠀⠀⠘⣿⣿⣿⣿⣿⠁⢿⣿⣿⣿⡟⠀⠀⣸⡏⢨⣿⣿
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⡠⠔⠃⢀⡞⢀⡎⣿⠀⠀⠀⢸⣿⠀⠀⠀⢻⣿⣿⣿⣿⠀⢸⣿⣿⣿⠃⠀⢠⡿⠁⣼⣿⡟
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⢠⠏⠀⢸⡇⣼⠀⠀⠀⢸⣿⠀⠀⣾⠀⣿⡿⡟⣿⠀⢸⣿⢿⡟⠀⠀⣼⠃⣸⣿⡿⠁⠀⣠
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢰⠏⠀⠀⣼⠀⣼⠀⠀⢀⣾⡟⠀⠀⢻⠀⣿⠧⡧⣾⠟⠛⠁⣞⠁⢀⡾⠁⢠⡿⠋⠀⢀⡴⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⠏⠀⠀⢀⡿⠀⠘⡄⠀⣼⣟⢀⠀⠀⠸⣼⠃⠀⠀⠀⠀⠀⠀⠉⡶⠋⠁⢠⡏⠀⢀⡴⠋
⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢀⡿⠀⠀⢀⣾⠃⣠⠞⢷⣴⣿⡟⠈⠙⢤⣀⡿⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊⣀⡴⠋
⠀⢀⡄⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣸⡇⡀⣠⣾⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡾⠋
⠀⠘⠃⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠛⠟⠁⠘⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣴⣿⠏
⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⣿⡿⠁
⠆⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⡟
⠠⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⠁
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠷⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠋⠠⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣀⡢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷
⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⡀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⡾⢂⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⢀⠀⠀⣘⢤⣄⠀⠐⢾⣾⣿⣿⣶⣤⡀
⠀⢀⡴⣂⡈⣇⣶⣟⣿⣿⣷⣤⣀⠙⠋⠉⠉⠻⣷⣦
⠀⠈⠛⠉⢙⣿⡿⣿⢿⣿⣿⠙⣷⡀⠀⠀⢀⠀⠈⢻⣇
⠀⠀⠙⢚⣿⣿⣿⡿⠋⢟⠑⠻⠏⠀⠀⠐⠈⢀⠀⠘⢿⡄⠀⠀⠠⣶⣦⠄
⠀⠀⠀⠀⠿⠷⠿⠄⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠦⠀⠈⠻⣦⣀⠀⠀⣉⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣯⣠⡾⠿⠧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠉⣹⣦⣤⡀⢀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠋⠁⠛⠛⣵⠆

⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢠⢄⠀⣀⣀⣷⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣫⣼⡅⢀⡴⡿⠟⠋⠉⢀⣠⣴⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⢋⡁⣀⠉⢀⣴⠂⠉⣹⣿⣶⣬⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣖⣂⠈⠙⠳⢤⡲⠇⣾⣼⣷⣶⣿⣿⣿⣿⣄⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⢿⣿⣿⣿⣿⣿⣦⠀⠁⠋⠙⠛⢿⣿⣿⣷⣯⣉⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢇⠀⡼⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⡛⠿⢿⣿⣾⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠆⠐⢾⢟⣿⣿⡾⣿⠀⠀⠠⠴⠀⠀⠀⣿⣿⣦⣽⠟⣽⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠒⢾⣟⣩⣷⣍⣓⣹⣇⠀⠀⠀⠀⠀⣸⠟⠈⣴⡇⡜⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⢈⠀⢬⡑⢶⡄⠙⣿⠟⠁⠀⠀⠀⠀⣠⣿⣿⣟⣵⣿⢷⠔⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢠⡗⠀⣬⣶⣿⠂⠀⠀⠀⠁⣰⣿⡏⠉⣁⠭⠶⠋⠀⠀⢀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⢶⢷⣴⣿⣿⠛⠂⠠⢄⣀⣾⣿⣿⡇⣿⡽⠁⣴⠖⠒⠀⠨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣼⣿⣿⣟⠂⠀⣀⣛⣿⣿⣿⣿⣿⣷⡾⠧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠺⡿⣿⣿⣿⣁⠒⣠⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢏⣼⣿⣿⠗⠈⢻⣾⣿⣿⢹⣿⣿⣿⡟⠧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢃⣼⣟⣿⣿⣿⣾⣽⣟⣻⠏⠀⠀⠀⠀⠀⠀⠄⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣽⡾⣿⢿⣫⣤⣴⣭⠝⢻⣽⠄⠀⠀⠀⢀⠂⣴⣿⣶⣦⣤⡜⠁⣄
⠀⠀⠈⢀⠀⠀⠀⢀⡀⢀⣾⣿⣿⣿⡾⢛⣷⣿⣿⣿⣿⣶⣿⣿⡄⠂⡀⠀⡞⡾⠋⠐⠉⠀⠉⠀⢿⡈⠁
⠀⠀⠀⠈⠛⠺⠦⠤⠔⣻⣿⣿⣿⣿⡶⣼⣿⣿⣿⠃⢈⠿⠿⣿⣧⣲⣳⡀⣿⡁⣴⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢹⣿⣿⣿⣷⣿⣿⣿⣿⡀⠀⠀⠠⢙⠿⣿⣿⣷⣿⣷⣿
⠀⠀⠀⠀⠀⠀⡼⠩⡦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠈⠛⠻⠙⠟⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡿⣛⣿⣿⣿⣿⣿⣿⣿⡟⠲⠌⠀⡀⠀⠀⠀⠈⢲⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣣⠃⠁⠈⠉⠩⣿⣿⣿⢿⣿⣿⣶⣀⠀⠀⢀⡠⠀⠀⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠘⢿⣿⣧⣿⣿⣿⣷⣄⠀⠀⠀⢀⣷⣾⣿⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⡿⢃⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠀⠀⠀⠀⠀⠀⠉⠙⢿⡿⡛⠛⠛⠛⠿⣿⢛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠀⠠⠀⠀⠐⠈⠀⢀⣴⠀⠀⠺⡿⢿⣿⣷⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⢦⣦⠀⠀⠀⠚⣻⣿⠀⠀⠶⠃⠀⠹⠟⠿⡾⢦
⠀⠀⠀⠀⠀⠀⣰⠀⢀⡀⠀⠀⠀⢀⣀⣡⡟⠀⣀⣰⣾⣿⠏⠀⠀⠀⠀⢀⣶⣄⠀⢹⣄⠇
⠀⠀⠀⠀⣀⢔⣧⠤⢀⣀⡤⠶⠶⠶⠶⣾⡿⢂⡉⠉⣠⡟⠀⠀⣀⠀⠀⣠⣽⣿⣤⣿⣫⡆
⠀⠀⠀⠀⣠⣟⣡⢚⣋⠉⣀⡀⠀⢀⣴⢿⣧⢾⡇⢘⣿⠀⠀⠀⢿⡆⢸⣿⠁⣾⢩⡿⠃
⠀⠀⠀⠀⣿⡟⠉⢉⡽⠿⠛⠉⢀⣾⣇⢉⠀⢀⠑⠘⡇⠀⠀⠀⠀⠀⠈⠻⠶⢿⣾⣷
⠀⠀⠀⠀⠙⢧⢀⡜⢀⢀⣤⣲⠏⠀⣏⣿⣆⣼⠇⣨⠁⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⡄⡄
⠀⠀⠀⠀⠀⠈⠉⢷⡟⠹⣿⡿⠾⢛⠐⢻⣋⡅⠊⣡⠏⣶⣆⠀⠀⠀⠀⠀⠀⠀⢹⡿⠙⠡⠺
⠀⠀⠀⠀⠀⠀⣠⣿⡄⠾⣩⣒⣴⡿⢟⣿⡏⠀⢀⣥⣴⠟⢻⣧⠀⠀⠀⠀⠀⠀⢿⠰⣄⠀⠂⠠
⠀⠀⠀⠀⠀⠈⠁⠀⠻⣼⣿⠏⠋⡐⠲⠞⡳⠞⠛⠀⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠑⠏⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣼⠷⠖⠊⠁⠞⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠋⠲⣂⠤⢔⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠉⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠀⠀⠀⠀⠀⠀⠈⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠎⣴⢢⣗⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡎⣄⠀⠀⠀⠀⠚⢄⠠⠿⣿⣇⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢥⣿⡄⠀⠀⠀⠀⠈⠀⣦⡟⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠑⢄⢀⠈⢡⣝⠀⠀⠄⠤⡄⢂⠉⢠⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠑⠘⢋⣦⡀⠹⣧⣄⣠⡆⠊⠀⣰⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⢸⠋⠀⢀⡄⢼⡟⢀⠉⠠⠋⠘⡡⢚⣣⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡎⠀⠀⢸⣇⣿⣷⡏⠀⠀⠈⠉⢠⡫⠛⠶⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡇⠀⠳⠸⣼⣿⣟⣶⣢⣠⡤⠆⠳⠆⣈⣷⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣠⡄⣷⣾⣿⡿⣻⣿⣯⣤⡎⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⡇⣿⣽⣿⠋⣼⣿⡿⠟⠛⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⣾⣹⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡟⣿⣷⣿⣿⠟⠁⠀⠀⠀⠠⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡀⠀⠀⠀⡠⠈⢠⡈⢄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠝⣻⣢⡖⠢⣁⠸⡗⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⠻⠿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⢛⣛⣻⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣤⣤⣶⣶⣶⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⢳⠀⢦⣄⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣶⣿⣿⠟⠻⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⡇⠀⠀⢸⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⠁⠀⢀⣾⣿⣿⠟⠛⠛⢷
⠀⠀⠀⠀⠰⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣠⣴⣿⣿⣿⣧⣤⣤⣄⡸
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠉⢿⣷
⠀⠀⠀⠀⠀⢾⣦⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁⠀⠀⢤⣄⣀⣠⣿⡿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⠻⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢰⣶⢀⡿⠉⠻⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⡄⠙⠋⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣠⣿⣿⣿⣿⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠻⣿⣿⣿⣷⡘⢷⣄⡀⠀⢀⣿⣿⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣷⡄⠙⠿⠿⠿⠿⠛⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⣤⡶⠄⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⢿⣿⣿⣷⠀⠘⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⢿⣿⣯⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⢀⢢⡄⣤⣻⣾⣿⣹⡏
⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠸⠿⠿⠿⠿⠾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⣿⠛⠙⠃⠀⠀⠀⠀⠸⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⡟
⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⢺⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠸⣿⡀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠈⠄⠀⠀⡞⡀⠄⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠠⣀⡠⠀⠀⠀⠀⠀⢀⠞⠉⠀⢀⠠⠄⠒⠠⣴⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠄⣰⠏⢀⡔⠉⠀⠀⡀⠔⠁⠀⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠔⠁⢀⣪⣾⢏⣴⡟⠀⠀⠀⠈⠀⢠⢆⠖⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⢀⠄⢀⡼⢋⠊⢸⡿⢁⠁⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⢀⢎⣴⠏⠀⠀⠀⠸⠁⠘⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠠⠄⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡇⣾⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⠀⠳⣄⠀⠀⠀⠀⠀⠀⢸⡇⢱⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⠏⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣶⣴⣽⣶⣦⣀⠀⠀⠈⢃⠀⢾⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢡⠀⠀⢸⡁⠄⠀⠀⠀⠀⢀⠀⠀⠠⢀⣠⣤⣾⠟⠋⢁⣴⠉⠙⠫⡉⠋⠐⠦⣀⠳⣌⢐⢂
⠀⠀⠀⢠⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢃⠐⢄⠀⠀⠄⠠⠙⠷⠒⠫⠋⠠⠋⠀⢠⠊⡵⠑⡀⠀⢱⡤⡄⠀⠀⠱⡈⠚⡏⢱⠀⢀⡀
⠀⠀⠀⢸⠈⡆⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠉⢄⠈⠀⠀⠀⠀⠄⠈⠀⠀⠁⠀⠀⠋⠀⠇⠀⠃⡀⠀⢠⡈⠀⠀⠀⠱⣀⠁⠘⡎⠀⠁
⠀⠀⠀⣧⣄⠹⢀⠀⠠⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠢⣤⣀⡀⢀⣠⡄⠀⠀⠀⢀⠀⠀⠤⠀⡰⠀⠀⠁⢀⠞⠁⠇⡤⣼⡆⢀⠁⡀⣿
⠀⠀⠀⣇⢘⠄⣏⠄⢀⡆⢀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠁⠒⠀⢀⠀⡀⠀⠀⠀⠀⢀⣼⠀⠀⠁⠀⢿⢀⡅⡼⠁⠂⠁⠐⣇⠀⡷⢨⣀⠉⢸
⠀⠀⠀⣿⠈⢠⠻⠈⠀⠀⠀⠂⡀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠦⡔⠈⠀⠀⠀⠀⠀⠸⣸⠏⠀⠀⠀⠀⠀⢸⠀⠁⢸⠇⢀⣼
⠀⠀⠀⢿⡄⣸⢀⡖⠈⠀⢠⠈⠁⡀⠀⠀⠀⠀⠀⠀⠐⠒⠄⡻⡄⠀⠠⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⡟⠄⠁⠀⡀⢂⠐⠀⡇⠀⠸⠀⢸⡏
⠀⠀⠀⠸⣟⣯⠀⠁⠀⣇⡨⣬⣁⠸⠀⡄⠀⠀⠀⠀⢀⣠⣽⣧⣽⡖⠿⣆⢀⡰⠀⠀⠘⠀⠀⠀⠄⡀⠀⠅⠐⡈⠁⠠⢀⢀⠄⣱⠀⠀⡆⣸⠇
⠀⠀⠀⠀⢻⢳⠀⢀⡼⠋⡰⣿⠝⠀⣆⠁⢠⠀⠀⠈⡟⠼⡟⠁⠀⠀⠀⠀⢹⣷⠞⠀⠚⠀⠀⠀⠀⠁⢄⣦⣿⡎⠐⠀⠀⠀⣰⡟⣇⠀⣧⡟
⠀⠀⠀⠀⠈⢿⢇⡿⠀⡼⢸⢃⠀⠄⡇⠜⠈⠀⣄⡈⡧⠀⠀⢠⠀⠀⠀⠀⢀⢏⡔⠀⠊⠀⠘⠀⢀⠓⢾⣧⠾⣝⡳⡥⢂⡔⠁⠀⢻⡆⡿⠁
⠀⠀⠀⠀⠀⠈⢿⡇⠀⡇⠘⠀⠉⠀⠛⠁⢀⠞⢉⢰⠃⢀⡀⠈⠄⠀⠤⠀⠀⠀⠀⠀⠀⠐⠉⠹⠦⡙⢦⡿⣿⣯⣿⣠⠏⠀⠀⠀⣸⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠣⠀⠘⠄⠀⠀⠀⠀⠂⠁⡠⠃⠃⡠⠜⠐⠂⠂⠌⠃⠈⠂⡀⠀⠀⠀⠀⠀⠆⠰⠋⠈⠀⢈⣙⡋⢠⢤⡀⡀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⢢⠀⢀⣀⠀⠈⠀⡐⡔⠀⠀⢀⠀⣀⢀⡘⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡜⣼⠀⢱⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠁⠒⠉⠉⠁⠀⣠⠞⠈⢀⢀⢤⠀⠲⢁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠈⣧⢰⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⡄⠀⢀⣴⠃⢣⡈⢷⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠁⠀⢈⢂⣸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢚⠙⢥⠉⣁⠶⠊⠷⠀⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠘⠒⠾⠮⢤⣀⣀⣀⠀⢀⣀⣀⣀⡠⠤⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠂⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠁⢈⠀⠀⠀⢀⡶
⠀⠀⢀⠱⣄⢀⣠⠄⠀⠀⠀⠀⣀⣠⠄⠁⢀⣴⣼⣃⡉⠃⢀⣤⡿
⠀⠐⠇⠰⣿⠾⠁⠀⠀⢀⣶⣿⣿⡏⠀⠀⣤⣿⡟⠉⠹⣷⡞⠁⠂
⠀⢀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⣟⠀⠀⣿⠃⣿⣧⣤⠴⣿⡗⢀
⠀⠀⠀⠶⣶⠶⣮⣷⣿⣿⠋⠐⡇⠠⣆⡻⡆⣿⡟⠁⢀⡀⠉⠙⠳⠀⠁
⠀⠀⠀⠀⠀⠉⠉⠙⢹⡿⢀⠀⣿⠀⣿⡇⡇⣿⣧⡀⠀⠉⠛⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡘⢠⣿⣀⠛⠀⣿⢻⣿⣧⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⢸⣿⠟⠀⠀⣿⢻⣿⠋⡧⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠼⠁⠀⠀⢀⢿⣿⠃⢠⣷⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢈⣾⡇⠀⠿⠋⣁⣤⢄⠀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠐⢸⣟⠁⣾⠀⣘⠂⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⣿⡁⠀⢠⣤⠛⣶⣆⢈⡿⠀⣤⢈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⢿⣿⡇⢸⡏⠀⠀⢷⣴⣟⣉⣿⠷⣴⡆⢀⡉⡄
⠀⠀⠀⠀⠀⠀⡀⢠⣾⣿⡟⣻⠁⣨⠟⢠⣿⠇⠀⠀⠈⢻⣼⡟⠷⣶⡏⢀⣘⠉⣩
⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣿⠇⣸⣴⡿⠋⠀⠀⠀⠀⠀⠙⠻⣿⣯⣤⣿⠋⣈⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣴⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣇⣸⠋⠁⡗
⠀⠀⠀⠀⠀⠀⠌⢻⣿⣇⠹⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡾⢣⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠹⣿⡀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣝⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢶⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠉⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣇⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⡐⣆⠈⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣷⡜⣦⡈⠻⣯⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣎⠻⣦⡈⢻⣿⣾⣍⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣸⣿⣿⣿⣿⣷⡈⢷⣄⠹⣿⣿⣿⣦⣈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣰⣿⣿⣿⣿⣿⣿⣿⡄⣿⣧⣹⣿⣿⣿⠛⢷⣤⡉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⣾⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡆⠀⠙⣿⣦⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⣾⣿⠟⠛⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢿⣷⡀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢉⣴⡾⠻⡿⠀⠀⢸⣿⠀⠀⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⠇⠀⢠⣿⠀⣿⣷⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢊⡤⠂⢡⠜⡐⣿⠁⠀⠀⢸⣿⠀⠀⠈⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⠀⠀⣸⡇⢰⣿⣿⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠖⠉⠀⣠⠃⠀⡿⢸⠀⠀⠀⢸⣿⠀⠀⣤⢸⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⢀⡿⠀⣾⣿⠏
⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⣴⠃⠀⢀⠇⢸⠀⠀⠀⣼⡟⠀⠀⣿⢸⣿⣙⡀⣿⣤⡿⢣⠟⠀⢠⡾⠁⣼⡿⠋⠀⢀⠞
⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣰⠃⠀⠀⣾⠀⠸⠀⠀⣰⡿⠁⠀⠀⢿⣸⠏⠉⠉⠉⠀⠀⠘⢢⣤⠟⠀⣸⠋⠀⢀⡴⠋
⠀⠀⠃⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢰⡇⠀⠀⢰⡏⢀⡠⣧⣠⣿⡷⠒⠦⡀⢸⡧⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠠⠃⣀⡴⠋
⠀⠀⡀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣿⠀⠀⣴⡟⠀⠊⠀⠈⠉⠉⠁⠀⠀⠙⠿⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⢀⣠⡾⠋
⠀⠸⠃⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⠿⠟⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣴⡿⠋
⡄⠀⠆⠀⠀⠤⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣰⣿⠏
⡄⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⠏
⠠⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⡏
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⣡⡿⠼⣗⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡶⢚⠀⠀⠀⡙⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠀⣼⡁⠀⢀⣨⣗⡰⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⢀⠘⣹⠅⠀⠀⠀⠀⣣⠀⠐⠂⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠟⢰⠈⠀⠁⠸⢯⣆⡀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢆⠀⠀⠀⠀⠐⢼⡇⠁⠫⠀⠀⠀⠌⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠶⣄⢈⠢⡀⠀⠀⠀⠚⢁⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠱⠁⡆⠀⠀⠠⠀⠁⠚⠁⠈
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢆⠀⠀⠀⠀⠀⠘⢇⣌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀⠄⠡⢄⣀⡀⠠⠁⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⠁⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠰⠕⠀⠉⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠋⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⠀⠀⢠⠃⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠈⠀⡀⠤⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⢀⡴⢁⡴⠀⠀⠀⠄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⣀⡼⢻⣧⠿⠁⠀⠀⠀⣠⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢂⡴⠁⠀⢸⠃⠆⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠰⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⡶⠶⣵⣶⣄⡀⠀⠡⡀⡏⠐
⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠂⠀⠸⠀⠀⠀⠀⠀⢤⣄⡰⠶⢞⠟⠁⡠⠏⠀⠉⢄⠀⠉⠂⠙⠦⣥⠄
⠀⠀⢰⠑⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠇⠰⠀⠈⢉⠂⠀⠈⢀⠋⢸
⠀⠀⢰⢄⠳⡀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⢠⠤⠀⠀⠀⡀⠀⠄⢠⠀⠀⠁⠴⠂⢠⠤⡇⢀⠀⣸
⠀⠀⢸⠸⢠⡔⠠⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠁⠀⠀⠄⠀⠀⠀⠰⠃⠀⠀⠘⠀⣦⠋⠀⠀⠨⠄⠸⢰⡄⢸
⠀⠀⢸⡁⡄⢁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢣⠀⢺⠀⣾
⠀⠀⠘⣷⡇⠈⠀⣆⣡⣂⠁⢀⠀⠀⠀⠀⣀⣺⣤⡦⠶⣄⣀⠄⠀⠑⠀⠀⠀⠀⠀⠠⡐⠈⠈⠀⢈⡀⠀⠀⡟
⠀⠀⠀⢻⣇⢀⡴⢋⠾⠟⠀⡄⠠⠀⠀⢸⠙⠏⠀⠀⠀⠀⢻⠞⠀⠀⢀⡀⢀⠐⣴⢷⣄⢀⠀⢀⠾⢣⠀⣿⠁
⠀⠀⠀⠀⢿⣾⠀⡇⠟⠤⠀⡆⠀⢠⠖⣺⢀⠀⠀⠀⠀⠀⠘⠚⠀⠀⠠⢤⡰⣍⢻⣯⣾⡕⡡⠃⠀⢸⢳⠃
⠀⠀⠀⠀⠀⠻⠀⠡⠀⠀⠀⠀⠐⠁⠂⠁⣸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠌⢡⠚⠋⠙⠿⢋⣁⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⢢⡀⠀⢄⣀⡀⠀⠁⢀⠌⠀⠀⢀⡀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢩⢸⠀⣱⠞⠁
⠀⠀⠀⠀⠀⠀⠈⢃⡀⠈⠁⠀⠠⠊⡀⠀⣔⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⡁⢸⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢧⡔⠚⣠⢵⡘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠁⠈⠀⠒⠴⠮⣅⣀⡀⠀⠀⣀⣀⡀⠤⠄⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠂⢿⠿⠋⠛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡴⣧⠈⠶⠀⠰⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣦⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⣤⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣤⣦⣀⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣧⣀⠀⠀⢀⣴⡿⡿⣯⣿⣿⣽⠉⠎⢩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣷⣯⣿⣟⣿⣷⣶⣿⠺⡟⣰⣿⡿⢶⣻⣷⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣙⢧⣿⣿⣿⣿⡻⣿⣾⣻⣿⣿⣿⣿⣟⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣹⣿⣽⣿⣿⣭⣿⣟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⠿⢯⣿⣿⢻⣭⣷⣯⣿⣷⣞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠾⠿⠛⠛⠁⣿⣿⠿⣻⣿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣛⣿⣞⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣯⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣻⣦⣤⣤⣤⣴⣶⣶⡶⣤⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣼⡷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⣿⣷⣿⣿⣷⣦⣾⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣿⣿⣵⣶⣤⣴⣿⣿⡿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠛⠿⣿⣶⣖⣒⢺⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣺⢿⣿⡯⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣫⣷⠿⠛⠛⠉
⠀⠀⠀⠀⠀⣀⣰⣾⣿⣯⠟⠁⠀⠀⠁⠰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣷⣶⠶⣄
⠀⠀⠀⠀⢞⣿⣿⣿⡿⠋⠶⠀⠀⢴⡄⡆⠀⠀⠀⠉⠹⣷⠀⠰⠚⣦⣰⣿⡿⣹⡿⣱⠋⠀⠀⠈
⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⠀⠀⢀⣀⣻⡑⠶⠞⣰⣶⣾⣿⣤⣤⣶⣿⣿⢟⣵⠟⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⣿⣿⢻⡿⠿⠟⠀⠘⠛⠛⣿⣝⣂⣈⣽⣿⣿⣿⣿⣿⣿⣿⣶⣿⡵⠚⠀⢠⡀⠀⠀⣰⢯⢆⡞⣹⠋
⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⣀⡀⠀⠀⣼⣿⣽⣿⠿⢿⣿⣿⣻⣿⣿⣿⣯⣭⣤⣀⣠⡼⠃⠀⢰⣏⡏⣼⣰⡷⠖⠒⣒⣢⠤⣄
⠀⠀⠀⠀⠀⠀⠈⡤⠽⣞⣷⡶⠀⠀⣿⠿⠿⢽⡻⣶⣮⣽⣿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⣾⣸⣼⣷⣿⣶⣿⡿⠿⠿⠿⠿⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠪⣟⣛⣿⣿⣿⣥⠀⠀⠙⠀⠀⠀⠀⡠⠋⣨⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣀⠀⠀⠈⠛⢧⣀⠀⠀⠀⢀⣼⣷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢉⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡉⢀⡟⠡⣀⠀⢀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣍⡇⠈⠉⠀⠈⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⡄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⠀⠾⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⣄⡀⠀⠀⠀⢀⣄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⣀⣤⣴⢶⣆⣤⡀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⡺⣇⣀⠀⠀⣀⣴⣿⡿⢿⣽⣿⣦⡍⠰⠉⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣷⣿⣿⣟⣿⣷⡶⣿⠻⡿⣠⣿⣿⠷⣿⣿⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⡻⢦⣿⣿⣿⣿⣻⣿⣿⣣⣿⣿⣿⣿⣿⣻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣹⣿⣭⣿⣽⣏⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣽⣽⠿⢿⣿⣿⢻⣯⣷⣿⣽⣿⣶⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡾⠾⠿⠋⣼⣟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⢿⣯⢷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣦⣀⠀⠀⣀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣽⣿⣿⣦⡀⠀⠀⠀⢠⣯⣿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣫⣿⣿⣄⣀⣠⣾⣷⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣀⡀⠀⠀⣼⣿⣯⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⣿⣷⣿⣿⣿⠿⣛⡿⢟⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠛⠿⠿⣭⣭⣽⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣨⡷
⠀⠀⠀⠀⠀⠀⠀⢠⢞⡽⣿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣷⠿⠋⠉⠉
⠀⠀⠀⠀⣠⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠶⠂⠀⢀⣀⡀⠀⠀⠀⠀⠀⣼⣿⣾⣿⢿⡿⠿⠶⡀
⠀⠀⠀⠀⣫⣿⣿⣿⠋⠘⠃⠀⠐⢆⡆⠀⢀⠀⠀⢘⣿⠀⠘⠙⣷⣾⣿⢏⣾⢣⠏
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⣀⣤⣽⣯⠛⠛⡼⣿⣿⢿⣶⣶⣿⣿⢟⣫⠾⡳⠋⠀⠀⠀⠀⢀⠀⢀⡀⣴⠖
⠀⠀⠀⠀⡇⣿⣿⠋⠉⠁⠀⠉⠉⢹⣷⣭⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠷⠋⠁⠀⣦⠀⠀⣰⢯⢏⡞⡸⠃⣀⣀
⠀⠀⠀⠀⠀⠘⠿⠠⣄⣠⢆⡀⠀⢸⣿⣿⣯⣭⣛⠿⣿⣿⣿⣿⣿⣶⠒⠲⠶⠖⠋⠀⢀⡟⡞⣼⣰⣟⣉⡭⠭⠭⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠘⢛⠯⠻⣿⠇⠀⠘⠋⠉⠑⢮⡻⣿⣿⣿⣿⣿⠟⠛⠛⡆⠀⠀⠀⠀⢸⠻⢿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠛⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠓⠛⠛⠛⠿⣷⡀⠀⠁⠀⠀⠀⣴⣀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⡄⠀⠀⠈⠛⠒⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⣀⣠⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⢠⡶⠿⠿⠛⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⠀⢠⣬⡟⠀⠀⠀⠀⣈⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⣟⣿⣴⣶⡄⠀⢼⠿⠷⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⡏⠁⠀⠁⠤⠤⠀⠀⢀⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢣⣾⣿⡀⠀⠀⢴⣶⣦⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃⣼⡏⢹⢷⡀⠀⠈⠉⠁⢀⣴⣿⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠰⡶⠛
⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⡾⠿⠂⢰⣅⣾⣶⣿⣷⣦⣣⡽⠿⢶⡶⠖⠊⠙⢿⠐⠁
⠀⠀⠀⠀⣠⡶⣯⠖⠛⠀⢠⡤⠂⠈⣿⣿⠛⡿⠛⠃⠋⢀⡿⣶⣶⣾⣭⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⢾⠙⠉⢀⣠⠶⠛⠳⠖⠠⢦⡽⣿⡀⠀⠀⠀⣀⠈⢁⠁⠈⣾⣏⠙⠛⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡜
⠀⠀⠀⠈⠳⠶⠋⢀⠔⠀⠀⠘⣄⠀⠙⢛⣷⠖⠶⡞⠅⣱⣾⣭⣼⣿⣿⣶⣤⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠘⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠏⠀⣰⠏⠁⠀⠀⠈⠀⣻⡘⠉⠉⢿⣟⠏⠉⠙⠿⣇⡀⠀⢤⡀⠀⠀⠀⠀⠆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠋⠀⢀⠆⣻⠀⢀⡒⠲⣢⣤⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠙⠣⡀⠀⠸
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠋⠀⠙⣿⣛⣿⡿⣿⣵⣾⣿⡻⣆⠀⠀⠀⠀⠀⠀⠀⣰⣻⠟⠲⣦⣹
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠛⠀⠀⠀⠀⣿⣯⣷⣾⣿⣿⣿⡜⣿⡈⣧⡀⠀⠀⠀⢀⣾⣵⢃⣾⢳⠙⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⣻⢤⠀⡨⡍⢙⣻⡇⠈⢿⣬⣿⣦⣤⣴⣿⣯⣵⡿⣿⢻⡿⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠉⣿⡇⠈⠃⠀⢹⡇⠀⢈⡟⣿⢧⡉⣉⢹⣿⠁⢀⣻⣾⠁⠀⠀⡇
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⡇⠀⢀⡀⠘⢀⢠⡾⣼⠏⠈⠓⣿⣷⣿⣠⠎⣿⡼⠀⠀⠆⠁
⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢰⣬⣄⠀⠀⠀⣼⣇⡴⠋⠀⠀⠸⣟⣱⠟⠠⠆⢰⣿⡟⡏⠁⠸⠉⠀⠀⣴
⠐⠀⠀⠀⠀⣀⠀⣀⣤⠰⣿⣄⠙⢳⡄⢀⡿⠋⠀⠀⠀⠀⢀⣏⣠⢦⡑⢸⢧⣿⡟⠁⢀⠃⠀⠀⠀⡏⢰
⠀⠀⠀⣰⣾⣷⣿⣿⣊⣿⣿⣽⠖⣰⡷⠋⠀⠀⠀⢀⣤⠶⣯⣦⣴⣄⣰⢟⣾⣯⢠⠄⢸⢸⠀⠀⢸⠇⡾
⠀⢀⡼⢫⣿⡛⠻⡿⠿⠍⠁⠀⠐⡏⠁⠀⠀⢠⣶⣿⣤⣄⡠⠄⡉⠙⠻⣿⣿⣟⠀⠀⠸⢸⡀⠀⡟⢀⡇
⠀⠸⠷⠋⠀⠀⠀⠀⢀⣰⡗⢠⣠⡧⠀⠀⢠⠞⠁⣾⡈⣹⡿⣦⡄⠢⡄⠸⣿⣯⠀⠀⢠⢸⡇⣾⢿⣿
⠀⠀⠀⠀⠀⣤⣤⡀⢠⣏⣱⣼⣿⠃⠀⢠⠃⠐⢀⣿⠋⠻⡖⢸⣿⣷⣤⡀⣽⡧⠀⠀⣾⢸⡟⣿⣾⡏
⠀⠀⠀⠀⢰⣟⠉⢻⣤⠶⣷⡆⣿⠀⢀⡎⠀⠀⣾⡏⢣⢂⣠⣿⠳⠈⢿⠿⣿⠁⢀⠐⣼⢻⣷⡿⢾⡇
⠀⠀⠀⠀⡆⠉⠀⣻⢀⠀⣿⣧⣟⠀⣸⠀⠀⡆⣿⣰⡆⣼⣿⣇⠢⠀⣸⡇⢻⣷⣀⣼⡏⣿⣿⡁⢨⠃
⠀⠀⠀⠀⡇⠀⠀⠘⣿⢦⣿⠈⠿⠀⣿⠀⠀⠀⢿⣿⢸⣿⣿⡟⢀⠀⣿⡷⢀⣿⣿⣇⣿⣽⣿⡀⣾⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠆⠀⠀⠈⢹⠠⡿⠀⠀⠀⢸⡇⠀⠄⢾⢻⡘⣿⡿⠁⣸⢶⣿⠀⡄⣿⣹⣿⣿⣿⢛⡿⢿⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠻⢸⡿⣽⠃⢀⣿⣿⠿⠄⢡⣿⡝⣿⣿⣏⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢣⡿⢡⡇⠀⣸⣿⣿⡀⠀⠏⣾⡀⣸⣿⣽⢿⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⠟⠁⡸⠁⢀⣿⣟⣿⠃⢸⠀⣿⠀⣿⣹⣿⣿⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⣴⠃⢰⣾⡏⡾⡙⠀⣾⣰⡿⠀⣿⣿⣿⡿⣷⡞⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁⠀⠀⢠⡾⠃⢠⣿⢻⣿⣴⠁⠀⢹⣟⠃⠀⣿⡟⣼⡇⠹⣷⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⣠⣠⢤⡾⡟⠁⢀⣼⢇⣼⣿⠃⠀⢀⣸⠙⠀⣼⣟⣷⣿⢸⠀⢿⣷
⠀⠀⠀⠀⢀⡤⣾⣟⠁⣀⣤⠶⠛⢋⣤⢞⡝⠀⣠⣼⣿⣾⡿⠃⠀⠀⡼⢡⠇⢠⣿⣿⣿⡿⠀⠖⠀⢿⡇
⠀⠀⠀⠀⠈⠓⢈⡿⠿⢯⣄⣠⣴⣋⣁⣮⣤⣾⣿⣿⣿⡿⠁⠀⠀⣸⣧⡏⢀⣿⣿⣿⣿⠛⠷⣦⣅⡘⣿⡆
⠀⠀⠀⠀⠀⠐⠁⠐⠒⠒⠛⠛⣿⣵⣿⣷⠟⢫⣝⣷⡿⠁⠀⠀⣰⠟⡎⠀⣾⡿⣹⣿⡁⠂⢉⣡⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢛⢿⡯⢾⡟⠀⠀⠰⢾⡏⠰⢃⣾⠟⣸⠟⠈⣿⣄⠀⣼⠃⠀⠈⢻⣧

⠀⠀⠀⠀⣠⡶⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⢀⣾⡋⠀⠀⠀⢙⣷⡄⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⢸⣿⡋⠉⠉⠉⠛⣿⡇⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⢿⣷⡀
⠀⠀⣼⣿⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢸⣇
⠀⢠⣿⣿⣆⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⢀⣾⣿
⠀⢸⣿⠿⠟⠑⠀⠂⠻⠿⣿⡇⠀⠀⠀⣿⣿⠿⠃⠒⠐⠛⠿⢿⣿⠀⠀⠀⠀⣿⢿⠛⠓⠐⠊⠛⡿⣟⠀⠀⠀⠀⣸⡿⠟⠃⠂⠐⠙⠿⢿⡇
⠀⡜⠁⠀⠈⠢⡀⠀⠀⠀⠀⠑⡀⠀⠠⠋⠀⠀⠑⠄⠀⠂⠀⠀⠙⠆⠀⢀⠔⠀⠈⠠⡀⠀⢀⠜⠀⠀⠂⠀⠀⠀⠁⠀⠐⢄⠀⠀⠠⠁⠀⠙⠄
⢸⣷⣄⡀⠀⠀⠬⠀⠀⢀⣠⣾⣧⠀⣷⣄⠀⠀⠀⠰⠇⠀⠀⠀⣀⣾⡀⣸⣷⣄⡀⠀⠀⠯⠀⠀⢀⣠⣾⡇⢀⣧⡀⠀⠀⠀⠸⠁⠀⠀⠀⢀⣾
⢿⣿⣿⣿⣿⣧⡄⣴⣿⣿⣿⣿⣿⠸⣿⣿⣷⣶⣤⣤⣤⣤⣶⣾⣿⣿⡇⣿⣿⣿⣿⣿⣧⢠⣼⣿⣿⣿⣿⡿⢸⣿⣿⣶⣦⣤⣀⣠⣤⣴⣾⣿⣿
⠸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⣿⡋⠛⠻⠉⠛⠛⠛⠁⠀⠠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⣸⣭⣭⣀⢠⣄⣤⠀⠀⠀⠀⠀⠈⠛⢉⣉⡈⠛⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣘⣛⣿⠏⠀⠀⠀⠀⠀⣰⡎⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⣀⢶⠗⢿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⢀⣄⣷⣿⣷⣤⣈⠙⠋⠀⠀⢠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⢘⣩⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠘⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠛⠁⠒⠀⠀⠀⣀⠀⡀⠀⠠⣴⣴⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣾⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⠛⣿⣯⣠⣤⣤⡂⣤⣯⡶⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣾⣻⣿⣿⣵⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⣿⡇⣸⣅⡀⠈⡧⢼⠟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣯⣿⡾⢿⣽⣋⣿⣿⣿⣿⢿⣿⣿⣿⣷⣖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣽⣿⣏⠁⠻⠃⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣽⣿⣿⣿⣯⣿⣶⣿⣽⣿⣟⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠁⠉⠈⠙⣷⡦⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣯⣭⣿⣾⣟⣻⣿⣫⣥⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⣼⢇⠟⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⠀⠀⠁⠀⠀⠹⣿⣿⣿⣿⣿⣶⣬⣿⠿⣭⣭⣿⣧⣿⣿⣿⣉
⠀⠀⠀⠀⠀⢀⡴⣿⡿⠁⠀⢁⠀⠀⣀⣾⣟⠄⠀⠀⠀⠀⠀⠀⠇⣸⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣶⣶⣿⠟⣯⣼⣯⣾⣿⣿
⠀⠀⠀⣀⣴⠏⣰⣿⡷⠃⣴⠟⡀⣾⣿⣿⠛⠀⠀⠀⠀⠀⡠⢂⡼⠃⢀⠀⠀⢸⣯⠛⣦⢄⣀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣾⣿⡟⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣾⣿⣿⣧⣾⣧⡶⢱⣿⣿⢀⠏⠀⠀⠀⣤⠜⣠⠋⠀⠀⡎⠀⣄⠀⠀⠈⠛⠶⠆⡀⢀⡀⠀⠀⠀⠉⠙⠿⠿⠿⠿⣿⣿⢿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⣿⡿⣱⠏⠀⡔⢠⣾⢋⡞⠁⠀⣰⠃⣧⠀⠈⠳⣄⠈⠲⢤⡴⣿⣿⣿⣟⠒
⠀⠀⠀⠀⠘⢿⠋⣿⡇⣿⠀⠀⠛⣷⣷⢂⣾⣷⣿⢇⣾⢀⡄⣰⡟⠠⣿⣧⡰⣆⠀⠁⠳⠦⣌⣣⣭⡙⠻⠿⠓⠒⠄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠀⣿⡁⠀⠀⢠⣶⣌⣿⣼⣧⣿⡟⣟⠋⠚⣰⡿⠃⠀⣿⣿⣷⡌⠳⣤⡀⠀⠀⠉⠉⠉⠃⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠠⣿⣤⠀⠀⠘⠿⠟⠩⠟⡿⢋⣾⣟⠀⢠⣿⠀⠀⠀⣿⣿⣿⣿⣄⠈⠻⡲⣄⠀⠠⣄⣀⠨⢅⣘⣻⠃⡄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⡘⠄⡀⢀⣠⣤⣴⣿⡏⢹⠀⡸⠋⠀⠀⣆⢸⣿⣿⣿⣿⣆⠀⠈⠑⢽⡲⢝⣿⣷⢸⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⠁⢡⡏⠀⡇⣶⠀⠂⡘⢆⢿⣏⠿⣎⠙⢷⣌⠒⢄⡉⠳⢯⣟⣺⣷⣭⣹⣿⣧⣌⠁⢶⣦⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡟⣹⡿⠁⣿⠙⠃⠀⣤⠀⢸⡇⢻⡆⠣⢈⠈⠎⢿⣦⣈⠱⣄⠘⠳⣦⣙⢣⣴⣬⣿⣿⣽⣛⠻⣿⣶⠀⠀⠈⠛⠃
⠀⠀⠀⠀⢀⣀⣠⠞⢛⡟⣴⡿⠁⡰⠿⡆⢀⢀⣿⠀⢸⣇⢐⡟⠀⠐⠒⠄⣁⠛⣯⣄⠀⠡⠄⠈⠛⢷⣭⣈⢛⣿⣷⣶⣲⣿⣛
⠀⠀⠀⠀⠈⠛⠁⠀⢸⣭⡟⠁⣸⠧⠀⠇⠹⡞⣿⠀⡈⣿⣞⠁⡟⠀⠀⠀⢨⠦⣽⣿⡆⠀⠀⠠⠀⠀⢈⣙⢿⣍⠁⠈⠋⠀⠉
⠀⢀⡤⣠⡄⣀⠀⣤⣶⡟⠀⢠⠏⠀⠀⠀⢠⣷⣝⠀⠑⣿⠙⢦⡑⠀⠀⠀⠀⠀⠀⠻⢿⣄⠀⠐⣄⡙⠣⣾⣭⣍⣶⡄
⠀⢨⣧⡿⠦⠧⠀⠛⠟⠟⢰⡟⠀⣤⢲⠀⢰⣿⣿⣷⡄⠘⢷⡈⠻⣶⠀⣄⠀⢀⣒⠀⠈⠻⢲⣀⠀⠻⢷⣬⣙⠿⢿⡟⠷⠂
⠀⠀⠉⠁⠀⠀⠀⠀⣠⣌⠇⣻⡄⢁⠘⡇⠀⢛⠻⠚⢷⠐⠀⠖⠀⡺⡟⢿⠿⠟⢁⣴⠆⠀⢄⠙⠊⠶⠀⠙⠿⢷⣶⡦⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠏⠙⢶⣿⣿⡾⢣⡑⡀⢹⣿⣿⣶⣄⢷⣶⣄⠉⠁⠻⡷⠦⡈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢿⡇⢀⡿⣁⢨⡋⠙⠻⠿⠿⠻⠅⠀⠀⠇⢀⣀⢀⡀⣠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡈⠁⠋⠀⠛⠀⠀⠀⠀⠀⣀⠰⡦⠄⡉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠁⠀⠉⠁⠈⠃⠰⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢶⠀⣄⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠈⣷⣾⡿⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠿⡇⠀⢀⣿⣇⣠⣤⣀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⣠⣾⣿⣟⣁⡀⢨
⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠻⣷
⠀⠀⠀⠀⢶⣼⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⡁⠀⠠⣤⣀⣴⡿
⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡍⢹⡟⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⡌⠻⠚⠁⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⣼⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣿⣿⣷⡘⢷⣄⡀⣀⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠹⣿⣿⣿⡄⠙⠛⠛⠛⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⣿⣿⣿⡄⠸⣿⣤⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠈⢿⣿⣷⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠹⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⢿⣷⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣁⣀⣰⣠⣀⣿⣯
⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⢻⣷⣏⣛⣻⣙⣻⣿⣿⡀
⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣤⣤⣀⡀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⣀⣤⣶⣶⣶⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⡿⠁
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⢼⣿⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠉⠉⠛⠋⠉⠉
⠸⣏⡀⠀⠀⠈⠙⠛⠿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⣴⡾⠛⠛⠷⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⢿⣿⣿⣿⣿⠃⠹⣿⣿⣿⣿⣿⣷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠊⠈⢹⣿⡏⠀⠀⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⣰⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠹⢟⣠⠤⠄⠀⣉⠛⢛⣛⣽⣿⣿⣿⣿⣿⠿⢋⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠈⢡⣾⣿⣿⣿⣿⠿⠋⠁⠐⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⣤⣤⣶⣿⣿⣿⣿⣿⣿⢶⣄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⡛⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠠⠠⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠉⠀⠈⠀⣰⣾⡿⢻⣿⣦⠀⠂⠃⠰⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⢀⣀⡀⠀⠀⣼⣿⡟⠀⣸⣿⠇⠀⠀⠀⠀⠀⠈⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠰⣶⣾⣧⠈⢁⣾⠟⢿⣿⣆⢠⣿⣿⣁⣾⠟⠁⠀⣠⣶⡿⣿⡆⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣌⠻⣿⠀⠸⡇⠀⢸⣿⣿⣸⣿⡟⠋⣡⣽⡏⢸⣿⣟⠀⠿⠃⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⣛⡧⢡⡄⠀⠀⠀⣸⣿⡿⠘⣿⡇⠀⣿⣿⠃⢰⠿⣿⣆⣀⣠⡾⠟⢋⣴⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠁⠀⠀⠀⠠⣤⣿⠿⠁⠀⠙⠷⠴⠛⠿⠴⠋⣠⢻⣿⠁⠀⠀⣀⠩⠶⠾⢿⣶⡄
⠀⠀⠀⠀⢠⡶⣶⣶⡄⠀⣠⣤⡄⠀⣠⣶⣦⡀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣀⠳⠾⠋⠀⠀⠀⠉⠀⠰⣶⣤⡀
⠀⠀⠀⠀⠈⠀⢸⣿⡿⣸⢋⣿⣿⣴⢏⣿⣿⡇⣀⣀⡀⣿⣿⣿⠇⠀⠀⣠⣾⡿⢿⣿⢠⣶⡆⠀⣾⣶⠀⢀⣿⣿⡇⢀⣴⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣷⡏⢸⣿⣿⡏⣼⣿⣿⣾⣿⣟⣿⠈⢻⣿⣷⣦⠀⣿⣿⠃⠛⢡⣿⣿⡇⣰⣿⣿⣦⡾⠟⠋⠀⡿⣫⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⢸⣿⣿⢰⣿⣿⠁⣿⣿⡏⠁⣠⠞⣾⣿⡟⢠⠟⠿⠦⠖⠋⠈⠉⢋⡵⣿⣿⡇⠀⠀⢠⣦⢘⣭⣥⡀
⠀⠀⠀⢀⣀⠀⢿⣿⠏⠀⠘⠛⠃⣿⣿⡏⣰⠋⠉⠙⠋⠁⠀⢿⣿⣧⠏⠀⠀⣴⡆⠀⠀⢠⡟⠀⣿⣿⠃⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠘⢿⣿⡿⢦⠀⠀⠀⠀⠀⠀⣿⣿⣰⠇⣠⡶⢶⡄⣴⣆⣤⣤⠀⣠⣤⣾⣿⠁⣀⡀⠘⠷⠾⣟⣁⡀⢠⣤⣤⣰⣿⠻⠇⣴⡄
⠀⠀⠘⠟⠛⠋⠁⢴⠄⠀⠀⠀⠀⠙⠛⠋⠀⣿⡗⠋⣰⣿⡿⣹⣿⢰⣿⣧⣿⡏⣰⣿⣇⣿⡇⢰⣿⡿⠃⣿⡷⢛⡼⢻⣶⡊⠉
⠀⠀⠀⠀⢀⣴⡶⠖⠀⠀⣀⣤⢤⣄⠀⠀⠀⠈⢉⣉⡁⠀⠀⢻⣷⠟⠉⠁⠙⠛⠋⠙⠋⠙⠳⠛⠛⠉⠉⠉⠉⠉⠀⠙⠛⠁
⠀⠀⠀⢀⣿⡟⠀⠀⣠⣾⡿⠁⠀⢹⡆⠀⠀⣼⣿⣏⡿⠀⣤⠀⠀⠀⢴⣦⠄⠀⠠⠤⠄⢠⣤⡀⠀⣠⣶⠶⣦⠀⠀⠀⠤
⠀⠀⠀⠈⣿⡇⠀⣰⣿⡿⠁⠀⢀⡾⠁⢀⡀⢻⣿⣿⣁⠀⠀⣠⣤⣤⣄⠀⢀⣤⡄⣤⣀⣰⡿⠏⠰⣿⣿⠀⣿⠀⢀⣀⡀
⠀⠀⠀⠀⠘⢷⣀⣿⣿⡇⣀⡴⠋⣠⣾⡿⢻⡏⠉⣹⣿⡿⣸⣿⡿⢹⡿⢠⣿⣿⠃⢸⢏⣵⣶⢿⣶⠻⢿⣿⣧⣤⡈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠁⠀⣠⣿⣿⣇⣼⠇⣸⣿⣿⠁⢹⣿⣿⠉⢀⡼⣿⣿⣀⡿⠸⣿⣿⠋⢁⣠⠞⣹⣿⣿⠁⢀⣿⡟
⠀⠀⠀⢠⡖⠉⠙⣿⣿⣄⡴⠚⠁⠙⠛⠛⠋⠀⢿⣿⣇⣠⡟⢉⣛⣛⠉⠀⠀⠉⠉⠀⠀⠈⠉⠛⡉⠀⠀⠹⣿⣧⢀⡼⠏
⠀⠀⠀⠀⠉⠙⠘⣿⣿⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠨⠏⠉⠁⠈⠙⠁⠙⠃⠘⠃⠀⠙⠀⠛⠃⠀⣬⠉⣭⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣼⡇⣶⠖⣘⠀⣾⣹⡷⢾⣅⢰⣿⣧⣼⡆⣾⣦⣿⠀⠀⣾⠅⢿⣠⣿⠡⠀⣿⠀⢠⣔⢦⣍⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⡾⠹⠇⠛⠀⠀⠧⠿⠻⠏⠟⠻⠄⠿⠈⠿⠀⠀⠛⠘⠚⠙⠛⠃⠀⠛⠀⠸⠿⠎⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢠⢠⢰⠄⡢⢔⡔⡶⡖⣶⢦⣠⢶⡖⡶⡖⣖⢤⡂⢤⢀⢠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠁⠓⠁⠀⠘⠙⠈⠀⠓⠃⠉⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⢈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣳⡬⠵⠒⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠉⠉⠀⠀⡀⠈⠃⠤⡀⢈⡃⠀⠒⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢈⠂⣀⠘⠁⠈⢱⢤⡐⠈⡀⠈⠒⠦⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡈⣢⣐⠋⢀⠾⠀⡈⠐⠄⣄⢀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢍⠉⢛⡳⠂⠀⠈⠂⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢄⠈⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠆⢠⠀⠄⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠧⠀⡀⠀⣆⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠁⠤⡐⢊⠐⢈⠁⠰⢠⡠⢀⠀⠀⠀⠀⣼⡿⣿⣷⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢄⠉⣄⠐⠈⢡⡀⠂⠈⣁⠐⢈⠩⢩⣿⣿⠟⠛⠺⠧⠣⠛⠏⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠠⠀⠐⣆⢀⠈⠡⡀⠖⠈⡀⠤⠀⢁⠀⢂⠩⡀⢪⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠡⡀⢔⠠⡝⠠⠄⠐⡀⠠⠄⠉⠐⠩⢓⡩⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠄⢀⡀⣐⢀⣑⢒⠄⠠⠊⠂⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⢿⣏⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⣈⣭⣿⣿⣿⣿⠟⠛⠉⠛⠻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⡴⠟⠉⠀⢹⣿⣿⣇⠀⠰⣶⣶⡄⢾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢠⡾⠋⣿⡿⣀⡀⠈⠉⠉⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠠⠆⢀⣴⡟⠁⠀⣿⠀⠈⣆⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⣠⣴⣿⡟⠀⠀⠀⣿⠀⠀⢿⣷⣧⣤⣾⣿⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠛⠛⣉⣿⣿⣏⣠⣴⣿⡟⠋⠀⠀⠀⣸⡿⠀⠀⢸⣿⣻⣿⡿⢋⣹⣇⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄⣸⣿⠿⢿⣿⣿⣿⠏⠀⠀⠀⠀⣴⣿⡃⠆⠀⣾⡿⢿⣿⣿⡟⢹⣿⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⠁⠀⣸⣿⡿⠿⢷⣄⠁⢀⣼⣿⣿⠃⠀⣸⡟⢳⣾⣿⣿⡃⣦⣿⢿⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠰⢿⣿⣿⣧⣤⣶⠟⠀⠀⠀⠈⣹⣿⣿⣿⠿⣿⣿⣿⣿⣧⣼⣿⣾⡿⣷⣿⣿⣿⡿⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⢶⠿⣿⣿⣿⣿⣀⣀⣀⣴⣾⠟⠋⡙⠁⢸⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣧⣤⣴⣶⣤⣍⣿⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠛⠉⣀⣴⠃⠀⣿⣿⣿⡿⠿⠆⠀⠀⠀⠛⢻⣿⣟⠿⣇⣈⣽⣿⣷⣤⣶⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡄⠀⠀⢁⠛⠋⠙⠛⣿⣿⣿⣿⣿⡿⠀⣾⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⢹⣶⣴⣿⣾⠃⠉⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠋⠀⠀⢀⠂⠀⠀⠀⠀⠙⠿⠿⠟⠛⣻⣿⠀⣻⣿⣿⣿⣿⠿⡟⠘⢷⣆⣀⣀⣴⢞⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡤⢫⡟⢱⣌⣡⠴⠇⠀⠀⠀⠀⢀⣤⠀⠶⣴⣾⣿⣿⣼⣿⣿⣿⣿⣿⣶⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣠⠎⣰⠏⠀⣠⣼⠇⠀⠀⠀⠀⣀⣤⡛⢩⡶⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠻⠏⣠⣾⣏⡙⠲⠦⣤⠽⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⢰⠃⡞⠁⣠⠎⠉⠀⠀⠀⠀⢀⣼⡟⠁⣠⠇⠰⠂⢀⣿⣿⣿⣿⣿⡿⣿⣿⠹⠄⠹⣿⣿⣟⣓⠶⣤⣤⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⡎⢸⣡⣾⠃⠀⠀⠀⠀⠀⠀⡞⢁⣅⠀⠁⠀⡄⠀⢸⣿⣿⣿⣿⣿⡷⠄⣸⣦⠎⠀⠆⠙⢿⣿⠷⣄⠀⠰⠃⠰⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣧⣼⡉⠁⠤⠀⠀⠀⠀⠀⣸⡿⠟⠁⠀⠀⣰⠃⢀⣿⣿⣿⣿⣿⣏⠀⠀⠙⠋⠒⠃⠀⠀⠀⢻⣷⣾⡀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣼⣧⣿⠁⠀⠠⠄⠀⠀⠀⠶⠟⠡⠄⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⣴⣎⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⣤⠾⠛⢿⣧⣃⠀⢤⡄⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠻⣿⣿⣿⣿⣽⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⣻⡟⠛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠈⠀⠀⢸⣤⣿⣀⣀⣀⡀⠀⢠⡀⠀⠠⠄⠀⠀⢠⡾⠃⢀⡔⢁⠞⠛⠻⣿⣿⣿⣿⣿⠛⠻⠷⣶⣤⣠⣾⠟⠁⢠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣽⣿⠋⠻⡅⠀⣰⣿⣁⡀⠀⠀⡀⠀⣼⡤⠖⢋⡴⠋⠀⠀⠀⠀⠉⠙⠻⠿⣿⣦⡤⠄⠉⠀⠀⣰⣶⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢠⠉⠁⠀⠀⢱⣾⣿⣿⣟⣷⣷⣿⣋⡿⠦⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣠⠂⠀⠀⠀⣠⣿⠁⠹⣿⣿⣏⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠈⢹⠀⢡⣈⣿⣯⡿⣿⣏⠙⢸⣷⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣼⣿⣿⠋⡔⠙⣿⣀⠀⣨⣦⠀⠀⠲⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣯⡌⠁⠀⠘⠻⠿⢿⣿⡗⢶⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠘⠿⣿⢿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⢻⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⠀⠶⠙⢻⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⡀⠀⠀⠠⡿⢿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣼⣻
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠘⢷⡄⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢋⣿⣻⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣾⣿⡻⣟⣿⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣟⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣿⠟⠉⠋⠙⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣀⡀⠀⡀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⣿⠀⠉⠀⠀⠈⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⣿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⣷⡄⠈⠉⠀⣾⣿⣿⡟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⢾⣿⠇⠀⠀⠀⠈⣽⣿⡿⢬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⡥⠿⣿⣷⢦⣠⡰⠾⢻⣧⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣾⣶⣿⣿⣧⠀⢙⡀⢀⣸⣿⠿⣿⣌⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣾⣿⡾⣹⣿⣷⢀⣽⣍⠀⢉⣿⣘⣛⣿⡅⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⣿⠟⠁⣾⣿⠉⠸⡿⠟⠀⢨⣿⣿⣼⡗⢻⣧⣹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠸⣿⣿⣘⣿⣿⣧⡴⠺⣿⢿⣿⣿⣿⣿⣿⣷⣾⣿⣼⣯⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⢻⣿⣿⢿⣿⣿⣿⣶⣶⣾⣿⠗⣸⡿⣿⣿⣾⢻⡟⣹⠏⠛⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠿⠀⠻⣌⢻⣿⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⠾⠁⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⣿⣤⠀⠐⢿⣷⣿⣿⣷⣽⠄⢹⡄⡾⣿⣿⠟⠑⠂⠀⠀⠘⣽⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢘⣿⣿⣶⣶⠐⣩⠟⠉⠈⠙⡾⠿⢦⣀⣠⠞⠲⣭⡐⠛⠃⠘⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠁⣠⠞⢡⠞⢠⡔⠈⠉⠁⠂⡀⠘⣿⣦⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠈⠻⢟⡁⣘⣯⡄⢿⠠⠆⢿⠂⣤⠄⠄⠁⠀⢸⡿⣿⢶⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢊⣽⣟⡡⠙⡏⠀⠀⠈⠵⢦⣶⣤⠿⠀⢸⣇⢡⡾⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠾⢋⣛⢁⣸⠀⠀⠀⠀⠀⢰⡞⢻⡇⠀⢰⡿⠋⠀⠁⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢦⣠⡤⠊⣠⢋⡟⢠⣦⡤⠂⠀⢸⣿⠘⠀⠀⢸⡇⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠄⣀⣠⡾⢁⡼⠤⣼⡏⢸⣇⠀⣿⣿⣆⠀⠀⣼⡇⠤⣾⠇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠟⠋⣴⡿⠁⠀⣿⠃⢠⡿⢁⣿⣿⣿⠀⢠⡿⠁⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⡴⢾⡿⠀⠀⠘⠀⣰⡾⢡⣾⡿⣼⣷⠀⣸⠇⠰⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⠀⢴⡿⠋⠀⠀⣢⠁⣠⡽⢁⣿⣿⡇⢸⡇⢰⣿⡴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡰⠛⣉⣴⣤⣀⡀⠘⣼⠃⠐⠉⢰⣿⣿⣿⠀⠈⢃⣾⠋⢠⣿
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠜⠳⠞⢋⣼⣶⢛⣶⠈⠀⠀⠐⣀⣼⡟⠁⣾⠀⣸⣴⠟⣼⠿⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠁⠐⠂⠀⠉⠉⠘⠛⠉⠋⢨⡵⠾⠋⠁⠀⢰⡏⢀⣿⠁⡰⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⢮⣀⡀⠈⠛⠀⠀⠀⠀⢄⡀⠀⣐⡠⠤⣾⣧⣾⠇⢒⣴⣿⠂⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⢀⡀⣰⣄⡀⠀⠀⠀⠀⣀⣤⣶⠀⠀⠀⠀⠈⢉⣉⣩⣥⡞⢻⣿⣥⠶⠏⠻⠽⠃⠀⠂
⠀⠀⠀⠀⠀⢀⣈⣀⡠⠚⠓⡶⠖⠛⠹⢏⣱⣿⠦⠄⠠⠔⠚⠉⠉⡙⠁⣈⣹⣿⠇⠀⠀⣀⠀⠙⠈⠀⡀⠀⣄⣀⣤⠤⠄⠀⡀
⠀⠀⠀⠀⢀⣨⡷⠊⠀⣠⡾⠳⢄⣀⣄⡈⢿⣟⠀⣀⣶⠚⣿⡆⣺⣿⣿⣿⢻⣯⢳⣀⣀⠿⢧⡀⠘⢙⣿⡿⠋⠁⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠙⠁⣀⠀⠲⣁⡀⠀⠀⠀⠀⢻⣾⣡⠤⠛⠁⠀⠈⠾⣿⣿⣻⣏⠀⣿⢻⣿⡏⠀⠈⢥⣦⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠻⣶⣷⡍⠁⠀⢀⣠⡴⠋⣻⢉⡀⠙⠁⢠⠀⣾⣿⣿⢿⡧⢄⣻⡿⠈⢡⣀⡀⠀⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠓
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣶⣿⣯⠄⠀⢿⣿⡍⣛⣦⣀⡟⠙⣿⣟⣬⣷⠾⠛⣀⣤⣜⣁⣴⡦⠈⢦⠀⠀⠀⠀⠀⠀⠀⢠⡤⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠋⠱⢾⣦⡤⠛⠁⠀⠀⠀⠀⠛⠙⠉⠁⠀⠿⢶⣶⣾⠛⠿⣾⣿⣿⠉⠙⠋⠛⠃⠀⠀⠈⠂⠀⢀⢠⣀⠿⠋⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⠀⠀⠀⠀⠀⢤⣴⠄⠀⠤⠀⠀⣠⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⠉⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⢠⡶⢂⣤⣤⠴⠊⣉⠀⠂⠀⠀⠀⣀⠀⠐⠲⢶⣶⠟⠉⠀⠀⠀⠀⠀⠈⠁⠒⠛⠛⣛⡱⠟⠋⠉⠀⠀⠀⠀⠉⠓⠒
⠀⢋⣤⡿⠀⠚⣉⣠⠶⠋⠁⠀⠀⠀⠀⠀⠘⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣹⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠐⣀⣀⠀⠀⢀⡤⠆
⠐⠛⠃⠀⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠉⠀⠀⠀⠀⠀⠀⢤⣤⣤⠌⠉⠉⠉⠀⠀⠒⠒⠉⠑⠒⠒⠆⢁⠀⠀⠉⠙⠒⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣴⣦⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠐⠄⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠚⠉⠉⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠁⣀⡀⠀⠀⠀⣦⣤⡀⠀⠀⠀⣠⣴⣄⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⡄
⠀⠀⠀⢠⣀⣼⣶⣄⣠⣿⣿⣄⣀⣼⣿⣿⣷⣄⣠⣾⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣦⣤⣠⣾⣿⣷⡀⠀⢀⣀⣎⠳⣄⠠
⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⡷⢀
⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡡⠄⠀⢀⠀⠀⠀⠀⠀⠝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣭⣭⡍⠁⠀⠀⠉⠙⢛⣿⣿⣀⣀⡀⣴⠾⠆⢀⣠⢄⠀⠀⠙⣿⣿⣿⣿⣯⣩⣭⣭⣥⣭⣭⣭⣉⡀
⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⡿⣟⡉⠁⠰⠄⠀⠀⢰⣿⣿⣿⣿⣿⣷⣷⡄⠀⠘⠛⠊⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀
⠀⠀⢺⣿⣿⣿⣿⣿⣿⠟⠑⠒⠀⣁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣠⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⠹⡿⠟⢿⠋⠁⠀⠀⠀⣀⠘⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡯⠁
⠀⠀⠀⠀⠀⠀⠈⡵⠗⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⠀⠀⣼⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠉⠉⠉⢿⣿⡟⠉⠋⢻⣿⡿⠋⠁⠉⠻⣿⠟⠁⠀⠀⠉⡹⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣉⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠎⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⡛⠉⠁⠀⠒⢁⠀⠄⠈⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠐⠀⠈⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢲⡄⠀⡀⠀⠐⠂⠀⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⡀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠻⠛⡉⠤⠀⠀⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠿⠿⠟⠁⠉⢻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣿⠁⠀⠀⠀⠀⣀⣤⢸⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠀⠶⠖⠀⠀⠉⠁⢸⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠉⠁⠀⠠⠂⠀⠀⠀⠁⠄⠴⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠉⠉⠉⠀⠀⠠⠤⢤⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣿⢟⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠮⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⡿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⡘⢎⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡤⣴⣿⣷⣶⡶⣶⠶⣄⢠⡾⠋⠀⠀⠀⣄⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢀⢸⠁⣠⡎⠿⠿⢿⣿⣿⣿⣎⢿⡃⠀⠀⠀⠀⣸⡇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠁⠀⠀⠉⡃⠀⠀⢊⣽⠯⡿⡹⡈⠱⢤⣀⣤⠶⢣⠇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢸⡀⠀⠀⠈⠀⢀⣤⡄⢸⡃⠐⠚⣱⣁⢀⣀⣀⣤⡶⠋⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣇⠉⠀⢦⡻⣶⣶⣰⠶⠟⠛⠀⠸⢷⣴⣿⣿⣯⣿⣿⣿⣯⡀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠋⠀⠉⢁⣀⠀⡀⠀⠀⣀⣻⣿⣿⠁⣠⢈⣹⣿⣷⢀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡳⣶⣾⠟⣷⠟⠃⠈⠁⠈⠙⡟⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣹⡿⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⣠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠲⠶⠟⢁⣟⠀⠀⠀⠀⠀⠀⠀⣠⣖⣋⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡀⠀⠀⠈⠛⠛⠉⡹⠀⠀⠀⢀⣠⣴⣾⡏⢯⣭⣿⣿⡾⠇⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⠀⠀⢀⡴⠁⠀⠀⡺⠿⠟⠁⠀⠀⠤⠾⠛⠋⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⣿⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⢘⣿⠕⣧⢀⠀⠄⠐⠀⠀⠀⢯⡗
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⣾⠃⠀⢷⡈⠀⠀⠀⠀⠀⠀⠘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⢿⠉⣿⠠⣿⠀⠀⠀⠑⠢⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣟⠛⠷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢲⠶⣲⣶⡶⠒⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⢀⠀⣇⣾⠟⣻⣶⣦⣽⣿⣿⣦⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⣿⣣⠀⠀⢻⣿⣾⠛⣻⣿⣿⣟⠉⣙⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢻⣷⣄⡀⢠⣿⣿⣟⣽⡿⢹⡟⠉⠛⢛⠃⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡘⠿⢭⣿⣿⣿⣿⣧⣹⣾⣿⣦⣿⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⡀⠈⠛⠒⠒⠛⠛⠿⢿⣿⣿⣿⣿⣿⣏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠁⢁⠀⠠⠤⣀⠀⠀⠀⠀⠀⠉⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⢀⠀⠣⠀⠸⡀⠀⢆⠀⠉⠓⠒⣲⣤⣶⣷⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⢸⠀⠀⠐⠊⡙⠷⣾⡆⡤⠒⠒⣳⡀⢸⡀⢀⠀⠈⢿⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠙⣦⠀⠀⡇⠀⠀⠀⠒⠀⠀⣹⣿⣄⣀⣴⠉⣷⠈⠃⠉⠦⠀⠄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⢸⡇⠀⡧⠀⠀⠀⠁⠀⡰⠻⣷⣈⣉⣿⣿⡟⠉⢆⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡞⠃⠁⠀⠀⠀⡀⠀⢸⠁⠀⣧⠀⠀⠁⠀⡸⠁⠀⠈⠉⠙⠻⠋⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡗⡁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⠏⠀⠀⠀⠀⠜
⠀⠀⠀⢠⣀⣤⡤⠒⠋⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⠄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠳⢀⡀⠀⠀⠀⠀⣀⣀⣀⢀⢳⣿⣿⣿⠀⠀⠀⠀⠀⢀⡜⠀⠀⠜⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠉⠙⠛⢿⣿⣇⠀⠀⢀⡄⠊⠀⣀⠎⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠈⠀⣀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⣆⣶⣾⣼⣴⣶⣴⣄⣄⠀⠀⠀⢀⠀⠈⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢡⠿⠿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠀⠈⠙⢿⣯⣾⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⠿⢿⠿⢿⡿⠷⢀⠀⡀⠔⠐⠃⠀⠠⠖⠀⠀⠀⠀⠀⠀⠘⠋⢘⠸⢹⠟⠙⠇⠏⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡶⣶⣤⣶⠄⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⠯⠿⣏⠑⠊⢉⣿⠟⠙⠢⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠲⠀⠀⠃⣾⣷⣍⠋⢋⣹⣿⣦⣼⣮⡵⢿⡦⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠘⡿⢿⡏⠻⣿⣏⡉⠀⠙⢿⣯⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⡔⠀⠀⠇⠀⣿⣤⡽⠟⠛⣶⣦⣄⣿⣜⠢⣿⣶⢶⣀
⠀⠀⣰⢞⠣⠀⠀⠀⠀⠀⠀⠀⣽⠈⣿⠇⠀⠀⠀⠛⠛⠻⣿⡷⣷⣮⣿⡿⠿⠧⢽⣶⣿⠿⠂⠀⠁
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⣷⣼⣿⣄⡀⢀⡀⠀⠀⠀⡟⢰⣿⠈⠉⠱⣦⣤⣾⣿⠿⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢛⣿⣿⣟⣟⣁⠀⠈⠁⢀⠀⠂⢠⣽⣧⡄⠘⢻⣷⣿⣿⣖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡅⢠⣌⠻⣯⡙⣿⡳⠀⠀⠈⡆⠀⠀⢻⣿⣷⣤⡞⠁⠘⠛⢿⠳⢦⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⠏⢹⡿⣿⠏⢳⡀⠁⣺⢿⣦⣤⠼⣿⣉⠓⠚⠒⠒⠀⠀⠁⠒⠃⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⣸⠛⠀⢿⠀⠇⠀⠀⠀⠚⠃⢀⣹⣿⠿⠿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⣾⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣖⡆⠀⠀⢀⠄⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢡⠀⠀⠀⠞⣾⡀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠂⠃⠀⠀⡸⠀⠛⠇⢠⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠋⠈⠀⠀⠀⡇⠀⠀⠀⠈⢻⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠳⠄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠙⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢲⡌⡆⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠤⠤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⠙⣽⠄⣂⣨⡍⢡⣤⣀⡤⡀⠂⠿⠠⠾⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣀⡄⢀⠀⠀⠀⠀⠈⠈⠃⠈⠀⠈⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠩⢐⣁⣴⣜⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⣋⠀⠀⠀⢀⡀⠀⡀⠀⠀⢻⣿⡷⠿⣿⣯⢠⢦⡄⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠉⢀⢆⠉⠠⠦⠀⠀⠀⠀⢨⡉⠀⠀⢿⣿⢾⣇⠔⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠄⠀⠀⠀⠀⠙⢰⢷⠀⠀⠀⣠⡔⠙⠀⠀⢀⢼⡻⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣠⣀⠃⠠⠀⠀⠀⠀⠙⠈⠉⠘⠀⠀⡀⢀⣄⠢⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠧⣤⡄⠀⠠⠄⠀⠀⠀⢠⢠⣆⡽⠌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⢿⡏⠀⠛⠓⠒⠀⠛⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣴⣤⣴⡀⢀⡀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⡿⠛⠉⠈⠙⠻⠻⣿⣟⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣏⡷⢂⣿⣷⣶⣶⣷⣾⡻⢿⣷⡾⣶⣦⡀⠄⢀⣀⣴⣶⣿⠛⣶⡄
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡗⢼⡈⢛⠉⣜⣿⣿⣿⣿⢶⣿⣦
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⣿⡿⢿⡿⠿⠿⣿⣿⣿⣽⣦⣤⣿⢶⣶⣦⣉⣿⣿⣿⣿⣶⣤⣤⣄⣤⠄
⠀⠀⠀⠠⢬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣙⣛⡛⠲⠓⠶⠶⠤⠟⣻⣿⣿⡿⠰⡾⠝⣿⣿⣭⣿⣿⣿⣿⣿⣿⣭⣤⠤⣤⠄
⠀⠀⠀⢠⣿⣏⣹⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣶⣠⣭⣥⣤⣄⣀⣀⡈⠁⡁⠈⠁⠛⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣧⣰⣷⡶
⠀⠉⠈⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣷⢀⣶⠀⠀⠀⢸⣶⣤⣀⣴⣾⠟⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠚⠉⠈⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⠾⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⡀⠀⣸⢻⣿⡅⠀⢀⣶⣆⠀⠀⠀⠀⠠⠤⠒⠀⠈⣁⣀⡀
⠀⠀⠀⠀⠀⢀⠀⠠⣴⣀⡀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣥⣁⣸⣿⠃⠀⣸⣿⣿⣿⣦⣿⠃⠀⠀⠀⠀⢹⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠐⠱⠀⠀⠉⢠⣀⡀⠉⠉⠉⠛⠛⠛⠛⠃⠉⢻⣿⣿⣿⣿⣿⠀⣀⣽⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇
⠀⠀⠀⠀⠠⠀⠛⠂⠰⣤⣶⣤⣌⣻⣶⣶⣤⣤⡀⠀⢀⣴⣧⣆⠛⠻⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⡿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣥⣴⣾⣿⣾⣦⣬⣾⣿⣿⣿⣿⠿⠿⠿⢒⣷⠀⣹⡆⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣉⣙⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣼⣿⡇⠙⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠥⠠⠤⠿⠍⠙⠻⠿⠿⠿⠆⠈⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⠿⣿⠿⠿⠿⠟⠋⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣭⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡿⠟⡳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⢀⣰⡿⢦⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣴⣏⡿⣀⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠯⢽⠃⠘⠙⢣⡽⠂
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢀⣀⣀⣹⡇
⠀⠈⠻⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣾⡃⠀⠀⠟⢳⡖⠳⢦⡀
⠀⠀⠈⣿⣿⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠙⠳⢶⣶⡋⠀⢸⣤⠙⢦⡀
⠀⠀⣸⢻⢿⣾⣿⣤⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡞⢳⡄⣴⠋⢨⠟⣆⣠⡽⠶⣦⢹
⠀⣰⠃⠈⠘⠋⠔⢒⣶⣶⣛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠼⠗⠚⠓⣋⡴⠛⢦⣭⣤⣷⣤⣤⠼
⣰⡇⠀⠀⠀⣰⠚⠉⠉⠉⠛⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⢤⣴⡶⠛⠁⠀⠀⠀⢀⣹⣿
⣿⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠳⣄⡀⠀⠀⠀⠛⢿⣿⡇
⢻⠀⠀⣌⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⣿⣿⡿⢳⣮⣝⣻⣶⣶⣶⣞⣻⠇
⠈⣇⠀⠀⠐⢿⣿⡲⣦⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢾⡿⢗⡼⠙⡯⢞⡥⣫⢟⠟⡹⢋⡽⢉⡿
⠀⠘⣧⡀⠀⠲⣍⠀⢬⣛⣭⡿⠿⠿⠿⠿⢿⣋⠸⣠⠕⢚⣥⠔⠂⣠⠏⠘⠑⠁⠀⠰⣋⣴⠟⠁
⠀⠀⠈⠙⣦⣄⡀⠀⠉⠛⠭⣓⠀⠠⠿⠿⠛⠛⢀⠀⠀⣉⣠⠴⠋⢁⡴⠂⠀⢀⡤⠞⠋⠁
⠀⠀⠀⠀⠈⠙⠛⠷⣤⣀⡀⠈⠁⠘⠛⠛⠛⠉⠁⠀⠈⠉⠀⢀⣀⣠⣤⠶⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠇⠀⠀⠸⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠞⡇⠀⠀⢸⠳⣌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢰⠋⠉⠉⠉⠁⠉⠉⠁⠀⠀⠈⠉⠉⠈⠉⠉⠉⠙⡆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠳⣀⡸⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⢀⣀⣀⢀⣀⣀⣀⣀⢇⣀⠞⠀⢨⠇
⠀⠀⠀⠀⠀⠀⣠⣪⢆⠀⠸⣓⣿⢦⠤⠤⠶⡷⡙⢤⡇⠀⠀⢸⡤⢋⢾⠶⠤⠤⡴⣽⣚⠇⠀⡴⣕⣄
⠀⠀⠀⣠⡤⠤⠃⠓⠋⠀⠀⠀⠀⠀⣀⣀⡤⠇⠈⠓⡄⠀⠀⢠⠚⠁⠸⢤⣀⣀⠀⠀⠀⠀⠀⠙⠚⠘⠤⢤⣄
⠀⠀⠀⣇⣀⣀⣄⢠⡴⡄⠀⢸⣩⣳⠃⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠘⣞⣍⡇⠀⢠⢦⡄⣠⣀⣀⣸
⠀⠀⠀⠈⠀⠀⠀⠑⠯⣏⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⣹⠽⠊⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠇⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣇⣀⠀⢀⡴⠒⠒⠛⠒⠒⠛⠒⠒⢦⡀⠀⣀⣸⣀⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠈⠑⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠊⠁⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⣤⣤⣤⣤⣤⣀⣿⣠⣤⣤⣤⣤⣤⣤⣤⣄⣄⣿⣀⣀⣠⣤⣄⣤⣄⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⡠⠁⡐⡁
⠀⢀⣀⠠⠀⠁⠠⠀⡠⠚⣿⣚⡗⠊⠙⣷⠤⡀
⠀⠈⠀⠀⠀⠀⠈⢿⣷⣾⣿⣿⠟⠛⠺⣿⡇⠀⠀⠤⠀⠀⠄⢀⡤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠄
⠀⠀⣀⠀⠀⠀⠀⠘⠻⣿⡿⠓⣂⠀⢀⣿⡶⠂
⠀⠘⠁⠀⠀⠀⠀⠀⠀⠚⠃⠈⠁⠀⡈⠉⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢦⠐⢓⠀⠀⢠⣠⠾⠁⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠂⠀⠐⠂⢸⠁⠀⠀⠀⠈⣹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠁
⠀⠀⠀⠀⠀⣔⠀⠀⠀⠠⠍⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠞⠇
⠀⠈⠀⠀⠀⠈⠈⠃⠀⠀⡠⠀⠀⠀⡀⠀⠄⠀⠁⣄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡎⠀⠀⠀⠀⠀⠀⠖⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲⣀⠙⠍
⠀⠠⠀⠀⠀⠀⠄⠀⣴⣊⢜⠇⠀⠀⠀⠀⠀⠀⡇⢵⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠭⠁
⠀⠀⠀⣈⠀⡄⠀⠀⠈⣷⣞⡂⡀⠀⣀⢀⣀⠸⢷⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⢘⠀⢀⠐⠀⠀⠁⠀⡼⠀⠀⠀⠈⠛⠀⠖⠀⠺⠁
⠀⠈⠀⢀⠀⠀⠀⠄⡄⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢸⣠⡁⠉⠂⡐⢨⠀⠀⠀⠀⠀⠀⢘⠃⢀⠉⠀⠀⠀⠀⠀⠀⡄⠀⠆
⠀⠸⠀⠀⠈⠐⢶⣟⠀⠐⠀⠀⠀⠀⠀⢇⡈⠀⠀⠀⠀⠀⠀⠀⡂⣤⠇
⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⠠⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣀⠄⠀⠀⢠⠀⠀⢸⣷⣿⣿⣯⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⣄⡀⠀⠀⠈⠀⠀⣠⣴⣿⠀⠀⢸⣿⠉⢻⣿⣿⣻⣋⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠝⣿⡇⠀⠀⢀⣠⣾⡿⠀⠀⠈⠀⠀⠀⡉⠉⠛⢏⢳⡄
⠀⠀⠀⠀⠀⠀⣰⡇⠀⠤⡄⣀⠄⢀⣀⡤⢖⣿⡀⠈⣤⠾⠿⣿⠃⠀⠀⠀⠀⠀⢾⣿⡆⠀⣼⡌⡃
⠀⠀⠀⠀⠠⢄⣽⠦⢒⣢⣤⠦⠘⠛⡛⢛⣻⣿⠋⣠⠄⢄⣼⠏⠀⠀⣤⡀⠀⣠⣾⠿⣷⣶⣿⣶⠃
⠀⠀⠀⠀⢀⣾⣡⣖⣉⣁⣀⣄⣀⡀⢓⣾⠟⣿⠸⢿⠀⣨⡟⠀⠀⠀⠿⣽⢹⣿⡅⢸⡟⣼⡟⠁
⠀⠀⠀⠀⢸⣿⠋⠀⣡⠿⠛⠋⠉⢀⣾⣯⡰⡉⠂⡌⠃⠙⡇⠀⠀⠀⠀⠀⠁⠘⠻⠾⣷⣼⣇
⠀⠀⠀⠀⠈⢿⣤⣐⡇⢀⢀⡤⢹⠏⠐⣟⢿⣿⣀⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡟⡿⢿⣿⠶⠾⣩⠟⡵⣡⡄⠚⣰⠆⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠝⠁⢶
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⡾⢋⠕⣫⣾⡷⣾⡿⡅⠀⢘⣋⣴⡿⢿⣆⠀⠀⠀⠀⠀⠀⢰⡏⢰⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠙⣆⣰⣯⡿⠍⠹⢄⣹⡷⣄⠴⠟⠙⠋⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠑⢼⡛⠦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠀⢠⣾⣤⡤⠖⢡⡞⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠟⠉⠁⠀⠀⠠⡄⠀⠀⠀⠐⢀⢄⠀⣀⡀⣤⠁⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠎⡹⠏⣱⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⠀⣤⠀⢀⠀⠀⠀⠀⠀⢠⡴⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡆⠀⠀⠀⠀⠠⣀⠀⠂⢰⡆⣶⡇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡐⡆⠀⠀⠀⠀⠚⢀⡀⢸⢿⣿⣡⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠈⣶⣿⡀⠀⠀⠀⠀⠀⠁⠸⣾⠏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠒⠇⣢⠀⠘⢩⡗⣄⠁⢈⡤⣤⠞⡛⠁⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡓⠤⢳⢳⣄⠈⢻⡄⠐⢀⡄⠰⠂⠀⡘⣳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠞⠃⠀⢎⡈⣿⡶⠀⠟⢉⠿⠁⠄⠀⠞⣱⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⢸⠃⠀⠀⣿⠀⣿⢣⡆⠀⠁⠀⠔⠀⡰⣳⢟⣤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡘⣧⠀⠀⢠⣷⢾⣿⣿⣡⡀⠀⠀⣀⣾⢟⡀⢨⡁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣷⢿⡀⣷⠸⡜⣷⣿⣷⣿⣾⡶⠟⢠⠔⢉⡼⠿⠃⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣾⢣⣞⣤⣿⣿⡿⢋⣾⣿⣷⣾⣇⠴⠋⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⣾⣧⣿⣹⣿⠏⣡⣿⣿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣠⣯⣻⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣟⣻⣿⣇⣿⣿⠏⠀⠀⠀⠀⢀⠆⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⡀⠀⠀⠀⡠⠊⣀⠀⢀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⡿⢷⢖⡶⠎⡁⢞⡳⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠟⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡻⠛⣲⣶⡶⠛⠛⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣀⠀⠀⡀⢸⢡⣾⠟⢻⣶⣶⣄⣹⣿⣿⣦⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠙⣿⢣⠈⠀⠸⣾⣿⡖⡿⢻⣿⣿⣿⡿⠛⠻⢷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⣧⡀⠀⢀⣘⣿⣾⣦⢚⣿⡿⣿⣿⠒⢶⠿⡿⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠹⣿⡶⠤⣺⣿⣿⣿⣾⠙⣄⣿⣇⡀⣤⣴⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣉⣛⡛⢻⣿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠂⠀⢄⡀⢈⠁⠈⠉⠉⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣄⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠐⠠⣀⡀⠀⠀⠀⠀⠀⠈⢉⠩⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠳⡀⠀⢇⠀⠈⡄⠀⠉⠛⠒⢂⣢⣤⣴⣿⣤⠾⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠀⠀⠀⠀⠀⡆⠀⠀⡠⠔⠒⠶⣦⣽⡄⣀⡼⠤⠼⡆⠀⢻⠀⠀⠀⠀⢫⣝⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠣⠈⢳⣄⠀⠀⠀⡀⡀⠀⠀⢀⠈⠀⠈⣿⣷⠁⠀⢀⡜⢻⡄⠸⡆⠘⣆⠀⠀⡙⢾⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢹⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⣸⣾⡏⠳⠶⠿⣦⣴⡿⢄⠀⠀⠈⠉⠉⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠀⠀⡰⠃⠙⠿⢥⣶⣾⣿⡿⠃⠀⠱⠈⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⠾⠁⠁⠀⠀⠀⠀⢀⠆⠀⢠⠃⠀⢸⠆⠀⠀⠀⡀⡰⠁⠀⠀⠀⠀⠈⠩⠉⠀⠠⠂⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⢸⡃⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠊⠀⠀⠀⢸⠃⠀⠀⠀⡜⠀⠀⠀⠀⢀⠔⠁⠂
⣄⢀⣀⣀⠠⠶⠓⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠨⠀⠀⠀⠀⠀⢸
⠘⢏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣤⣶⣼⣷⡇⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠠⠃⠀⠀⠀⠀⠀⢬
⠀⠀⠑⠒⠤⠤⠤⠤⠤⠴⠟⠛⠢⠶⢼⢿⣿⣿⡇⠀⠀⠀⠀⠀⡠⠋⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣿⡟⠦⠀⠠⠔⠊⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣀⣀⣀⣀⡄⠐⠋
⣿⣿⡿⠻⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠘⢄⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⡀⠀⠀⢀⠎⠀⠀⠀⡀⠀⠆⠀⣀⠄⠊⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⣤⠃⠰⣦⠀⣸⣿⣤⡘⠈⢀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣷⣦⣄⢀⣼⣿⣧⣿⣿⣿⣷⣾⣿⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣿⠈⢻⣿⣿⡟⣿⠟⣿⣿⡿⠁⢿⣧⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⢸⣿⠋⢠⣿⣆⠈⢻⣷⠀⠘⣿⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠸⣷⡀⣿⣿⣿⢀⣼⠏⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡛⠶⣬⣻⣾⣿⣷⣿⣵⠞⠋⠀⠒⠒⠒⠒⠒⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠉⠀⠀⠀⠀⠀⠉⠙⠻⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢷⡄
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣿⣧⣄⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣀⣀⣀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠈⣿⣿⠙⢿⣷⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣾⣿⠿⠿⠛⠛⠛⠛⠿⢿⣿⣶⣤⣄⡀⣸⣼⣿⢃⣠⣿⡿
⠀⠀⠀⢈⡀⠀⢀⣀⣤⣼⣿⣷⣶⣶⣶⣤⣤⣀⢀⣠⣶⣿⡿⠋⠁⠀⠀⢲⣄⠀⠀⠀⠀⣀⣀⣭⣿⣿⣿⣿⣿⣿⡿⠟⠛⠷⠦
⠉⠙⢿⣶⣶⣾⡿⠿⠛⠋⠉⠉⠉⠉⠉⣙⣿⣿⣿⣿⣿⣽⣷⣤⣤⣤⣤⣼⣿⣶⣾⣿⣿⠿⠿⠛⠛⠉⠻⡇
⠀⣴⣿⣿⣯⣡⡀⠀⠀⢀⣀⣠⣴⣾⣿⠿⠛⠉⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁⠘⣿⡇⠀⠀⠀⠀⠀⡈
⠀⣿⣿⣈⣻⣿⣿⣿⣿⠿⠿⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⠀⠠⠁
⠀⠈⣿⣿⠿⠿⠛⠋⠑⢄⠀⠀⠀⠙⠻⠶⠖⠀⠚⠛⠓⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀⣴⣿⣿⣶⡶⢛⢋⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣿⣷⣶⣿⣿⣷⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣭⣶⣾⣿⣶⣦⡀⠀⠀⠀⢠⠁⠉⠛⣿⡱⠄⠈⢻⣿⣏⣹⣿⣿⣿⣅⣤⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠁⠀⠛⠛⠛⠁⠀⠀⠀⠈⠀⠀⢀⡝⢿⣶⠾⣿⣿⣿⣴⢻⣱⣿⠀⣨⡭⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⣛⡚⣻⣿⣿⣿⣦⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠂⠀⠀⠠⠀⡀⠀⠈⠉⠉⠙⠛⠛⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⢀⠐⠦⣤⣀⠀⠀⢀⣤⣈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠿⠟⠛⡻⠃⠀⢸⣦⡀⠀⠀⠀⢀⠃⠀⠀⠠⢤⣄⣰⠀⠀⣀⣸⡄⠀⡄⠀⠀⠀⢖⠛⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠋⠳⣆⠀⠀⢈⠁⠀⠁⡀⠀⠈⢿⣷⠁⠀⡠⢿⡀⠷⠐⢄⠀⠘⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣴⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠀⢀⣿⣏⠳⠾⣧⣴⡗⢀⠀⠀⠀⠀⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠉⣻⣿⣿⠀⢀⣀⡤⠐⠃⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢰⠃⠈⣻⣚⣿⣿⠟⠀⠀⠃⠀⠠⡀⢈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⠇⠀⠀⣠⣿⡿⠯⠊⠉⠉⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢸⠀⠀⠀⢀⠃⣀⣾⣿⣿⡟⠁⢠⣾⣷⣤⣀⣀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡿⠏⠀⣤⣾⣯⡥⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⢸⠀⠀⠀⠌⠀⠀⠉⠙⠟⣠⣦⠀⠈⠛⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⢀⣴⡏⠀⢀⣴⡎⠀⠀⢸⣄⡀⠀⠀⠠⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣉⠀⠀⠀⠀⠀⢀⣀⡀⠀⢦⣷⣿⣇⢸⣿⠀⢠⣿⡿⠁⠀⠰⠉⢿⣿⣶⣤⡶⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠉⢳⡖⠚⠋⣩⣿⣿⣿⣿⣛⢿⣿⣸⡏⢀⣿⠟⠁⢀⠔⠀⠀⠸⣿⣿⣿⣿⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⣿⠃⢠⣾⣿⡿⠋⠉⠀⠈⢻⣏⡈⠁⠁⠀⣀⠄⠈⠀⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣴⣿⠏⠀⢸⣿⠋⠀⠀⠀⠀⢀⣾⣿⢟⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣼⣿⠁⠀⠀⣸⠇⣠⣤⣶⣶⣾⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⡇⠀⡰⢀⡿⣸⡿⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⠇⣼⠇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣡⢏⣼⡟⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠒⠒⠒⢚⣋⣽⣿⣿⣿⡿⠋
⣀⣀⣈⣙⣛⣿⣿⣿⣿⣿⣟⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣾⣆⠀⣼⣿⣿⣿⣄⣴⣿⣿⣿⣿⣷⠀⠀⠀⣀⣀⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⣿⣿
⠀⠀⠀⣿⣿⣸⣿⡟⣿⣿⣿⣿⡿⠋⣿⣿⣿⠀⢠⣾⣿⣿⣿⡆⢀⣼⣿⣿⣿⣿⣿⡇⣠⣴⣾⣿⣷⢰⣶⡆⠀⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡇⢻⣿⣿⣿⠃⢠⣿⣿⣿⢀⣿⣿⣯⣿⣿⠃⠻⣿⣿⡏⠀⠀⢈⣾⣿⡿⠋⠁⠀⣾⣿⡇⢀⣿⣿
⠀⠀⠀⠸⣿⣿⣿⡇⢸⣿⣿⣿⠀⢸⣿⣿⣿⢾⣿⣿⡿⠛⠁⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⣿⣿⡆⢸⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣧⠸⣿⣿⣿⠀⣾⣿⣿⡿⠀⢻⣿⣿⣦⣀⡀⠈⣿⣿⡇⠀⠀⠸⣿⣿⣦⣤⡀⠀⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⡀⣿⣿⣿⢀⣿⣿⣿⡇⠀⠀⠙⠿⣿⣿⣿⠂⠻⠿⠃⠀⠀⠀⠈⠻⠿⠿⠃⠀⠹⠿⠇⠈⠛⠋
⠀⠀⠀⠀⠀⠘⢿⣿⠇⠈⠛⠁⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⣤⣶⣾⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣤⣤⣶⣶⣤⡀⠀⢀⣀⣀⣀⣀⣀⡤⠔⠀⣰⣿⣿⣿⠇
⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⠾⠛⠉⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣉⣁⣀⣀⣤⣾⣿⣿⣿⠏
⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⢛⣉⣥⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡄⣀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣄⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⡉⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⣀⢤⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⢉⠀⣀⣠⡔⣠⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠙⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠉⠁⠀⠀⠀⠘⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣿⠃⠀⠀⠀⠀⠘⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠻⣿⣿⣿⣿⣿⡏⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣜⣿⣿⣿⣿⠇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⢸⡇
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠸
⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡀
⣿⡀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⣿⣟⣦⡀⠑⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀
⣿⣿⣿⣿⣤⣴⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⣾⠃⢀⠀⢠⣤⢀⣤⡄⢀⠀⢀⣄⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⢀⣼⠃⣰⠏⢀⣿⠁⣼⠃⣴⠏⢰⠋⣸⡏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣡⡞⢹⡧⠊⠛⠂⣰⡟⢁⣿⠈⠳⠂⠉⠉⡟⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠊⣸⠏⢠⠇⢠⡆⢀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⢁⡀⠁⢀⡟⢀⡾⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⣾⠟⣱⠏⠀⠀⡾⢁⡾⣳⠀⣞⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠃⠀⠉⠁⠀⠀⠉⠈⢱⡏⠀⠀⢀⠤⠀⠀⠀⣰⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⢀⡖⠀⣤⣀⢀⣤⡈⣀⠀⣠⡏⣾⢀⣤⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⢿⡟⣠⣟⡁⣾⡟⠁⣿⠈⢠⡿⢠⡟⣼⢣⡾⢁⡾⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣿⠜⠁⡨⡀⠛⠀⠀⠉⠀⠘⢃⡟⠀⠈⣾⠁⠸⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡼⢑⡀⠀⣠⣀⠀⢀⣴⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⡟⡹⢲⡟⠁⠀⣸⠇⣸⠏⠀⣠⠆⣠⠄⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠘⠊⡁⠈⣀⠀⢠⠏⣰⢟⡆⣸⡋⠐⠿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣼⠁⠀⠈⠁⠈⣾⠑⠀⢀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣰⠇⡘⢲⡟⣰⠇⢰⡏⠀⠀⢠⡿⢒⡾⠇⣠⠟⢃⡾⠁⣰⡆⣴⠂⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠔⠀⠈⠁⠛⠀⠸⠂⠀⠀⠿⠃⠈⠓⠀⠛⠂⠘⠓⠀⠿⠰⠟⠁⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⢠⡴⠀⣀⡀⠀⢀⣀⠀⢀⣤⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣹⡷⣿⠃⣠⡟⠊⣰⣿⠛⢱⡟⠛⠠⣾⢋⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢱⠏⣼⢃⠜⠙⠓⠁⠿⠃⠀⠸⠗⠀⠀⠙⣩⡿⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠰⠂⠀⠀⠀⠀⠀⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⢰⠀⠀⠀⢰⠀⠀⢠⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⢀⠐⣀⡸⠁⠀⠀⡘⠃⠀⠀⠀⣀⠀⠀⠈⠷⠀⠀⢠⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠆⠀⠀⢸⣀⢁⠁⠀⠀⠀⠁⠄⠀⠀⠀⡽⡇⠀⠀⢠⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⢆⡇⠀⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⢎⡵⠋⠀⠀⠀⠀⢀⠞⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠃⢈⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⡸⠔⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠄⠀⠀⠀⢄⠻⠀⠀⠀⠀⠴⠀⠀⠀⢆⡀⠀⠀⠀⠀⣀⠀⢠⡄⠀⠀⠀⠀⠀⠇⡇⠀⠀⠀⡇⠀⣷⡀
⠀⠀⠰⠘⡀⠀⠀⡸⠅⠘⠀⠀⠀⠈⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⣴⡧⠧⡖⠴⠆⠀⠀⢰⡇⠀⠀⠀⢤⠁⣸⣅⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠤⣀⡀⣠⠀⢀⡄⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡬⣿⠀⠀⠀⢸⡉⠋
⠀⠀⠀⠀⡱⢿⣿⠷⣴⠮⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡝⣿⡗⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⡉⠲⣈⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⡇⠀⠀⠀⡇⠀⠀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⢈⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠁⠄⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠔⢩⠘⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢱⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢧⠀⠀⠀⡐⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⣇⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⡁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⠟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⠌⠀⢤⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⣉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠠⠰⠗⣼⣧⡀⠊⠀⢀⡒⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣇⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠙⢫⡋⠛⠃⠀⡤⠈⠁⡗⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠓⢀⠀⠀⠀⠷⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠤⠤⠈⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⡄⠠⢦⠀⠀⠈⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⣴⣄⢆⠀⠀⠀⠢⠀⠰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢣⠐⡇⠀⠀⣀⡀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⢢⢰⠀⠖⠀⢸⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⡨⠐⠂⠀⠀⠩⢣⣄⠈⣷⡘⢧⠀⠀⠀⠀⠀⠘⢧⡤⠌⠰⢷⣄⠠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡌⠀⠀⠀⠄⠀⠀⠈⠉⠷⣬⣷⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡂⢀⠄⠀⢿⣳⣴⠀⠀⠈⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠠⢊⠤⠀⠻⢿⠞⠄⠀⠀⠒⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣤⣘⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠷⠆⣠⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠚⢿⢿⣿⣿⣿⣿⠄⠀⠀⠀⠀⢀⣀⣤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⠉⠀⢸⣿⣿⣅⠉⠀⠀⠀⠀⠀⠀⠙⣮⡌⠀⢛⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣴⣶⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣿⠀⠀⢺⡿⢶⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢋⣿⣿⣿⣿⡿⠻⣿⣿⣿⡄⠀⠀⠀⠀⠈⢿⣿⣶⣾⠧⣿⠏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⠻⣿⣧⣴⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣄⠀⠀⠈⠙⠿⣧⡀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣨⡿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠙⠳⠖⠒⠀⣹⣿⡿⠋
⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣼⠖⡿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏
⣀⣀⣸⣤⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣆⠞⢃⣤⣶⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣿⣿⠃
⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⣰⠾⣿⡟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⡀⣀⣀⡤⣊⣾⣿⣿⡏⠀⠐
⠀⠹⣿⣟⣿⣄⣄⠀⠄⢾⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⡤
⠀⠈⠸⣿⣿⣿⣿⣶⡀⠘⣿⣿⣿⣿⣛⣛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⡿⣃⡀
⠀⠀⠀⠈⠙⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧⣠⣸⣯⣿⣿⣿⡿⠋⠠⠾⠿⠟⠋⠉⠈⡾⠛⠁
⠀⠀⠤⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣎⣹⣆⡀⠠⣀⠀⠀⢀⠈⠀⠿⢇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠿⠻⠛⠿⢿⠿⣿⣷⣍⡉⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⡋⠀⣡⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠄⠙⠿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣏⡛⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⠉⠀⠀⠈⠉⠉⠉⠉⠓⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡐⢌⠢⡣⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢒⣕⣮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⣉⠉⠉⠉⠉⠉⠚⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠉⠂⡄⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀⠀⠀⠀⠀⢀⡴⣸⡆⠀⠀⠀⢀⡼⠁⢰
⠀⠀⠀⠀⠀⠊⠁⣀⡀⡤⠄⠀⡀⠀⠀⡘⠀⠀⠲⢄⠀⠀⠀⠀⠀⢐⠀⣹⡀⠀⠀⢠⣿⡵⢁⢇⠀⠀⣠⠞⠁⢠⠃
⠀⠀⠀⠀⣆⠀⢠⢋⡼⠔⠒⠊⠃⣠⠖⠒⠒⠀⠀⠀⠉⠒⣒⣢⠾⠋⢀⠝⠡⠀⠀⣿⡧⣣⠎⣈⣤⡾⠋⠀⡴⠁
⠀⠀⠀⠀⡝⢧⢀⠎⠀⣠⠖⠁⣴⠗⠛⣩⠛⠉⠚⢛⡛⠋⠉⠀⠀⢀⣤⠴⢧⠀⠀⣿⣷⡷⠚⢻⡿⠀⣠⠊
⠀⠀⠀⡐⢱⡏⣾⣰⡿⢓⣡⠞⢁⠄⣰⠃⢀⡴⣊⣥⣤⣤⣄⣀⣀⡀⠀⢀⠜⠀⢀⡞⡉⠨⢸⠈⡿⠛⠁
⠀⠀⠀⣇⢿⢿⡛⠛⡳⣭⣶⣾⡵⠞⣡⢴⡫⠊⠁⠀⠈⠑⠂⠤⠤⠐⠒⠁⠀⠀⢸⢰⠀⠀⠈⠀⡇
⠀⠀⠀⢫⡪⣶⣯⣤⡄⠻⠞⠒⢂⣚⡧⠭⠭⠭⠄⠀⢈⣙⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢆⠀⠀⡄⡇
⠀⠀⠀⠀⠘⣻⠿⠛⣁⠀⠀⠀⢠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⢂⠀⢀⠃
⡀⠀⠀⠐⠬⠥⠒⠉⢩⡀⠠⠤⠞⠀⠃⠤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈
⠀⠐⠃⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⡅⡗⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣠⣄⣴⣾⣳⣟⣾⢧⡄⠀⠀⠀⢀⣀⠀⠀⠀⡠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣥⣀⠀⠀⠘⠻⢿⣿⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣯⣿⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢆⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⣾⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣃⢰⠟⠘⡇⠸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡘⢣⣠⣇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⠘⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠩⣙⢿⣿⣶⣿⡵⢫⣼⡇⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠉⢀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⡀⢰⡇⠀⢀⡜⠢⢻⣿⣿⢠⡶⣾⠃⠀⠀⠀⠀⢀⡾⠉⠀⠀⣀⣤⣶⠇⣸⠇
⠀⠀⠀⠀⠀⢠⣞⣡⡞⠳⡈⠙⠻⣏⠐⡏⠀⠀⠀⣿⣿⠋⠰⣌⢳⡀⠀⠀⢀⡾⠁⡤⠒⠾⣍⡉⠁⣰⠏
⠀⠀⠀⠀⠀⠈⣯⡙⢧⡀⠘⡄⠀⠈⢷⠀⣾⡆⢠⣿⠡⡄⠀⠙⠈⢹⡆⢀⡾⢁⡔⠀⠀⠰⠠⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⠶⢖⣶
⠀⠀⠀⠀⠀⠀⠸⣿⣟⢷⣄⠿⢄⡀⠘⣇⠉⠀⢸⢿⡄⠀⠀⠀⡄⢸⠀⡼⣁⡞⠀⠀⠋⡰⠁⣰⠏⠀⠀⠀⠀⣀⣤⡖⠛⠉⠁⠈⢉⣠⠖⣹⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⢱⠀⠀⠉⢢⢹⣤⡌⣾⢸⠿⣶⠂⡀⠂⣿⣼⣡⣽⠴⠞⢷⡔⢁⣼⠏⠀⢀⣠⡴⠟⠉⠀⣸⠷⠒⠀⢈⣿⣆⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⢌⡆⢿⢠⡏⣿⡆⢾⠀⠀⢠⣿⠋⡝⠀⢀⡌⠀⢳⣿⣟⣤⠶⣛⡵⣂⡤⠄⠈⠀⠀⠀⢀⡼⣋⡵⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⠀⠂⠸⡘⠘⣿⣁⣿⡵⠻⡄⠀⣿⠇⠈⣀⣴⣾⠀⠀⠈⣟⣫⡵⣿⡿⠞⢉⡤⢂⠠⠀⠔⣀⡼⠞⠁
⠀⠀⠀⠀⠀⢸⡟⢥⣴⣶⡮⠛⠇⢀⡀⣷⢨⣿⣼⡇⠀⢀⡧⢠⡟⡰⠚⠿⣯⡇⢀⡀⢴⣿⡿⠋⣀⣠⣀⣀⣀⣀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⣷⣀⠈⢿⡁⠀⠀⠌⠻⣿⡟⣿⣿⠇⡷⠊⢀⣿⠔⠀⠀⠀⢠⠋⣩⣠⡯⠿⣞⣻⣿⠁⠀⠀⣀⢄⡿⠁
⠀⢀⣀⣀⣀⣀⣀⣙⣳⣄⣙⣦⣔⣧⣤⣮⣛⣽⣿⣀⣿⣇⣿⣏⣀⣀⣀⣠⣦⣾⣥⣶⣶⣶⣷⣎⣹⣁⣴⣊⣠⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣤⢤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠠⠐⣌⢳⡇⢮⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀⢹⡀⢥⡈⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢁⡘⡇⢨⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣥⢠⡀⠁⠚⠀⡄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣠⢃⡾⠉⣽⣿⣯⣙⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡟⢩⠀⡎⠀⠀⠈⢿⣿⡣⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣇⠀⠀⠀⠔⣼⡇⠀⠀⢀⠆⣨⠙⠀⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠣⠚⠁⠃⠀⢠⠋⡠⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⠀⠀⢠⠀⠀⠀⠀⡼⢾⠠⢺⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⣄⠙⠒⠀⢀⡞⢀⣧⠳⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢘⡆⠀⢀⡞⠀⠀⠉⠙⢃⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣼⠁⠀⠀⢀⣴⢖⠘⠫⢘⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠙⢦⣤⣴⣿⠇⠀⠀⠰⣀⢪⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⣼⠿⠳⣇⣉⢀⢁⣬⡻⡾
⠀⠀⠀⠀⠀⠀⠰⠀⠈⠄⠀⠀⡸⠁⠀⠀⠀⠀⣴⡛⠦⠌⠃⣂⣩⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣋⡁⢃⣸⣬⡿⠿⣿⣏⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠔⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⣷⣙⣧⠚⡟⢃⢌⡀⠝⡱⢈⠟⠵⢲⠶⣤⢤⣴⣶⣿⣿⣏⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⣴⣷⣮⡟⣦⣍⣶⣤⢣⣌⣴⣭⢦⡍⣰⣿⣿⣿⡋⠁⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⠉⠉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠃⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣦⣤⠤⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣴⠔⠉⠳⣷⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡠⠴⣦⣭⡵⣶⣿⣵⡴⣛⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢯⡛⠒⠲⠶⢿⣆⢴⡿⠛⢉⡙⠆
⠀⠀⠀⠀⠀⠸⠳⢥⠀⢀⣤⠞⣣⣾⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⡰⢄⠀⠀⢀⠜⠻⢦⣤⣀⣤⣿⡟⢾⡢⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠃⢰⣿⣿⣿⣿⡟⠁⠀⡘⡿⣿⣶⣄⠀⠙⣿⣧⣔⡘⠉⠠⠊⢍⠉⠉⢁⣠⣴⣇⢿⡦⣄⣀⠠
⠀⠀⠀⠀⣀⠀⠀⠀⠠⢤⣀⣸⣿⣿⣿⣿⣧⣶⢂⣭⣅⣉⠉⠉⠁⠀⠘⣿⣿⣟⣦⢤⣾⣿⣿⣿⣿⣿⣛⠗⢳
⠀⢀⡞⠋⠉⠙⠳⢦⣤⣤⣾⡿⠏⠙⠛⠟⠛⠉⠉⠉⠙⢋⡻⠃⣈⣩⠟⠓⠲⡖⢻⣿⣿⣽⣿⣿⣽⣿⣮⠞⠙⠓⠃
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠎⠛⠛⠛⠓⠊⠉⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡠⢦⣽⣦⣿⣾⣿⣿⣿⣷⡿⣿⡶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⣟⣷⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢏⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠛⠀⠀⢹⠃⣽⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣇⠘⢷⣄⡠⣷⣿⣿⢿⣿⡿⠿⠟⠉⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠆⠀⣉⠻⣷⣟⣇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣸⡷⠛⠻⣯⡉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠋⢙⣦⣴⠋⠀⠀⢀⣸⣷⣦⡴⣶⣴⣾⣷⣶⣶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣤⣤⣴⣾⣿⣿⣶⠾⠿⣻⠛⠛⠻⡷⣿⡉⠈⠀⢸⣏⠻⢮⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⡋⢁⣤⠿⠋⢃⣿⡙⠳⢶⣁⣀⡀⢀⣀⣬⢱⣾⣾⣿⣟⣦⠸⡁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣱⠞⠁⣠⡴⣏⠀⢳⡀⣀⣽⣶⣿⣿⠿⠟⠛⠉⠀⠈⢿⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⣴⣾⣁⣀⣿⣤⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣠⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⠟
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠟⠁
⠀⠀⠈⠙⠻⢿⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠦
⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠠⠤⠤⠤⣶⡒⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠓⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮
⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣰⣖⠀⢰⠂
⠀⠀⠀⢀⡷⠆⣴⡆⠀⠀⠀⠀⠀⠙⡄⠀⠀⣀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢖⠀⠈⣿⡀⠐⢾⠀⠀⢀
⠀⠀⠀⣿⡟⢠⣿⠿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⢸⡅⠀⠀⠀⠀⠀⢰⣾⢠⣴⣿⡅⠀⠀⠖⣢⠋
⢳⡄⢠⣿⠃⣼⣿⡣⠛⣦⠀⠀⠀⠀⠀⠀⣿⢟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠘⣿⣌⠁⠀⢰⣿⠙⠲
⠁⣄⡈⢻⣿⣿⣅⠀⠀⠈⠂⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠴⣿⣿⣴⣿⢿⢠⠀⣸⣿⡷⠤
⣾⡷⣀⣽⠉⠻⣿⢀⣦⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡇⠀⠀⠀⠀⠈⡀⢰⡒⢻⣟⣿⡽⠈⢡⡀⠠⡄⠁
⠀⠖⢢⣿⡉⣀⢻⣯⣿⡇⠀⢀⣤⣾⣿⠟⠛⠿⠿⠓⠂⠂⠐⠀⢀⡈⠒⠙⢺⡏⠉⢻⣄⣿⣯⣤⣷⣄
⣴⣷⠛⠉⢁⢁⣾⣄⡙⠃⢀⣼⣷⣦⡿⠷⣂⣀⣀⣠⣀⠠⠀⠀⠸⣷⣬⣇⣿⣷⣤⠀⢈⠁⠀⠈⠉⠻⣦
⣿⡅⠀⠀⠙⣿⣿⣿⣿⠿⣴⣿⣿⠗⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⢠⣾⣿⣾⣏⣼⣿⣾⣿⣆⡏⡀⡀⢀⠈
⣿⣷⠃⠀⡄⢸⣿⣿⣷⣾⡛⣿⣿⠁⣴⣆⠀⠀⠀⠀⠀⠀⠀⠑⣾⣿⢷⣿⠙⣿⢿⣻⣿⣿⣿⢐⢳⡿
⣿⡟⠁⣾⡇⠀⡒⠩⣿⣿⣿⣿⣟⠀⢻⣾⣆⠀⠀⢲⣶⣶⣶⣿⣿⣿⡟⠉⠉⠳⣼⣿⣿⡏⣿⡘⠈⢠⡞
⣿⣷⠀⠈⡙⠀⠈⠀⠙⠛⢿⣿⣷⡄⠀⠛⡻⢇⡑⢤⣿⣿⣿⣿⣿⣿⠃⠀⣗⢀⣿⠇⠀⠉⠈⣿⣦⡌⠙
⣿⣿⣷⢸⣇⠀⠘⠧⠤⢄⠀⠉⠃⠂⠀⠀⠀⠀⠀⠈⢉⣾⣿⣿⣿⡏⠀⣰⣿⣿⣯⣴⣿⣦⡀⢹⡅⠹⡑
⠙⠛⠛⠛⢿⣿⡏⠀⠴⣄⡉⣉⠀⠀⠤⠄⣀⣤⣴⣶⣿⣿⡿⠿⠚⠀⢴⣿⣿⣿⣿⠿⢶⣔⠈⠻⢯⣀⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⠿⠿⠛⠛⠓⠀⠙⠛⠻⠛⠛⠛⠙⠛⢹⣿⡟⠂⠲
⠀⠀⢀⠔⠋⡹⠯⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠀⠀⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠀⠘⠆⢀
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣦⠄⠀⠛⠃⠰⠦⣶⣇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⣾⠀⡎⠀⠀⠀⠀⠀⢀⣄⣿⠆
⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣀⣤⠄⠀⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⢀⣀⣀⠀⢀⡀⠀⠀⠈⠸⡄
⠀⠀⠀⠹⣿⣶⢄⣠⡤⠒⠒⠻⠿⠟⠿⠿⠓⠂⠀⠀⣤⠖⠋⠉⠀⠈⣿⣿⠉⠙⠿⠟⢿⣿⡗⠀⠀⠈⢀⡄
⠀⠀⠀⠀⢻⣝⢾⡟⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠻⠆⠀⠀⠀⠹⠿⠦⠀⠀⠀⠈⠻⣧⣴⣾⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢡⣾⣿⣟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⣿⣿⣿⡏⠛⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⣾⣧⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣄⠀⣀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣍⡉⢸⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠿⠛⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢤⠈⡇⢻⣸⠃⡴⠆⣶⠄⣶⢴⢴⠄⡰⣦⢰⡄⡙⢦⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠷⠀⠻⠂⠳⠀⠻⠀⠻⠸⠘⠎⠓⠓⠘⠇⠳⠊




⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣭⣟⣿⣾⡄⢠⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠩⢩⣷⡠⠤⠿⣧⣀⣙⣪⣥⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢾⡿⡟⢶⣟⡋⠉⠻⣿⣨⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡆⠀⠀⣀⣷⣤⣝⠋⢷⣦⣸⡭⠺⢿⣶⡄⣀
⠀⠰⠷⠑⠂⠀⠀⠀⠀⠸⠈⣿⠁⠀⠀⠉⠉⢙⡟⣿⠿⠯⡉⠙⢺⣿⣍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣿⣿⠷⠀⠀⠐⠀⠘⠀⣻⣄⠀⠽⣯⣽⣯⣉
⠀⠀⠀⠀⠀⠀⢀⠀⡁⣨⡻⣯⣻⣷⠄⠀⢈⡀⠀⢹⣿⣦⣤⠋⠙⠻⡳⢄⡀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⢩⡿⡿⠙⠆⣁⡾⢷⣤⣜⣯⣍⠉⠒⠂⠀⠈⠐⠓⠁
⠀⠀⠀⠀⠀⠀⠂⠀⣾⠀⠘⠀⠀⠀⠀⠈⣀⡠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢶⠃⠀⠀⡬⣤⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠰⠁⠻⠀⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠙⣴⡀⠀⢠⠀⣀⢐⣐⠂⠬⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠄⠀⠀⠀⠀⠀⠠⣀⠀⡀⠀⠀⠀⠘⠋⠉⠀⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⢣⣤⡴⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⠂⡀⠠⢀⡀⠀⠀⠀⠿⠛⠙⣿⣠⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠱⣀⡌⠀⠀⢀⠠⠃⠀⠀⣻⠿⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠄⠀⠀⠈⠋⠒⠉⠃⠀⢀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠳⣆⡀⢀⣀⠀⢀⡠⣀⠵⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠈⠈⠁⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿