Andesite Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠶⠶⢶⣾⠶⢶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⡛⠿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠉⠀⠁⠈⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⡿⠿⠿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⢀⣠⣤⠴⠶⡾⢿⣿⠿⠛⠉⠛⠋⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣤⣼⣿⣿⣿⡟
⠀⠀⠀⢠⣿⠉⠀⠀⠊⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠻⣆
⠀⠀⠀⣿⣿⢷⣤⡀⠔⠀⠀⠀⠐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⣽
⠀⠀⢼⣿⣿⣻⡿⢟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣿
⠀⠀⣾⣿⣿⣿⡟⠋⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⣴⣶⣶⣿⣿⠟⠁
⠀⠀⢹⣿⣿⣷⡶⠛⣹⡇⠀⠀⠀⠀⠀⠀⢠⣞⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣤⣬⠁⠀⠀⠀⢈⣭⣽⣿⣿⠁
⠀⠀⢸⣿⣿⣿⡶⠋⣹⡇⠀⠀⠀⠀⠀⠀⠀⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⢀⣴⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠹⢿⣿⣧
⠀⢀⣿⣿⣿⣯⣶⠟⠁⣿⡀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠛⠛⠋⠋⠉⠉⠐⠛⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⢸⣿⣿⣿⣻⣍⣠⠶⢻⣿⣶⣾⣿⣷⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠶⠀⢹⣿⡇
⠀⠀⣿⣿⣿⣿⠛⠁⠀⣈⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠘⠛⠁⠀⠀⢀⠀⣀⡀⣈⣿⠇
⠀⠀⣸⣿⣿⣿⣶⠶⠛⠋⠉⣻⡿⠁⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿⠋
⠀⣠⣿⣿⣿⣿⠷⣀⣤⣶⣛⣭⠷⣄⡀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣾⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉
⣰⣿⣿⣽⣷⣿⣿⣟⣻⣯⣿⠶⠾⣛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣾⣿⣿⠿⠛⠉
⣿⣾⣿⣯⣿⡿⣿⣛⣯⡭⣶⣞⣛⠉⠀⠙⣧⡀⠀⢠⡄⠀⠀⠈⠉⠀⣀⣤⣬⣿⣿⠿⠛⠉
⣿⣿⣿⣿⡿⣟⣻⣿⣶⣿⣯⣭⣠⣤⠶⠶⣻⠟⠀⠀⠀⠀⣁⣀⣴⣶⣿⡿⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣋⣤⣤⣤⣾⠀⣠⣴⣤⠾⣿⡿⠟⠋⠁
⠸⠿⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡴⣶⣿⣞⣿⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠋⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⣷⠀⠀⠀⠀⠀⠀⢠⡒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢂⡞⠂⠈⠉⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠺⠀⢤⠄⠄⢀⡤⢰⠃⠔⡐⢀⠜⠀⣠⠀⢀⡜⣀⠉⠁⠀⡠⠊
⣄⣀⣀⣄⣀⣄⣀⣀⣀⣠⣤⣀⣄⣤⣥⣤⣆⣅⣀⣈⣈⣄⣦⣈⣶⣉⣶⣧⣔⣉⣈⣡⣱⣆⣥⣉⣡⣴⣀⣁⣤⣄⣀⣀⣀⣄⣀⣠⣄⣀⣀⣄⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣿⣯⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣿⣿⣿⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⡀⢠⠂⠙⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣿⣿⣿⣷⣯⣤⣴⣿⣿⠟⢿⣿⣿⡏⠉⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣷⡤⢦⣿⣿⣿⣾⣧⠀⠁⢄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣿⣿⣏⠀⠌⠁⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠂
⠀⠀⠀⠀⣸⡿⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠠⠀⣾⣿⣟⣿⡏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣧
⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣤⣦⣾⣿⣿⡇⣿⣧⡇⠀⢨⣿⣿⣿⣿⣿⣿⣟⢙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢰⣿⣽⣿⡿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠃⠀⣾⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⡇⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⣿⡟⠻⣿⣿⣾⣉⣿⣿⣿⣿⠟⠋⠉⠻⣿⣿⣿⣿⡿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣶⣬⣽⣿⣿⣿⣿⣧⣄⡀⠲⠄⠀⠈⠛⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⡟⠙⠛⠙⠟⠟
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠻⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣦⣦⡤⠤
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⢧⠘⣿⣿⣿⣷⡄⠀⡀⢀⡀⠀⠀⠀⢹⣶⠶⠾⡾⠿⠾⠶⠿⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠳⠈⠹⠨⠩⠲⠁⠙⠄⠈⠇⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣇
⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣸⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢻⡿⠿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣻⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠛⡻⠿⠋⡙⠛⡛⢛⡫⠏⠉⠉⠹⠟⣡⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡛⡋⣦⡀⠿⣶⢆⢀⡶⠦⠿⠛⠂⠀⠄⠃⠒⠛⠿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠃⠉⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣽⣭⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣯⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠚⠋⢀⡼⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⣿⣿⣶⣶⣤⣀⡐⠡⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣠⣯⣿⣿⣿⣿⣿⣿⠁⢻⣤⣤⢼⣾⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣟⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⢿⣿⣯⣯⠿⠾⠿⠃⠙⣯⣿⣓⢈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⢿⣧⣷⣶⣩⡛⠋⣥⣴⣶⣦⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣼⣿⣷⣦⣾⣿⣿⣿⣾⣿⣟⠻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⢿⣿⣇⣹⠟⢻⠛⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⢻⣶⣊⠉⠾⠞⣿⣿⣿⣷⠞⣿⣷⣶⣿⣿⣏⣰⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⢿⠙⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣻⣿⣿⣿⣿⣽⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠟⠿⢿⡏⠽⣿⡿⠿⠋⠈⠉⠉



⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡦⢤⡾⠀⠀⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠻⠼⢉⠀⠁⠠⡜⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠀⠂⢀⠀⠀⠀⠀⡤⣭⡼⡂⠀⢴⢠⡀⠈⣻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠴⡀⢀⠿⠖⡀⠠⠀⠀⠈⠀⠀⠀⠁⠀⠈⢠⣽⣿⣿⣫⠻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⣤⠮⠄⡀⠄⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣖⣀⣁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣒⣶⣾⣿⣿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠿⠿⣿⣿⡿⠿⠿⣿⡿⠿⠿⠿⢿⣿⠿⠿⠿⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠒⠛⠻⠟⡿⠿⠿⠿⠿⠿⠟⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣶⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢨⣽⣦
⠀⠀⠀⠀⠀⠀⣠⠴⠖⣺⠻⠟⠋⠉⠛⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⠀⠀⠀⠀⠀⠈⠉⠠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⢰⣿⣄⡀⠐⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠈⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⣠⡟
⠀⠀⠀⠀⠐⣿⣿⣿⣥⢿⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠘⠃⠀⠀⠈⠛⠀⠀⠀⠀⠀⣠⣀⣄⣰⠆⠀⠀⠺⣿⣿⡿⠋
⠀⠀⠀⠀⠀⣿⣿⣯⢞⣿⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⢀⣠⣾⣿⣿⠟⡉⠀⠀⠀⠘⢻⣿⡇
⠀⠀⠀⠀⣸⣿⣿⣿⢋⣹⣧⣀⣠⣄⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠈⠁⠀⠀⠀⢀⡘⢿⣷
⠀⠀⠀⠀⠸⣿⣿⡿⠋⢁⣿⣿⣿⠿⠛⠋⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠿⠂⠀⠀⢈⡁⣸⡿
⠀⠀⠀⠀⢀⣿⣿⣷⠞⠋⣉⣿⡃⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⣀⣠⣴⠶⠶⠾⠿⢿⡿⠟⠁
⠀⠀⠀⢠⣾⣿⣿⣿⣶⣿⣷⣿⡽⢦⡀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⠛⠉
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⣿⣾⠛⠉⢻⣄⠀⣤⠀⠘⠛⢀⣤⣼⡿⠟⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⢖⠛⣹⡏⢀⣀⣠⣤⣾⠿⠛⠁
⠀⠀⠀⠸⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠒⠒⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⡾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦
⠀⠀⠀⠀⣀⣀⡤⡤⢶⠶⠟⠛⠋⠛⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣴⣾⣿
⠀⠀⢀⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢧
⠀⠀⣸⣿⣒⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸
⠀⢀⣿⣽⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠞
⠀⠘⣿⣾⣭⠄⠊⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣀⣄⣀⠀⠀⠀⠀⠈⢋⡛⡟⠁
⠀⢀⡿⣿⡧⠀⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠶⡇
⠀⣸⣿⣽⡷⠈⠁⢠⣄⠀⣀⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⡄
⠀⢹⣿⣤⠴⠒⠀⠈⣿⣿⢿⠟⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿
⠀⠈⣿⣿⣦⡤⠐⠊⠙⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣠⣴⣶⣃⡴⠏
⢀⣼⣿⡿⣝⠀⠀⠀⠀⠐⢂⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠊⠉⠁⠀⠀⠀⠀⠈⠁
⣾⣿⡷⢿⣿⣥⠤⠒⠊⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣤⣈⣤⠶⠚⠉
⣯⢷⣿⣯⡽⢲⣂⣠⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉
⣿⣯⣿⣷⣿⣿⣿⣾⠟⢉⣀⠀⠠⠀⢀⠀⡤⣚⡾⠟⠋⠁
⠙⠛⠻⠷⠿⠿⠿⢾⣿⣿⣹⣐⣶⣆⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣄⠀⢽⣷⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⣤⣿⣷⣶⠶⠿⠿⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣟⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣏⠁⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣾⠟⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⠋⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣄⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠈⣿⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣆⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠁⠀⢻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠁⢹⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⡈⣣⠀⢠⠀⡄⠀⠰⠆⣀⢠⠤⡀⢠⠀⡶⢀⡄⡤⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠎⠀⠀⠃⠐⠀⠆⠳⠐⡆⠃⠤⠀⠘⠘⠀⠳⠘⠢⠄⠀⠀⠀⠀⠠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠉⠙⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠉⠉⠩⢓⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡚⡉⠀⠀⠀⠀⠐⠀⠀⠀⠉⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠈⢡⠿⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⢀⠀⢠⠄⡀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⢀⡤⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⡀
⠀⠀⣠⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣤⣶⠶⠾⠛⠉⠉⠀⠁⠁⠀⠈⢢⡀
⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⡄
⠈⢿⠁⡀⠠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢳
⡤⠏⠀⠀⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⢀
⠑⠲⣤⡀⠀⠀⢠⣲⣦⠖⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠁
⠀⠀⠀⠙⠳⣿⣿⣿⣿⣴⣄⡀⡀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⢀⡀⡀⠀⠀⠀⣀⡀⠀⢀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠛⠿⣾⣝⣫⣧⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢿⣿⣾⣭⣶⣾⣷⣿⡿⠟⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣿⣶⣤⣴⣤⣦⣤⣶⣤⣤⣴⣶⣾⣿⣿⣿⣿⣟⣛⣛⣉⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢀⣤⣶⠆⠄⠀⠀⠀⠀⢀⡀⠀⣠⡾⠟⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣍⣷⣿⣧⣴⣦⣤⡀⠀⠀⠀⠀⡀⠀⠉⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡿⣿⣶⣼⣣⣿⣿⣿⣿⣷⡶⣾⣿⣷⣷⣾⣎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣙⣾⡟⠩⣯⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣏⢉⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣟⡿⣿⠿⡟⢿⣤⣤⣠⣨⣟⢻⣿⡿⠛⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣟⣄⢻⣿⣿⡿⣿⣝⣠⣿⣧⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣬⣿⣯⣿⣩⡟⣿⣿⣿⣿⣿⢿⣯⣅⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢿⡿⢛⣿⣷⣿⣿⣷⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⡤⣄⣀⣠⣄⢀⣄⣀⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⣿⣿⣿⡿⠻⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣼⠟⣿⣿⣯⢛⣿⡿⣿⣿⣿⣟⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠿⣿⣿⣞⢻⣿⣿⣿⣿⣿⣯⣾⣻⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠉⢹⠉⠙⣿⣿⣏⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣶⣾⡟⢰⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣙⣿⢿⣿⣿⣿⡋⢸⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁



⢀⠀⡀⡀⠀⠀⡀⢀⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⣿⣿⢛⠿⢛⠛⢿⢟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣶⣿⢉⣿⣖⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣾⣉⣿⣶⣿⣿⢦⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣿⣾⣠⠊⣿⠋⣽⣿⣿⣆⠀⡀⣔⡻⠿⡏⣷⣷⡿⣿⣿⣿⣿⣦⣼⣿⢧⣿⣻⣾⣛⣿⠆
⠀⠀⠀⡀⣦⣄⣿⣿⣿⣿⣿⣿⡗⢾⠉⣉⣻⣿⣿⣿⠀⠰⣿⣯⣤⣿⣿⣿⣷⣻⣿⣿⣿⣿⡟⠻⡟⢿⣿⣽⡟⣏
⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣏⣿⣿⣿⣿⡇⠀⠙⣿⣈⣿⣿⣟⣿⣿⣟⣯⣿⣿⡷⣤⣭⡸⣿⣿⠿⣿⡷
⠀⢀⣿⣿⣿⡿⢿⣿⣿⡿⣿⣿⠟⠻⢟⡿⠛⣿⣿⠻⡧⠀⠀⡿⣿⣿⡿⢿⣇⣽⣿⣿⣿⣿⡐⣎⠉⣁⣿⣿⣃⣼⠃
⠀⣼⣿⣿⣿⣿⣿⣽⠛⢽⣿⣿⣦⣼⣿⣿⣷⣿⣿⣎⠻⡀⠀⠹⣟⢿⡿⣷⣿⢙⣿⠛⢻⣿⣿⣰⣯⣿⣿⣽⣿⠋
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣱⡀⠀⢿⣿⣿⡿⣛⣻⣿⣦⣾⣿⣿⣿⣜⣻⢿⣿⡏
⠈⠻⣦⣽⠿⣿⣿⣿⣿⣿⣹⣿⣟⣻⣿⣿⡟⣻⣟⣻⣿⣿⣧⠀⢈⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡿⡿⠁
⠀⠀⠙⠻⢺⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠃⠀⠈⠻⠾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠃
⠀⠀⠀⠀⠈⠉⠙⠻⠿⢿⡟⣿⣿⠿⠿⠿⠿⠛⠙⠉⠁⠀⠀⠀⠀⠀⠀⠻⣻⣿⣿⣿⣿⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣄⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠒⣭⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⣠⣦⣰⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣭⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠨⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣍⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣀⡀⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠿⠛⠉⠋⠋⠋⠛⠛⠁⠁⠈⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⣶⣎⠉⣠⠤⢄⡀⠘⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢶⣶⠿⢷⡾⣽⣉⣻⡿⠭⣉⣉⠩⣉⠙⢦⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠡⠊⣰⠋⠀⠈⢡⣾⠿⢛⣻⢦⣠⣤⣤⣀⠀⠙⢄⢃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠃⡆⢸⢠⢏⢃⣾⠟⠁⠙⠒⠲⢦⡉⢳⡄⠈⠢⠀⢳⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢴⣏⣼⠴⢊⠜⡠⣣⠏⠀⢱⢿⠀⠀⠀⠀⠀⠀⢱⡀⢣⣐⠠⢶⣈⡥⠶⣒⢲⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⣡⢴⠶⠛⢉⡴⢞⡣⠵⠚⠁⡠⣢⡿⢸⠀⢀⣤⠀⠀⠀⠀⢳⠤⠈⠩⠉⠒⠈⢁⣀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣠⢁⡏⢀⡜⠁⣰⠋⠀⠀⢀⢾⣫⠞⢁⣾⣄⠀⠁⣠⣴⠶⠟⠻⠿⢶⡶⠖⠲⢟⠀⠈⡁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢾⢈⠀⣼⠀⠀⠇⢠⠪⣮⢖⡿⣷⡚⠿⣦⡉⠀⠀⠉⣰⠿⢿⣿⡖⢸⣿⡸⢀⢌⡴⢊⡔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢠⣿⠀⠈⡄⢸⠘⢡⣿⠀⠈⠛⠛⠛⠁⠀⠀⠀⠛⠛⠛⠋⠀⣼⢋⡵⢡⠊⠀⢞
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⠁⡞⣆⠀⢳⡈⢧⣆⢿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⢻⡾⠀⠸⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡘⢬⣢⡀⢣⠈⡟⡎⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⢷⡀⠀⠈⠙⠲⢤⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣎⠹⣿⡆⡆⡇⢸⠈⣧⠀⠀⠐⠋⣙⣛⡙⠒⠀⠀⣠⣿⣷⣝⠛⢟⠲⢦⠐⠀⣷⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣜⣽⢁⠁⡸⠀⠟⣷⣄⠀⠀⠀⠉⠀⠀⣀⣼⣿⣿⣿⣿⠇⣸⡼⢸⠀⣠⠏⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⠝⠡⠂⣠⠃⡜⠀⣿⣿⣿⣦⣤⣤⣴⣾⡿⠿⣛⡻⣭⡷⠞⣉⣴⡥⢚⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣏⡬⠂⣠⠔⡡⠊⢀⣴⣿⣿⣿⣿⣿⠟⢉⠴⠊⠁⡠⠚⣡⢶⣛⠭⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡾⢁⢾⡟⠗⠈⢹⣿⣿⣿⣿⣿⣿⣇⢠⡏⠀⢠⠞⣠⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⡜⠷⠶⠼⠾⠿⠿⢿⣿⣿⣿⣿⣆⢳⠀⡞⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠑⠲⠤⢄⣀⠀⠀⠑⠘⣿⣿⡿⢸⠃⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠚⠛⢦⠀⠀⢫⠒⠴⠋⢠⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡀⠑⠢⠐⢁⡌⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣈⠐⢤⠶⡫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⢀⡐⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⠐⢋⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡠⠐⡫⢥⢷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢔⠀⣄⠀⠐⠂⡄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⡈⠁⠚⠫⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠘⢫⣤⠄⠰⣀⠀⠘⠠⢄⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠤⢌⠡⢂⣰⡦⠈⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⡆⠀⠀⢊⡀⠉⠐⣀⠀⡊⠀⠁⠀⠀⣀⠀⠀⠀⠐⠂⠈⠃⠔⠦⠘⡌⠀⠀⠀⠼⠿⠁⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⠀⠀⠈⠀⢀⡴⠊⠀⠀⠀⢏⠀⠁⢂⠴⠁⠀⠁⠐⢢⡀⠀⠀⠀⠀⠉⠀⠀⠠⢤⣄⡀⠀⠀⠀⠰⣧⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⢀⠁⠠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠴⢦⡀⠀⠀⢀⠀⢀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣄⠠⠆⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠘⠆⣄⠀⠀⠀⠀⠠⡆⠳
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀⢁⠀⠀⡜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⢠⠧⡈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠤⠎⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⡠⠂⣰⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠴⢶⡖⢠⠿⠯⠐⣿⠀⡁⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠂⣠⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⢲⣤⠼⡃⠤⠀⣴⠒⣀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⣿⠀⠀⠀⣸⡇⠀⠀⠁⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⠃⠀⠀⠐⠉⠱⠀⠀⠀⠐⠂⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡔⠀⠀⠀⠀⠁⠑⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⢀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠓⡂⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠐⠀⠛⠀⢠⢀⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠇⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠛⠀⡀⢀⣈⡀⢀⠖⠠⠌⠂⠀⣀⣀⣀⡀⠞⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠉⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⣄⠁⢀⡾⢋⣬⡙⢧⡀⣶⣀⡴⠋⢀⣨⡉⠠⣄⢠⠀⠀⠀⣿⠀⠀⠀⡰⠁⠠⠄⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠐⠓⠀⠀⠀⠈⢿⡷⣤⣤⣤⣤⣀⡋⡴⠊⠉⢶⠌⣷⢸⡟⢀⡰⠋⠉⠉⠳⠊⡠⠷⢴⣿⡟⠀⠀⠀⠀⠈⠀⠀⠈⣠⠆
⠀⠀⠀⠀⠀⠰⠉⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠙⠛⠣⠳⠞⠞⠁⠁⠀⠀⠀⣾⢙⣷⠁⣸⠁⠀⠀⠀⠀⠀⠛⠓⠓⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠄⠰⢷⠿⠛⢟⠱⠙⠃⡰⠖⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢠⡤⠀⠘⠠⠀⣀⠀⠀⠀⠀⣤⣤⣄⠈⡁⢆⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⠏⡤⠤⠴⠾⠀⠀⣁⠀⠀⠈⠛⠁⠀⡀⠀⠁⠀⠈⠉⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡤⢤⠶⢦⣴⠄⠀⠀⠀⠀⠀⠀⠁⠈⠴⠿⠀⠀⢀⠶⠤⠀⠀⠀⠀⠀⠀⠀⣀⡠⡴⠛⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠁⠀⠖⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⠄⠈⠁⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⠀⠀⠘⠣⣄⡀⢀⣠⡀⠀⠈⠅⠀⠠⠀⣞⠁⠻⠀⠀⠀⡸⠀⢐⠀⠀⠀⠀⠾⠀⠀⠂⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⡀⠀⠀⠂
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠛⠁⠀⠙⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠎⠉⠀⠀⠠
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠊⠀⠀⠄⠀⠀⠀⠰⠄⠀⠀⠀⠠⠀⠀⠠⢀⡀⠀⠀⢀⡨⠁⠀⢤⠄
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⣈⢩⣦⣔⠀⡄⠀⠂⠰⢀⠀⠀⠀⢀⣄⠀⠀⠛⠈⠁⠈⠃⠈
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠈⠀⠀⠀⠀⠐⠀⢀⡀⣾⣥⡟⢲⡾⣉⣽⣾⢿⣾⡖⣿⡫⠙⠖⠀⠈⡂⠒⢀⠈
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣀⠾⠛⠁⠈⠙⠛⠁⠟⢀⠛⠀⠙⠉⠀⠛⡆
⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡈⠳⠀⢀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢀⡀
⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠰⠊⡽⣩⡌⢥⣿⡉⠀⣀⡈⢉⡁⠀⢀⢀⡄⠀⢡⠀⠁
⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠘
⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠛⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠙⣆
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⣆
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣤⠴⠷⠒⠒⠒⢦⣀
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠦
⠘⣧⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⠎⠀⠀⠀⠀⠢⣄⣀
⠀⣸⠟⠉⠉⠉⠉⠉⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠤⠴⠒⣿
⡾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢻⡀
⢧⠈⡗⠀⠤⠤⠤⠤⢤⣤⣤⣀⣼⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⢾⡆⠉⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠘⢦⣻⠀⠀⠀⠀⠀⢀⣀⣠⠞⠁⠀⣀⣬⠭⠭⠿⠿⠟⠛⢛⠷⣄⠀⠻⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠉⠓⠲⠶⠖⠚⠉⠉⠀⠀⢠⡞⠓⠤⣀⣀⣀⣀⣀⣀⡞⠀⢸⠀⠀⠈⠙⠛⠒⠲⠤⡤⠤⠶⠶⠒⠛⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠈⠉⠉⠉⢹⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣤⠴⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣤⡂⠀⠀⣰⣷⡀⠀⠀⣢⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣆
⠀⠀⠀⠀⢠⣶⠾⢶⠂⠀⠀⠉⠛⠋⠈⠐⠗⠈⠈⠛⠋⠁⠀⠀⢠⣶⠛⣿⣿⣿⣶⡄⠀⠀⢰⣿⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠾⠛⠛⠻⠞⠁⠀⠀⠀⠰⢛⣹⣿⢿⡿⡟⢁⣗⠀⠀⢸⣋⣿⣿⡿⡇
⠀⠀⠀⢀⠔⣛⣣⣤⣤⣴⣶⣶⣤⣄⡀⠀⠀⡀⢀⡀⢠⠀⠀⢰⣾⠏⠁⠀⠀⢂⣾⣯⡇⠀⢸⣯⣿⣿⣿⡇
⠀⠀⢰⣿⣴⣿⣿⣾⢿⣿⣿⣿⠿⢿⣟⣦⡀⠻⣬⣥⡾⠀⠀⢸⡇⠀⠀⣀⠀⡼⠃⡉⠇⠀⠈⣿⣿⣿⣿⠃
⠀⠀⣾⠻⠍⠈⠉⢻⠛⡁⠙⠁⠀⠈⠉⠈⠀⠀⠀⠀⣀⡀⠀⢸⣿⡃⠤⠩⡊⢱⣟⡾⠇⠀⠀⣿⣿⣿⠃
⠀⣰⣿⠿⠚⣿⣦⠈⢸⣿⠏⠻⢿⡆⠀⠀⢀⢄⣀⣤⠞⠁⠀⡘⠉⠛⠚⠃⠦⠞⠉⠀⢀⡀⠀⠈⢻⠋
⠀⠘⠿⠆⠀⠈⠻⠶⠈⠻⠦⠀⠘⠁⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠒⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⢄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠄⠀⠆⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠈⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠈⠁⠆⠀⠀⠀⠀⢂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⢆⠀⠀⠐
⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⣀⠄
⠀⠀⠛⠀⢦⡀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⢀⢈⠛
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⡶⠶⠶⠶⢶⢶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⢀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⠀⠀⠀⢠⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡇⠀⠀⠀⣸⡁⣀⣲⠶⣆⡠⢸⣀⠀⢨⢿⠯⡀⠀⠐⠀⢰⡵⢮⣄⡀⠀⠀⠀⠀⠀⣶⡆⣿⣧⠀⣤
⠀⠙⠒⠂⠀⠑⠬⣀⣌⣊⣠⡀⠵⠃⠀⠀⠈⠀⠀⠂⠀⣐⠥⠄⠀⡤⢳⠈⢁⡀⠀⠀⣿⡇⣿⣿⢸⣿⠄⠐
⠀⠀⣤⣴⣄⡀⠘⢾⠻⠿⢫⠜⠀⢀⣀⣀⠀⠀⠀⢈⠠⢒⡀⠀⠀⠀⡘⠃⠠⠀⠀⠀⠛⠛⠂⠀⠘⠛⠃⣖
⠀⠐⣿⣞⡽⠂⠀⡸⠀⠀⠸⡄⠀⢇⣸⣷⡛⠓⠀⠀⡐⠉⠘⡳⠒⡋⠡⡄⠀⠀⠀⢀⠀⢸⡆⠀⣦⠀⠀⠿⠆
⠀⠀⠀⠈⢀⠤⠊⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠰⠀⡀⠠⡶⢄⠀⠀⠀⡀⠃⠀⠛⠀⢰
⠀⠀⢀⠞⠁⠀⠀⢐⡆⡀⡦⠄⠀⠀⠈⢢⡀⠀⡐⠀⠀⠀⠀⠀⠀⢰⠁⠀⢻⣼⣧⠸⠀⠋⠀⢀⡀⠀⠈⡄
⠀⢠⡏⠀⠀⠀⠠⠲⡼⣚⣕⡃⡇⠀⠀⠀⢳⡀⣆⣀⠀⣀⣠⠀⠀⠈⡀⠀⠀⠋⠉⠃⠀⠀⠀⢶⠦⠀⠀⠀⠇
⠀⣼⠀⠀⠀⠀⠠⠱⠒⠚⠶⠖⠁⠀⠀⠀⠀⡇⢉⡉⠶⢙⡁⠀⠀⠐⠗⠀⠀⠸⠀⢴⠄⠀⠀⠒⢀⡀⠀⠂⠆
⠀⢿⠀⢀⢀⡀⡀⠀⠀⠁⠁⠀⠀⠀⣠⠀⠀⡇⠘⠓⠀⠚⠀⠀⠀⠈⠉⠀⠀⠀⠡⡀⠀⡀⠀⠀⠀⢠⣤
⠀⠸⡆⠀⠀⠄⢉⠠⠀⣄⡀⠄⡨⠠⠑⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠢⠀⠑⣄⠀⠀⠀⠀⠙⢋⠌
⠀⠀⠱⣕⠀⠀⢀⠈⠂⠉⠐⡀⡀⠀⠀⡠⠃⢀⢄⠀⠀⠀⠀⢸⣶⣦⠉⠁⣴⣶⠀⠀⢸⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠈⠓⠤⣀⡀⠁⠀⠀⢀⣀⠴⢊⡔⣸⠏⠈⢿⡑⣀⠀⠀⣻⠇⠀⠀⢸⡏⠀⠀⡀⠀⠀⠖⠄⠀⠇
⠀⡃⠀⢘⠀⠀⠀⠉⠉⠉⠉⠁⠀⢠⣊⣿⠃⣠⣤⡀⠻⣿⣠⠀⠈⢶⡆⣶⡖⠁⠀⠀⡇⠀⠠⣤⠄⠀⢀
⠀⠼⠛⠥⠀⠐⠊⠉⠐⡀⠀⠀⠀⡜⣰⠃⠈⠬⠥⠀⠀⠹⣘⡆⠀⢸⡋⢹⠁⠀⠀⠈⠑⠒⠒⠒⠒⠒⠋
⠀⠀⠒⠀⣰⡀⠀⠀⠀⣤⡀⠀⠀⠸⠥⠤⠤⠤⠤⠤⠤⠴⠽⠀⠀⠀⣼⣸⠀⠀⠀⠀⢀⡄⢒⣋⣉⣉⡝⠙
⠀⠀⠀⢸⡉⠃⢀⡄⠀⠍⣱⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⣒⠤⡀⠀⠀⢸⡇⠀⠀⠀⣠⢇⣴⣾⣉⣇⣟⡅⡀
⠀⠀⠀⠀⢧⣤⠀⠃⢠⣤⠆⠀⡀⢗⡀⠀⠀⠀⠁⠀⠀⢸⣕⡈⢆⠀⢸⡇⠀⠀⠀⡟⢰⡏⣺⣿⣿⣿⣷⡟⡆
⠀⠀⠀⠀⠈⠹⠀⠀⠨⠁⠀⡀⠀⠀⣤⣤⡀⠀⠀⠀⠀⢦⠃⠆⡸⠀⠀⢀⠀⠀⠀⢇⢘⣿⡿⣿⣿⠿⣿⢋⠇
⠀⠀⠀⠀⠀⠀⣜⣻⡄⠀⠈⠊⠈⠀⠿⡾⠇⠈⠦⡀⠀⠎⣊⠔⠁⠀⢘⣱⡾⠀⠀⠈⠣⢼⣙⡓⠓⣛⣩⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⣻⠋⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣀
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⠁⠈⠀⠀⠀⠀⠀⠀⠀⢈⣳⡄
⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⠎⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⡄
⠀⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢸⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣀⠀⠀⢦⡀⠀⠀⢠⣾⠀⠈⢷⣄⠀⠀⡠⡿⢡⣾⠃⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⢠⡇⣄⣀⠀⢀⣨⢷⣤⠈⢻⣄⡰⡟⠟⠀⠀⠀⠣⢳⡴⣹⢡⢃⣧⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠸⡇⠈⠙⢷⢦⡙⣦⣥⢑⣄⣯⡥⠤⠤⣤⣤⣤⡀⢰⢁⣇⠃⣸⢫⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣇⠈⠛⢦⡑⣝⢿⣿⠋⠀⠀⠀⠀⡰⠃⠈⠻⣟⡏⢸⡏⢠⠃⣿⡟⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠹⢤⡴⠒⠛⢾⣎⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⣻⡇⢸⢇⡼⠴⠾⠷⣶⠒⠢⡀⠀⢸⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠸⢄⣁⣀⡤⠟⠳⢤⣀⣀⠤⠤⠤⠤⠴⠚⠛⠷⠞⠺⣤⣀⣀⣠⠏⣀⠴⠧⠤⠼⠤⠤⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠋⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠀⠀⡀⠀⠀⢀⠜⠅⠁⠀⢠⣀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠳⣄⠀⠀⢀⢀⠀⠀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡅⠀⡀⣼⡯⠄⠛⠀⢀⠀⠀⠀⠈⠈⡒⢲⡉⠀⠀⠀⠀⣀⠄⠚⠂⢽⣯⠀⠀⢀⠇⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡁⠀⠀⠿⣷⡤⠀⠀⣀⣈⣦⣤⣤⣾⣯⣾⣷⣦⣤⣤⣈⣀⠀⠀⢤⣾⠯⠀⠀⢈⠀⡔
⠀⠀⠀⠰⠄⠀⠀⠀⠀⠇⡐⢀⠀⠀⢁⣤⠄⠀⠀⠀⠘⡩⢿⢁⣀⣀⣈⣿⢯⡃⠀⠀⠀⠠⣴⣉⠀⠀⡀⠐⡰⠁⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣻⠛⠛⢡⣄⣠⣤⠄⣬⢴⣿⠆⢬⣧⢰⣿⣦⣤⡢⣤⣄⣠⣄⠛⠛⢿⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡨⠀⠀⠈⠀⠁⠀⠀⠘⠽⠓⢔⣓⠖⠿⠃⠀⠀⠈⠀⠀⠀⠀⢍⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⡀⣠⠀⠜⢀⠃⠐⡃⠘⡆⠱⠀⢄⢀⣄⡀⣀⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢭⡀⠀⢸⠤⢅⡀⠤⡕⠀⢀⡩⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢗⠂⠀⣘⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


⣶⣖⣲⡶⢶⣶⠶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠁⠀⠠⠄⢀⣨⣴⣶⠆
⠀⠀⠀⠀⢀⡈⢠⡁⡢⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⢀⣤⠾⠋
⠀⠀⠀⠀⠀⢼⣦⣼⣿⡶⢉⡖⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣄⠀⠀⠂⠀⠁⠀⠀⠀⠀⢀⡴⢋⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠜⣿⣿⡽⠷⢿⠃⡈⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠈⢀⣤⡐⠀⠀⠀⠀⠀⠀⢀⡤⢻⢶⢨⠻⠒⠊
⠀⠀⠀⠀⠀⠀⠓⣿⣉⣱⣖⡾⠇⠤⠀⠀⢢⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⡀⠈⠁⠁⠀⠀⠀⠀⠀⠐⠛⠀⠼⢤⢀⡀⢠
⠀⠀⠀⠀⠀⠄⠀⢈⣹⣮⡭⣷⡠⠀⠠⢰⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅⠀⠐⠀⠀⠀⠀⠀⠀⣠⣴⡀⠀⠾⠶⠐⠂⠐
⠀⠀⠀⠀⠀⠂⠀⠀⠹⢟⣷⣚⠳⠁⠘⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⡀⣀⢀⠈
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠙⣭⣭⡄⠐⢻⣏⠐⠈⠀⠀⠀⠀⠀⠠⣀⠂⡡⠀⠀⠀⠀⠀⠬⠉⠁⠘⠀⢠⠯⠠⠴⠀⠀⠀⠄⠀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠷⡇⠀⠘⣿⠆⠡⠀⠠⣠⠀⠀⠀⠛⠈⠓⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠋⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠿⡀⠀⠁⠀⠀⠀⣀⠐⠀⠀⠀⢰⠀⠄⢐⡄⠀⠶⣤⠤⠄⡐⠂⠀⢆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠘⢛⣟⡉⠉⠉⠀⠀⢀⠌⢁⡦⠒⠦⠽⢁⡀⠀⠀⠳⠀⠀⠈⠛⠉⠉⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⠀⠀⠁⣀⠤⠒⠁⠀⠀⡛⠲⣼⣦⠄⠀⠙⢆⠳⠆⡀⠐⠰⠀⠊⢁⠀⠀⠀⠈⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠓⠄⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢀⡗⢦⡅⢸⣧⠁⠀⢄⠀⠈⠓⠀⠖⠈⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⣍⣉⣉⢩⡿⡀⠀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠘⣾⠯⠤⣈⠛⠍⠩⠄⠀⡴⠁⠀⠀⣤⡀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⢻⠶⠖⠦⠛⠆⠐⠂⠀⠋⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⣤⣀⣀⠴⠞⠆⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠁⠀⢀⠀⠀⣎⠾⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠀⢷⣄⡀⠶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⡜⠀⠀⠀⠀⠀⠀⢸⠏⠀⢻⣶⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡇⠀⠀⠐⠃⠀⠀⢰⠆⠀⠈⠋⠁⠦⠀⠀⠀⠄⠀⠀⠠⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢰⠆⠀⠀⢘⣿⠀⠀⢡⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣼⠀⠀⠀⢸⠆⠀⠀⢘⣥⠀⠀⢸⡇⠸⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⠄⠠⠴⠠⠖⠀⠾⠀⡍⠀⠀⠀⢼⡀⠀⠀⠀⣳⠆⠀⠘⡇⠀⠠⠆⠻⠧⠀⠄⠀⠀⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠆⣐⢀⣀⣴⠄⠀⠀⡀⡿⠣⠀⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠁⡀⠉⡉⠂⠀⠀⢡⠀⢤⠀⠀⠀⠀⠀⢀⡠⠈⠁⠀⠰
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠁⠘⠁⠠⠀⠃⡈⢀⠘⠑⢀⠀⠠⡜⠫⠃
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢠⠉⠀⠊⠐⠀⠡⡄⠀⠶⠀⢠⠤
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠡⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠘⠀⠀⠀⠀⢶⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠶⡄⠀⠂⣠⣄⠀⠀⢨⡠⠄⠁⠀⠀⠀⣤⠀⠀⠀⠈⠈⠀⠀⠀⠀⢴⡄⠀⠀⢲⠂
⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠿⠀⢀⣶⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⠠⠄⠐⠀⡘⠒⣈⠉⠠⠙⠃⠀⠀⠀⠀⣾⡄⠀⠿⣁⠀⠀⠀⠁
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣤⠀⠛⢷⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠁⠀⠀⢸⠟⠃⣤⣀⠈⠏
⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠽
⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠸⣍⡇⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠸⠂⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⢀⠠⠀⠀⢠⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⢤⡴⡦⠴⠶⠒⡖⠓⠀⠘⠛⠉⠁⠀⠂⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢰⠀⠂⠀⠀⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠔⠀⣸⡄⠠⠆⠨⠀⠀⠀⠀⠀⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠀⢠⣔⠉⠻⠖⠀⠀⠀⠀⠀⠀⡄⡀⣠⡾⠁⠐⢠⠀⠀⠀⠀⠀⢸⡄⣀⡀⢀⢀⢀⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⠀⠚⣷⡄⣿⠁⠒⠂⣠⠀⠀⠀⠀⠀⠐⠘⠓⠓⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⡞⣧⠕⠋⠁⠀⠀⠀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣼⣿⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⣿⣷⡀⠈⡄⠁⠈⠀⡀

⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡄⡀⢀⢀⠀⠀⠀⠀⢀⡀⠲⣶⣶⠃⡀⢀
⠀⠀⠈⡷⠀⠚⠀⡼⠟⠋⠉⠻⠟⠉⠉⠉⢸⡇⠀⠀⠀⠵⢦⣷⣦⠀⠀⠤⣤⡤⠀⠘⠛⠀⠉⠁⠘⢀⣴⡀
⠀⠀⠐⠿⠿⢇⠀⠀⢀⣀⢀⣀⣴⣶⣄⠀⡀⠑⠂⠀⠀⠀⠘⠷⢤⣤⣄⡀⠀⠀⠀⠀⠀⠙⠲⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠛⠛⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡐⠀⢀⠙⡆⠀⠀⠀⠀⠀⠀⢰⣶⡆⢐⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠆⠀⠀⠀⢠⠇⣼⣷⡀⠰⠆⠐⠀⠀⠀⠀⠀⢰⠈⠿⠃⠈⢉
⠀⠀⠀⠀⠉⢹⣆⠀⠀⣿⠇⠠⠿⠛⠋⠀⠀⠀⠀⠸⡄⢀⣿⣿⣷⣦⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠘⠛⠛⠃⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⢀⣤⠀⠀⠀⠀⣹⣞⢿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠸⠀⠘⠻⣻⠀⠀⠀⠀⢸⡏⢫⣿⠀⠀⠀⠀⠀⠃⣾⣿⡇⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣦⡱⠀⡇⠀⠀⠀⠀⠀⠀⠈⠟⠽⠀⠋⠀⠀⠀⠀⣿⣽⣷⣶⡄⠀⠸⣶⡧⠂
⠀⠀⠀⠈⠛⠒⠘⠋⠀⠀⠀⠀⠘⠛⠋⠘⠧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠧⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠐⠫⣤⣤⢤⣀⡀⠀⠀⣒⣀⠀⢀⠘⠲⡤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠉⠀⠀⠰⠆⠀⡉⢀⡠⠀⠀⢠⠉⠱⢧⡀⠀⠴⠓⠘⢇⡀⢈⡒⠄⣉⢳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢠⡸⣷⠀⢀⡠⠀⢠⡲⣷⠶⠋⠁⢀⣤⠿⠀⠤⠬⣧⡄⠀⠀⠠⠄⣈⢂⠱⡄⠀⠉⠙⠳⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠘⣮⡁⣻⡞⣤⣶⣿⠾⠉⣴⠤⣄⠠⢂⠀⠀⠀⠀⠀⠨⡦⠀⠙⠐⢠⡀⠈⠑⢷⡀⢀⠀⠀⢿⣾
⠀⠀⠀⠀⠀⡄⢀⠷⠈⢻⣿⢟⡿⠋⠄⢀⡊⠔⠒⠐⠦⠉⠁⠀⠀⠀⠀⠀⠚⢃⣶⢀⢸⡄⠐⠄⢸⡏⢻⣄⠀⣜⢿⡀⣰⣆
⠀⠀⠀⣶⠀⠇⠈⠀⣴⡟⣿⣼⡵⡛⡉⡁⡀⠀⣠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠾⢢⣧⣦⣀⡀⡏⠈⣟⢣⢸⠘⣿⡁⣿
⠀⠀⢀⢸⡄⣸⡄⢰⣯⣼⢏⣿⡦⡷⢔⢖⠳⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⢳⡈⠉⡿⢇⣼⣦⢻⡜⢻⣿⠏
⠀⣀⠘⡀⢳⡱⢈⣿⣣⠏⣾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠙⢦⣧⠀⠐⠻⣿⣦⣼⣿⠰⠆
⠀⠸⡄⢹⠈⣿⡾⣣⡿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢦⡀⣿⣧⢹⣿⠓⣎
⠀⠀⢻⣆⠐⠸⣿⣟⣰⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⢿⣿⠈⣿⡄⡧
⣤⠀⢠⠿⣧⣤⣿⣏⣼⡟⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠺⣿⢦⣿⣯⣗
⠘⣷⡌⡟⡼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢳⣿⣆⣿⡻⠇
⠀⠘⣧⢹⡁⣿⣿⡏⢀⣀⠀⢠⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣹⣿⣿⣿⠃
⠀⢀⠸⣯⣧⣿⣿⡇⣻⠛⢈⡮⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣦⢄⠈⠳⢼⣿⣿⡿⣆
⠠⣼⣇⣿⣇⣽⣿⣯⠁⠀⢺⣿⢗⡀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⢶⣿⢼⣿⣿⡇⢺
⠀⠨⡯⡞⢿⣿⣿⣿⡄⠀⣝⣻⣟⡇⢀⣦⣷⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⠧⠐⢾⣿⣿⠃⣾⠀⢀
⠀⠀⢹⠔⣨⢻⣿⣿⣷⡀⢘⣜⣷⠥⣸⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⠥⢠⣿⣿⣿⢀⡏⠀⡌
⠀⠀⠀⢻⡕⡀⢿⣿⣿⣷⡄⠱⡿⢹⣿⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⡀⠀⠀⠀⠀⠀⠀⢰⢶⣿⢉⣿⣿⣿⣿⡾⠀⠈
⠀⠀⠀⠀⠈⢷⣼⣿⣿⣿⣿⣎⣻⣿⣿⣭⣶⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⢩⡿⣿⢦⠀⠀⠀⣼⣿⠎⣿⢓⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣬⣄⢺⡗⣏⣿⣿⣧⡄⠀⠰⠀⠀⠀⠺⢺⣻⣖⣾⣶⣧⣟⣜⣽⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡉⠉⠙⢿⣿⡿⠛⠛⠛⠛⠛⠓⡦⠶⣖⡗⡰⠚⠋⠄⣤⣶⠄⢨⣿⣿⣿⣿⡿⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠓⠒⣼⣿⣷⡖⠐⣠⣼⣔⠈⠀⠀⡠⠛⢢⣀⣸⣧⡤⠿⠶⠿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠙⣿⣿⣍⣤⣭⣿⣶⣍⣠⠖⠛⣏⡞⠉⠀⠀⢀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠙⢿⠁⢠⠊⠀⠑⠠⡜⠑⠀⠀⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠒⠠⢑⠢⣀⣀⡠⠂⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠀⠀⡸⠁⠀⠑⠠⢆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⡀⠀⠀⠀⠀⡱⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠈⡖⢤⣀⣐⠁⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⠎⡐⠁⠀⠀⠉⠒⢄⡀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⢊⡜⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠉⠉⠉⠉⠉⢩⡟⠒⠦⠤⣀⡀⠀⠀⠑⢌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠈⠉⢳⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠤⣀⣀⡀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢈⠷⡀⠀⠀⠀⢥⣤⣭⠑⠂⠠⠤⢀⠄⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⢃⡬⠘⣦⡀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⣰⡗⠉⠀⠀⠘⠿⢦⠀⢹⡏⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠄⠀⠀⠑⢂⠀⠀⠀⠀⠑⠂⠃⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠓⡀⠀⠀⠀⠀⠀⠀⠀⠜⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠆
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠐⡀⠀⠀⠀⠀⠀⠌⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢰⢖⠄⠡⠒⢎⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡼⣀⠀⠀⠀⠀⠄⡃⠀⠀⠀⡂⠀⠀⠀⠀⢀⠴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢱
⠀⠀⠀⠀⠙⡦⣁⠒⠠⠄⣰⣕⠠⠤⢒⣔⠠⠤⠒⢊⠥⠞
⠀⠀⠀⠀⠀⠈⠢⢉⠒⠠⠀⠤⠤⠤⠤⠠⠀⠒⣉⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠠⠄⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⠉⠉⠉⠙⠊⠁⠀⠀⠀⢙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡥⠿⠂⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⣀⣤⠀⠐⡾⠟⣯⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⢀⠀⢀⣠⠤⠤⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣠⡴⠃⠠⠐⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠲⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⠋⢁⣽⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⣤⣉⣄⣀⡀⢴⣿⣿⣿⣿⡟⡝⣼⢯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠓⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⣠⣾⠿⣿⢿⡟⢱⣿⣿⡿⣿⠑⣰⣼⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠠⣴⣿⡿⠷⣄⠀⠁⠈⠋⠉⠀⠈⢉⣼⡿⣫⣾⣣⡾⣫⣹⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣤⣼⣧⣠⣤⣤⣤⢄⠤⠤⠤⢤⣼⠁⠀⠀⠀⠠⠀⠀⠁⠈⠀⠀⠀⠈⢳⣆⢠⡇⡄⣌⠛⡹⢻⣿⡟⡿⣫⣾⠟⣩⡿⣿⣿⣿⣇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⢁⢀⡀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣀⣤⣼⣿⣾⡇⠠⡿⡄⣷⠟⣫⡮⣼⠟⣡⢞⢟⡵⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣸⣾⡄⠐⢀⣀⢠⣤⣼⣻⣟⢿⣿⡿⣿⣿⣿⠁⠘⡇⣀⣸⣞⣅⠻⠁⠘⠃⠉⠉⠉⣩⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠠⠀⢠⣥⣾⣿⣿⣿⣠⡿⢃⣞⡿⠡⠙⢋⡞⡑⣙⣿⣿⣿⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢀⣠⡾⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⠀⠀⠈⣀⣤⡼⢹⣿⣿⡟⠀⠀⠻⠁⠁⠀⠀⠐⠛⢿⣿⣭⣿⣿⣿⣿⠃⠀⠀⠀⡀⠀⢀⢠⣛⢉⡵⠫⠪⣾⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⢻⡿⣆⣸⣶⣿⣟⣯⣴⣾⣿⣿⣷⡴⠿⢶⠂⠶⣶⣷⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣧⡄⠘⣸⡷⣿⣿⣾⣏⠀⠠⢁⣛⡙⠁
⠀⠀⠀⠀⠉⡉⠀⠠⠠⣶⢾⡿⠧⠀⠈⠘⠛⠋⠉⢀⡀⠀⣲⠶⢶⣤⣬⣭⣍⣉⣉⢠⣄⣤⠄⢀⡿⠿⠿⠷⠶⢛⣋⠁⠄⢀⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠄⠈⠀⠠⠄⠀⠈⠉⠁⠀⠈⠉⠉⠉⠉⢋⠀⠀⠠⠄⠀⠻⠶⠶⠶⠀⢀⣀⣤⡤⠖⠉⠛⠛⠒⠳⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠐⣌⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢩⣽⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣠⡁⠀⠀⠀⠀⠀⢸⣿⣇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠙⠉⠁⠀⠀⠀⠀⠀⠰⠿⠿⠖⠋⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣥⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⣻⠶⠀⠀⠀⠀⠀⠀⢾⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢳⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⡿⡉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⡖⠹⣷⠋⠉⠪⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣳⡀⠀⠀⠀⠀⠀⠀⠀⡰⣾⣿⡿⠀⠀⠀⠀⠀⠠⠀⠀⠀⣻⣶⣦⣠⡇⠀⠀⠀⢳⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⢹⠀⠀⠀⠀⠀⠀⠀⢠⢻⣻⡿⠀⠀⠀⠀⠀⠀⣶⡅⠀⢠⣾⡿⠿⠿⣅⡄⠀⠀⠸⣏⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⣿⠲⠃⠀⠀⠀⠀⢀⠀⡷⣠⣤⣿⠋⠀⠀⡀⠙⢷⡀⠀⠀⢸⡄⢰
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⢀⢠⡶⣶⡿⠋⠁⠈⠉⠄⠀⠀⡆⠀⠘⡇⠀⠀⢸⡠⣿
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⣿⠇⠀⠀⠀⠅⠲⣾⠃⠀⠀⠀⠀⠀⢀⣼⠅⠀⢀⡷⠀⠀⠀⡄⣽
⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣸⣯⠀⢠⣤⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⣾⣟⠀⠀⢸⡿⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⢳⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⡀⡒⢵⢷⡿⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠘⣧⠀⢸⠓⡇
⠀⠀⠀⠀⠀⠀⠱⢦⣿⣿⡗⢄⡀⠀⠀⢀⣀⠀⣿⣿⢿⣥⣤⣭⠿⠁⠀⠀⠀⠀⢀⣠⣴⣯⠶⠂⠀⢀⢀⡴⣿⡧⡸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢄⣀⣈⣙⣀⣹⡿⠛⠉⠁⠙⢦⣠⡀⣤⣠⣾⣿⣿⣿⣆⣤⣒⣰⠻⡏⠰⠟⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠚⠿⠿⠿⠯⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠱⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣸⠀⢀⣠⣤⣄⣠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣄⣠⣤⣄⡀⠀⡆⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣫⡆⢰⢁⣸⣿⣟⣻⣿⡿⣿⡟⠛⠋⠁⠈⠙⠛⢻⣿⢿⣿⣟⣻⣿⣇⡀⡆⢰⣝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡇⢸⡸⣿⣿⣾⣿⣻⣿⣾⠇⣤⣶⠄⠠⣶⣤⠸⣷⣿⣟⣿⣷⣿⣿⢇⡇⢸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢃⠸⠷⣿⣿⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣾⣿⣿⣿⠾⠇⡘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡜⡄⢿⣿⣿⣿⡿⢿⣿⣿⣿⣄⠀⠒⠂⠀⣠⣿⣿⣿⣿⢿⣿⣿⣿⡿⢠⢣⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠱⡌⠻⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣿⠟⢡⠆⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡜⢦⡈⠻⡿⠟⠛⠛⠋⠀⡀⢠⡀⣀⠀⠙⠛⠛⠻⢿⠛⢁⡴⢣⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣍⡞⠀⠀⠀⠀⢔⡴⣾⢟⡿⡷⣤⠀⡀⠀⠀⠀⢳⣩⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠊⠓⣬⣝⢫⣤⠚⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠈⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠜⢿⣿⣿⡏⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠀⠀⠀⢹⣿⣿⡿⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠢⡙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⠔⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⠲⢄⠐⠶⣤⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⣤⣤⠴⠂⡠⠖⠁⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠲⢤⣉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣉⡤⠖⠉⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠉⠑⠒⠲⠶⠶⠶⠶⠖⠒⠛⠉⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⠴⠚⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⡦⠀⠀⠀⠀⠀⠀⢠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⣠⡄⠀⠾⢻⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⡀⠀⠀⠠⠒⠐⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⡴⠞⠁⠈⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠿⠋⢡⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢤⡀⠀⠀⠀⠀⢀⣤⣡⣤⡤⣰⣿⣿⡿⠿⣻⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⢈⣿⣦⠀⠀⠐⠿⠯⠛⠿⢸⣿⣿⡽⣢⡶⣿⣿⣿⡇
⠀⠀⢀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣰⠁⠀⠀⠀⠄⠂⠙⠉⠁⠘⢦⡀⣤⡀⡐⢶⢿⣷⢿⣿⣻⣟⣿⣿⣿⣷
⠀⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣼⣷⡏⢠⠧⠼⠟⡻⣮⠟⡫⣺⣫⣺⣿⡇
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢀⣼⣿⡄⣠⡤⣴⡾⢽⡟⡿⠟⣻⣿⣃⣈⣤⣴⡯⠖⠃⠀⠁⠀⢀⣴⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢙⣻⢿⣿⣿⠋⠸⡿⠡⠀⠘⠴⣾⣿⣻⣿⣿⣿⠉⠀⠀⠀⠀⢀⠶⢻⠽⢛⣿⣿
⠀⠀⠀⢀⡀⠀⢸⡷⣁⣶⣾⣿⣯⣾⣿⣿⡤⠷⠶⠰⣶⣶⣶⣾⡿⠿⢿⣿⣿⣶⡤⠘⣵⣶⣿⣷⡉⠀⠀⣟⠋
⠀⠀⠀⠉⠄⠀⠀⠷⠿⠷⠀⠀⠙⠉⠁⠠⠀⣹⠒⠶⣶⣤⣤⣤⡠⠤⠖⠠⣟⠛⣛⠛⠉⠁⠀⠠⣤⣀⡠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣮⣿⡷⠶⠤⣤⣤⣠⣴⣶⠧⠚⠛⠉⠀⠀⠈⡀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⢿⣉⡉⣉⠙⠟⣳⡮⣗⠒⠖⠻⠿⠳⣦⣤⣤⣄⡤⢀⣀⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠉⠉⠁⣠⠏⠀⠀⢹⡆⣌⡀⠀⠿⠛⠉⠉⠉⡠⠜⠛⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠉⠀⠀⣰⣿⣗⣻⡿⠇⠀⠄⠒⠛⢁⠀⠀⠀⠒⢛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⠂⠄⠒⠀⠀⠄⠐⣦⣬⠟⠋⠁⠀⠀⠀⠀⠀⠖⢀⢴⡾⠃⢺⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠷⢿⠟⢁⣀⡀⢀⡀⣠⣤⠄⣽⠇⠴⠟⠲⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⡤⠶⠛⠂⠈⠴⣉⣀⠻⠜⠓⠒⠠⠄⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢀⣦⣶⣤⣤⠙⠀⠀⠤⠄⠀⠬⢁⣀⡐⠠⠀⠀⢄⠉⠀⠀⠀⠀⠀⢀⣼⡷⠋⠁
⠀⠀⠀⠀⠀⠀⡀⣬⡆⠀⠀⠀⠒⠀⠀⠀⢶⡶⠟⠁⣠⠆⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⢀⠀⠉⠉⠀⠦⠀⠐⣾⡆⣠⠿⣁⣤⠀⠈⠉⠁
⠀⠀⠀⠀⢀⡶⠈⠀⠀⠀⠀⠀⠠⣀⠀⡀⠈⠙⣄⠠⠬⠀⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣸⡷⠦⠀⠀⠀⠀⠀⠀⢀⡀⢀⠈⡀⠀⠀⠀⠀⢠⣄⣤⣰⡄
⠀⠀⠀⠈⠙⠁⠀⠀⠀⠠⣀⣀⠴⠟⠐⠚⠂⠚⠃⣀⠀⠀⠀⠀⠐⠒⠚⠃⠀⠀⢤⣶⢾⡁⣀⣀⠀⢀⣨⣧⠀⠀⢻⡥⠘⠃⠀⠀⢠⡀⠀⠾⠛⠛⠋⠁⠁
⠂⠀⠀⣀⢠⣴⣶⠀⠀⣰⣟⣀⠀⠤⡀⣤⣤⣤⣤⠽⠆⢄⠀⠀⠐⠦⣤⣤⣤⠄⢀⣄⡀⢀⣀⠈⠀⠘⠁⠀⠀⠀⠀⠀⠐⠀⠐⢨⣸⣿⡆⠀⠀⠀⠄⡀
⠀⠀⠀⠛⠛⠉⡁⠀⣴⡟⢈⡀⣠⠔⢛⣻⡏⠀⣀⣀⠠⠴⠃⠤⣀⢴⠄⠉⠁⠀⢸⡿⠀⠀⠉⠀⠀⣴⣿⣦⠀⡀⣀⣀⣀⣤⣤⣾⠋⠀⠀⠀⠀⣀⣴⣷⡀
⠀⠀⠀⠀⠀⠀⠁⠚⠋⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠈⠉⢻⠛⠂⠀⠀⢙⡟⠉⠙⠛⠀⣡⡈⣶⣶⣿⣿⣿⣟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣠⣿⣟⠃⢀⣴⣶⡆⠀⠀⢙⣶⣶⣽⣌⢩⡌⠛⠻⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⢾⡛⠉⠁⠀⠀⢠⡓⣚⣁⣠⣾⢾⠿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣀⠀⡀⠀⢁⠍⠉⢉⣷⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡄⣀⣠⣾⡿⢀⠔⠁⠀⢠⣿⡿⠟⠉⠀⠀⠀⠀⠀⣆⢀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣤⣶⣾⣿⣟⠟⠋⠚⠁⠀⢀⡴⠋⠁⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⣡⠇⡀⠀⠀⣤⡴⠋⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⡿⢿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠀⢀⣼⠃⠀⠀⠀⠀⠀⠶⢤⣶⣿⣿⠿⠟⠟⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢴⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⠃⠀⠰⠤⣤⣄⣰⣄⣤⣠⣴⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠓⠶⢤⡄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⠀⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠐⣄⣤⣀⡜⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⣏⠀⢈⡇⠀⣀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⠗⠨⠍⢉⡛⣋⠡⠅⠚⢭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⡇⠀⠀⠙⠀⠀⠀⠘⠀⠀⠐⣗⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠁⠐⠀⢙⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡿⠉⠁⠁⠀⠈⡹⢩⠁⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⢞⠁⠘⠀⠀⠀⠠⠁⡄⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠋⠉⠉⠉⠃⠀⠙⠀⢄⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠊⠉⠑⢆⠀⣦⠄⠀⠀⠀⠀⠠⡄⠀⠀⠈⢆⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⣷⡀⢀⣠⠄⡸⢣⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢿⣧⡉⠀⢀⡁⢼⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⣤⣤⣍⣳⣴⠉⠀⢸⣯⣀⣄⣤⣤⣀⣠⣇⣠⣄⣠⠇⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠤⠼⠤⠾⠤⠤⠤⠤⠤⢤⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠧⠤⢴⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢽⠀⠀⠀⡠⠐⠂⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠡⡈⠑⠤⡀⢴⠁⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠭⠟⠦⠄⢿⡼⣿⣿⢵⣏⣉⣉⣉⣉⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⣤⡀⠙⡤⠐⢁⠆⠀⠀⠀⠀⠀⡠⠶⠏⠚⢿⡦⠵⠶⠶⠯⣾⡙⣉⣉⣙⣉⣷⣲⣛⣲⣿⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⠛⢄⡠⢎⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⢰⡿⠭⡭⠭⠭⣿⢿⣒⣛⣓⠫⣟⣲⣒⣾⣿⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠁⡔⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⠽⠭⠽⠯⣿⡿⣷⣺⣷⢬⣷⢶⣶⠯⣿⠤⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠭⠭⠭⠭⣿⣯⠯⠿⠯⣽⡋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣶⠒⠒⣶⠶⠶⣶⠶⠶⣶⠶⣶⠶⡶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⣶⠶⠶⣶⣶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢧⠈⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢈⣧⠀⠀⢀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠠⠁⠈⠈⣇⠀⠀⡤⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⡅⠀⠀⠉⠈⠓⣘⠀⠀⠀⠍⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠢⢔⠇⠐⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠜⠀⠀⠀⠁⢨⠄⠀⠈⢰⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠙⡤⢸⠄⠀⡀⠸⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠛⡌⠀⠀⠘⠉⠆⢸⠀⠫⠀⠀⠀⠀⠄⢂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡅⠀⠀⠀⠀⠀⢣⠀⠨⡀⠐⠠⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡃⠀⠀⠀⠁⠠⢸⠀⠒⢆⠁⡠⢀⠄⠀⡧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢭⠅⠂⠀⠈⠀⣤⠉⠀⡲⢐⠀⠂⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⢄⠀⠁⠀⢰⠁⠀⠀⠠⠒⠒⢚⠒⠂⠰⣶⢵⠈⡆
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠊⣀⠀⠀⢸⡀⠀⡀⠀⣸⠀⠀⠀⠀⠀⠉⠭⠤⢤⠬⡠⢍⠀⢷⡤⠄
⠀⠀⠀⠀⡄⢧⡀⠀⠐⠀⠀⢀⠞⠁⠀⠀⢈⠂⠀⠀⠄⠳⠀⢀⡼⠁⠀⠂⠀⠀⢸⠀⠂⠀⠀⠺⡇
⠀⠀⠀⠀⠈⠲⡄⠄⠀⠀⠆⢸⠁⠀⠀⢠⠆⠈⠀⡀⠀⠐⡴⠁⠀⠀⠀⠀⠡⠲⠈⡆⠀⠁⠀⣠⠇⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠢⠤⣐⣁⠘⠀⠀⠠⠁⠀⠀⠀⠉⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡂⡴⠊⠠⠒⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠤⠤⠄⠤⠍⣂⣓⡀⢀⣠⣌⣠⣤⡤⢠⡄⠊⠁⠠⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢣
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠄⠀⠀⠀⠀⠸⡁⠔⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠔⠁⠀⠀⠰⠀⢠⠀⠀⠂⠀⠀⡀⠀⠀⠀⢸⠁⡀⠀⠀⢀⠀⠂⢉⡁⠈⠤⠀⠀⠃⠀⠀⠈⡐⠀⢠⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⡈⠄⠈⠃
⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⠀⠀⢠⠌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠎⡉⠉⠐⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠁⠁⠀⠀⠘⠀⠀⠀⠀⠤⠄⠀⠀⠀⠊⠀⠀⠀⠘⠓⠀⠒⠂⠂⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⢲⠀⠀⠀⠀⠐⠈⠐⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢠⡀⠀⡄⠀⠀⠀⠀⠤⠆⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠚⠀⠐⠉⠀⡀⠀⠀⡄⠀⠐⠠⠐⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠅⠀⠀⠀⠄⡀⠀⠀⢸⠁⠀⠀⠀⢠⠂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠘⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠐⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡶⠀⠊⠉⠈⠉⠁⠀⠠⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⡿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣤⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⠛⠡⠄⠂⠀⠀⠲⠤⠶⠤⣤⣤⣤⣠⡀⡀⠰⠶⡤⠀⠀⠀⠀⠀⠀⢰⡇⠀⡄
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣒⠒⢴⣾⣶⣴⣢⣦⣴⣤⣄⢈⠉⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⡁⠀⢆
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢟⡿⠿⠷⠺⠟⠿⠶⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⡆⡀⠀⡀
⠀⠀⠀⠀⡠⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡷⠶⣶⣯⠃⠉⠀⠤⣤⠀⣀⠀⠀⢀⡀⠤⠀⠀⠐⣢⣢⡀⣏⣰⣿⣧⡗⡇⢀
⠀⠀⠀⠀⠀⡱⣷⣈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣘⣿⣀⣀⠀⠀⠀⠀⢀⣄⡜⠿⣿⣿⣿⣿⣿⣽⣷⣿⣷⠥
⠀⠀⢠⣤⣬⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠀⠐⠊⠠⠚⠙⣶⣿⠿⢿⣿⣿⠛⠉⡭⠁
⠀⠠⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⣸⣤⣶⣴⣿⠛⠀⣀⣼⣏⣁⡀⢹⡃
⠀⠀⠒⠡⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⢻⣿⡛⠛⠛⠛⠿⠭⢿⠿⠿⠉⣿⠟⠻⣿⠿⣿⠿⠿⠿⠿⠿⢿⣿⣷⣾⣿⣿⣿⣿⣿⠺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠲⠚⠛⠎⠙⠒⠄⠀⠀⠀⠀⡀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠁⠈⠉⠁⠉⠁⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠚⢛⠛⠛⠛⢃⡀⢀⠀⢂⡂⠒⠛⠓⠆⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠛⠗⠆⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠀⣸⢀
⠌⠀⠀⠐⠀⠀⠈⠂⠀⠀⠠⣤⢀⡄⠈⠀⠀⢀⣉⠠⡤⠅⠦⢤⢴⡅⡈⣞⠛⣣⣔⡐⢀⡛⢁⡋⠘⠀⠂⠋⠛⠠⠞⠠⠁⠋⠀⢸⣶⠂⢰⡿⠈
⠇⠀⠄⠠⠨⠄⢄⣀⡀⢀⡙⠈⠋⢉⡉⢈⣂⣀⣂⠐⠒⠀⠆⠒⠐⠀⠶⠂⠴⡀⠠⠁⣤⠄⠈⢁⣁⠁⠋⠐⠀⠒⠖⢲⣴⠀⠀⢸⠉⠀⣿⠃⠀⠀⢀
⠀⠰⠀⠷⠂⠛⠙⠳⠂⠒⠖⠂⠐⠢⠨⡄⠠⠁⠬⠄⡁⣋⠁⣀⢘⠀⠂⠐⠰⠤⠄⢀⠀⢠⡄⣈⠁⢈⡚⠀⠘⠁⠞⡔⠈⣧⠀⠀⠀⣘⣿⠀⠀⢰⠇
⠄⠰⠀⠏⠀⠖⠚⠋⠙⠁⠉⠃⠉⠃⠘⠉⠂⠐⠂⠶⠀⠆⠆⡤⢠⢈⢉⣄⢂⣐⣂⠆⠤⠬⠀⡃⣘⢘⣹⡀⠉⢀⡤⢘⡇⠀⠀⠀⠀⣿⠏⠀⢀⡟
⠀⠆⠰⠟⠀⠞⠘⠃⠀⠂⠞⠉⠙⠇⠀⠸⠃⠻⠆⠶⠚⠂⠰⠖⠰⠆⠬⢩⡀⣀⠈⠂⠘⠃⠐⠀⠯⠨⠝⠛⢻⣅⠁⠾⠀⠀⡠⠂⣸⠏⠀⠀⣼⠁
⠀⢰⡴⢶⡀⢲⠀⠸⠀⠺⠀⠐⣿⠧⠐⠀⡆⣰⡆⡰⠂⠀⡖⢰⠆⢴⠆⢠⢀⠁⢀⠙⠀⠂⠣⠂⠆⣠⣄⠘⠛⠋⠀⠀⢀⡾⠁⠀⡟⠀⠀⠀⣽
⠁⠀⣁⠀⡁⡀⡄⢠⣁⠀⢀⠀⣤⠀⢀⣀⠀⢀⡁⠀⡀⠀⢁⠀⠀⠈⠀⡁⠁⠀⠋⠘⠜⠑⠛⠂⠀⠀⠀⠀⠀⠀⣠⣴⣾⡁⠀⣰⠇⠀⠀⠀⣧⢰
⣤⠀⠹⠆⠁⠀⠣⠀⠘⠀⠛⠀⠉⠀⠀⠙⠀⠸⠁⠀⠿⠀⠏⠰⠀⠀⠘⠃⡇⠀⡾⠁⡀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠚⠻⠟⠻⠶⠿⣤⣀⣈⣘⡇
⠀⠀⠀⢠⠄⠀⠀⠀⠐⠀⣠⠀⢰⡄⠀⢠⢤⣠⡄⠀⣤⡄⣠⠀⢀⣀⠀⠀⢀⡀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠤⠀⠀⡀⠉⠓⠒⠶
⡶⠈⢀⠰⡆⠀⡘⠈⠇⠀⠸⠇⠀⠁⠀⠛⠀⠀⠀⠰⠇⠁⠋⠀⠈⠁⠀⠀⡞⠀⡿⠀⢀⡴⠀⠀⠀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠛⠓⠀⠀⠀⠀⠒⠂⠀⠀⠰⠶⠦⠄⠀⠀⠀⠀⣰⠃⠀⡼⠁⠀⠀⠀⣀⣇⠀⠀⣤⠀⠀⠀⠀⠀⠢
⠀⠀⠀⡀⢠⡀⠀⣄⠀⠀⣠⠄⠀⣄⠀⠀⢠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⢰⠇⠀⠀⠀⡐⠏⠅⠀⡀⠁⠀⠀⠀⠀⠀⠙⠃
⠘⠇⠀⢀⠀⠁⠁⣬⣄⣀⠀⠴⣦⠀⠀⠀⠀⢀⣈⣤⡁⠀⠙⢳⡄⠀⠀⠀⠠⢀⣼⠋⠀⡼⠀⠀⢵⠰⠂⡀⣀⠀⠀⠀⠀⠶
⡃⠐⠻⠿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠁⠀⠀⣈⠀⠿⠴⠄⢀⠈⠁⣠⡼⠃⠀⠀⡀⠀⠂⠀⠈
⠷⠀⠀⠀⠠⣶⠶⣾⣦⠀⠀⠀⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠈⢉⠶⢖⠒⠀⠀⠀⠀⠩⣦⠀⢠⡈⠁⠀⠀⠀⠀⢤
⣤⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⡀⣄⠀⠀⠉⠋⠱⠄⠠⠄⠸⣷⡙⠂⠈⠰⠆⠉⠀⠃⠀⠀⠒⠈⠁
⠀⠘⠓⠀⠀⠀⠀⠀⠽⠀⠀⠈⠠⠀⠈⠓⠀⢀⡀⠤⠄⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣗⡂⠉⢛⠛⠛⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠫⠁⣡⠤⣀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠎⡁⠊⠄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠅⠴⠓⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢉⣙⣤⣀⢠⠀⠈⠠⠈⠛⠿⠛⠛⠻⠟⠉⣀⠠⢩⢆⣴⣌⣁⢉⡿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠋⢉⣻⣿⣿⠷⠒⠐⡤⠀⠊⠀⠀⠲⢶⣤⡈⠀⠀⠝⠃⢺⣿⣿⣿⣶⣤⡄⡸⢿⣿⣿⣿
⣿⣿⣿⣿⠿⠛⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⣿⡀⡀⠀⡀⠀⠈⠉⠙⣿⣿⣿⣦⡀⢿⣿⣿
⣿⣿⣿⣷⣴⣾⠟⠿⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⣼⣿⠃⠀⠐⠀⠀⠀⠀⠐⠛⠿⢿⣿⣧⣶⣿⣿
⣿⣿⣿⣿⡿⢋⡀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠑⠘⠛⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣼⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢤⡄⠴⠶⠰⡄⠀⣀⡀⠀⠀⠀⠀⠀⠔⠛⠛⣿⣿⣿⣿
⣿⣿⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢲⡂⠁⠂⢰⣥⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿
⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⡰⠁⠀⠠⢻⣿⣿⣷⠠⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠈⢻⣿
⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣀⠀⣀⠈⠉⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⠏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣬⠀⠀⠈⠇⠀⠀⢀⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣶⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⡁⠀⡀⣠⠆⠈⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠌⢁⡼⢋⡍⢳⡴⣇⡴⠋⣡⣍⠰⡰⡀⠀⣰⠇⠀⠀⢀⠄⢀⣀⣾⣿
⣿⣿⡀⠉⠀⠈⠁⠀⠀⠘⢿⣶⣶⣲⡤⠰⠉⠘⣳⢿⡾⢀⠞⠀⠀⠉⢠⣿⡿⠏⠀⠀⠀⠀⠀⠀⠼⣿⣿
⣿⣿⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠐⢀⠀⢠⡮⠞⡗⠸⠂⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣸⣽⣿
⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⢀⡀⠐⠊⡠⠄⠀⠁⢠⡥⠀⠈⢠⠤⢄⣈⢒⡤⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿
⣿⣿⣿⣟⠻⠃⠀⢀⣀⣀⣀⡈⠐⠂⠋⠀⠀⢀⢠⡀⠀⢀⡀⠀⠀⠀⠀⠈⠁⣀⡤⠄⠀⠀⠀⢟⣻⣿⣿
⣿⣿⡟⠿⠷⠀⠀⠈⠑⢟⢛⣻⣷⣄⠀⠄⠀⠀⠁⠀⠀⠀⠁⠀⠠⠀⣤⡶⠿⡷⠂⠀⠀⠀⠚⣿⢟⣻⣿
⣿⣿⣵⣤⣤⣠⣤⡄⠀⠀⠋⠤⠄⠹⠆⠀⠂⠀⠀⠀⠈⠃⠀⠀⠀⠼⠛⠛⠛⠃⠀⠀⠀⠀⢀⣀⣌⢹⣿
⣿⣿⣿⣿⣍⠉⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣋⣽⣿⣿
⣿⣿⢟⡋⠙⠁⠀⠀⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⣁⣠⣤⣄⢰⣶⣿⣿
⣿⣿⣿⣳⣤⠐⠚⠀⠀⡀⠀⠀⠁⠀⠠⡄⠁⠐⠀⠀⠀⠃⠀⠀⠀⠀⢠⡠⠄⠀⠠⠈⠈⠋⠙⠹⣛⢿⣿
⣿⣿⣿⡿⠂⠀⠀⢀⠀⠀⠀⠀⠐⠘⢢⣞⡷⣰⣔⣤⣤⣤⣴⡶⠳⠀⠁⠠⠄⠠⠀⢀⣠⣤⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣣⣶⣿⣿⣿⣄⢀⣀⢀⠾⠋⠉⠘⠋⠘⠉⠃⠙⠉⠙⣦⣤⣀⣤⠰⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣂⢠⡤⠤⠀⠄⣀⠀⢀⣤⡀⠀⠉⢻⣛⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣶⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠉⠈⠀⠈⠡⡀⠈⠈⠨⠈⠉⠩⠡⠀⠀⠀⠀⠂⠀⠀⡠⠀⣠⣀⠀⡀⠀⢠⠄⡍⠉⢉⠩⢤⠀⣠⢠⢠⠄⢠⣆⡀⢠⡇⠆
⠅⠀⠀⠀⡀⡀⠀⠀⠀⠈⠶⠃⠄⠤⠄⠀⠉⡯⢀⠉⡋⡉⢀⡙⡐⠚⠚⢀⠂⠐⠆⠆⠠⠄⠄⡈⡥⣄⡀⠀⢸⠟⠀⣿⠁
⠁⠠⢠⡤⠱⠘⠯⠠⠭⠤⠠⢈⢃⠈⠙⣙⡂⠒⠖⠂⠀⠄⠤⠠⢡⢀⠁⡈⢁⡀⠘⠃⠢⠂⠰⠂⡤⡈⢣⠀⠈⠀⢸⡏⠀⠀⡔
⠀⠶⠰⠂⠐⠔⠃⠒⠀⠒⠐⠂⠒⠒⠀⠆⠤⠁⠍⠬⠅⡍⠀⣀⢀⣀⠤⠡⠌⠁⠃⡊⢛⡇⠘⢀⡄⢰⠊⠀⠀⠀⣿⠃⠀⣼⠁
⠐⠄⠾⠃⠘⠈⠀⠀⠀⠉⠙⠃⠀⠛⠈⠃⠐⠚⠀⠲⠂⠆⠠⠩⢤⡄⢙⠀⠃⠐⠐⠇⠍⠛⣛⣏⠁⠏⠀⡀⠀⢸⠃⠀⢠⡇
⡀⢰⠚⠆⠘⠀⠛⡀⠃⠀⠻⠓⠈⠰⠤⠿⠰⠃⠀⠇⠗⠰⠖⠠⡠⢀⡄⡃⡃⡓⠐⠠⠾⠄⠉⠁⠀⠀⣼⠁⠀⡟⠀⠀⢸⠁
⠀⠀⣦⢠⠀⡆⠲⣦⢀⡆⠴⠀⠠⡶⠀⡆⠀⣆⢀⡄⡀⠀⠀⠄⡀⠀⣨⠉⠁⠉⠀⠀⠠⠀⡀⣀⣲⣿⣧⣄⣼⠃⠀⠀⣸
⠋⠀⠉⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⠀⠁⠀⡉⡈⠀⠁⠀⠀⠀⠃⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠉⠉⠑⠒⠲⠾⣀⣀
⡄⠀⠀⣅⠀⠠⠰⠄⠀⡧⠀⠇⠀⠞⠉⠋⠀⡏⠃⠇⠀⠛⠀⠂⡼⢠⡇⠀⣠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠
⠁⠀⠀⠈⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠤⠀⠀⠠⢤⠄⠀⠀⠀⠁⡼⠃⢠⠃⠀⠀⢀⣹⠀⠀⣠⠀⠀⠀⠀⠠
⠀⠀⢀⠀⡄⠄⡄⠀⠀⠤⠀⢤⠀⠀⠠⠀⡀⡀⠀⡀⠀⠀⠀⠐⠀⠀⠀⡟⠀⠀⠀⡘⠉⠀⠀⠁⠀⠀⠀⠀⠉⠃
⠈⠀⣀⠀⠈⠀⠼⢤⠀⠐⠶⠀⠀⠀⠀⠤⢤⡄⠀⠉⠳⢀⡀⠀⠐⣠⠟⠀⡰⠁⠀⠖⠂⠀⢀⠀⠀⠀⠐⠂
⡅⠈⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢤⢄⢙⣛⠃⠀⠀⢰⡾⠁⠀⠠⠀⠈
⠉⠀⠀⠀⠙⠋⠛⠃⠀⠀⠀⠀⠀⢴⠶⡀⠀⠀⢠⡀⣌⠉⢄⡀⠄⠠⠀⠙⣀⠐⠆⠀⠀⠀⠀⠉
⠉⠴⠄⠁⢀⠀⠐⣆⠀⠐⢘⡂⠰⠄⠀⠁⠀⡀⠌⠛⠀⠀⠈⠉⠀⠀⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣐⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠚⢀⢠⣶⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⢈⠀⠂⠀⠀⠀⠀⠄⡘⠃⠀⠀⠣⠥⠔⠒⠢⡤⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡭⠁⠀⠀⠀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠱⡶⠀⠁⠀⡀⠁⠀⠀⢐⡶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢡⢷⡀⠀⠂⠀⠀⠀⠠⢦⡄⠀⠀⠀⠑⢈⡑⢄⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠤⠄⢀⠟⠆⠀⠐⠀⠀⠋⢈⠠⡁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢸⠁⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠐⠒⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢄⠁⠀⠀⠐⠄⡀⠀⡔⠃⠀⠀⡆⠀⠙⡦⠰⡋⠀⢘⠀⢀⠀⠀⠀⠀⠀⠲⠂⠈
⠀⠀⠀⠀⠀⠁⠀⠈⠄⠀⠆⠲⠀⠀⠀⠀⠀⠄⠀⡴⠀⠀⠀⠀⠸⠗⠛⠀⠀⠀⠀⠈⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⡄⠀⠀⠂⠐⠀⠀⠀⢐⡇⠠⠾⠗⠒⠖⠒⠀⢀⡀⠤
⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⡴⠁⡸⠁⠀⠀⠀⠀⠀⠀⣚⠁⠩⠔⠂⠠⠒⠂⠀⠀⠊⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠗⣀⠀⠐⡡⢤⠾⠃⠀⠀⠀⢠⢀⠀⠀⢀⣼⢀⡖⠲⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠶⠇⠀⠀⠀⠐⠄⠀⠀⠀⢄⢸⠀⠖⠒⠒⠲⢾⣥⡼⢰⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠚⠂⠘⠠⠘⠂⠀⠀⠀⢂⠂⠀⣰⡇⠀⠻⢦⣸⣋⣠⠄⢆⡀⠀⠂⢀⠀⠀⠀⠀⠁⢌
⠀⠀⠀⠠⠠⠄⠠⠀⠰⠤⣤⡀⠄⠛⠄⣀⠁⠀⠂⠈⠀⠉⠋⢧⠀⠨⠀⠀⠐⠄⢀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠢⠍⠀⠀⠀⠀⠀⠀⠀⠀⠉⠕⠀⣀⢴⡿⢂⡀⠰⢤⠀⠁⢘⡄⠀⠀⡄⠀⠀⢀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠂⡴⠚⠉⠀⠉⠋⠉⠹⣷⣀⠉⠀⠈⠻⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣖⠃⠀⠂⠀⠀⠀⠀⠀⣍⡹⣿⣲⡃⠀⠈⠃⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠐⠀⠀⠡⠀⠀⠀⠀⠀⠀⢿⠀⠂⠀⠤⠤⠀⠠⠤⠔⢓⡿⢹⠁⠀⠀⠀⠀⢀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠄⠒⢠⢀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢰⣄⣚⢀⡜⠀⠀⢀⢠⠐⡀⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠙⠌⠀⠌⠃⠁⡀⠀⠀⣠⢛⡽⠧⠋⠄⠌⠼⠋⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠉

⠀⡴⡶⠦⠤⠀⠀⠀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⡤⠀⠀⠀⠀⠀⠀⡀⠀⢠
⡄⠀⠀⠀⠈⠀⠀⠀⣅⣀⣀⡠⢀⠤⡤⠵⢤⠶⠄⢶⢒⡴⡄⣐⢂⡂⡂⡀⠐⠀⠆⠀⠋⠀⣧⠂⣾⠈
⠃⡀⣀⢐⡴⣦⢂⣂⠈⣐⠆⠘⠬⠄⠩⠬⠈⠈⢈⢁⣂⠐⠐⠒⠀⠰⠤⡥⢁⡌⡉⠻⡀⠘⠁⢸⠇⠀⣠
⠀⡄⠔⠠⠴⠒⠆⠐⠐⠂⠘⠂⠠⠡⠅⠥⢴⢀⠒⣀⢀⣤⠌⢈⠁⠃⠒⣒⠐⢀⡈⡶⠁⠀⢀⣿⠁⢰⠇
⠐⠐⠛⠐⠈⢃⢀⠈⢉⡃⢀⠃⠙⠐⡛⠀⠒⠰⠐⠫⢤⠈⢁⢈⡐⠘⠉⠋⣹⡯⠘⠃⣠⠂⣼⠃⠀⣾
⠄⠛⠙⠀⠃⢁⠈⠁⢘⠉⠀⠘⠚⠀⠁⠘⠘⠁⠋⠐⠀⠰⢠⡄⠬⠌⠘⠃⠀⠀⣀⣴⠇⢀⡇⠀⠀⡇⡄
⡤⠘⠇⠃⠳⠉⠃⠸⠈⠁⠈⠃⠸⠀⠻⠰⠱⠀⠀⠃⠆⡰⠂⠀⠀⠀⠀⠀⠒⠒⠛⠿⠳⠾⢥⣀⣐⡇
⡀⠀⢐⠀⢀⢠⠁⢰⠀⠆⠀⡖⠶⠀⡖⠦⠆⠰⠆⠄⡤⢸⠁⢀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠐⠀⠠⠀⡉⠙
⠁⠀⠈⠃⠀⠀⠀⠤⠴⠄⠀⠀⠠⠀⠁⠠⣤⠀⠀⠀⠁⡞⢀⡎⠀⠀⣈⡇⠀⣀⠀⠀⠀⠠
⢀⠀⠠⢤⠀⠄⠀⠰⠂⠢⠀⠀⠄⠄⠀⢀⣀⠀⠀⠐⠀⢀⡸⠁⡀⢠⠛⠀⠀⠀⠀⠀⠀⢈⠁
⠌⣠⣴⠄⠀⠚⠒⠀⠙⠂⠀⠀⠐⠒⠂⠀⠈⢣⣤⡀⠑⠞⢁⡜⠀⠈⠋⠀⠐⠂⠀⠀⠉
⠇⠀⠀⠠⠶⣶⠄⠀⠀⠀⠀⣀⡁⠀⠀⢀⢛⠶⡖⠃⡀⠀⠻⠄⢠⡈⠀⠀⠀⠤
⠂⣠⠐⠀⠀⠠⡄⠀⠔⠀⢨⡉⠘⠀⠀⠘⠮⠁⠀⠃⠀⠀⠄⠈⠁
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠂⠀⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠙⣻⣿⣮⡻⢷⠶⢤⣄⣀⡀⠀⠀⢀⣾⣿⣟⣷⣆⣴⡶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⢋⡩⠿⣧⣄⡈⢹⡿⠿⡓⠒⠒⠈⣉⢲⣤⣀⠌⠙⠛⠛⠋⠉⣹⣷⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣍⠀⠀⠉⠀⠀⠈⠻⢷⣀⣘⡒⠖⠶⠬⠥⠤⣬⠿⢤⣀⠀⠀⠀⠀⠀⠈⣿⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣷⣶⣤⡀⠀⠀⠈⠉⠁⠀⠚⠗⠀⣘⣷⣦⣾⣿⣯⣶⣤⣤⣴⣶⣄⣠⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡉⣹⣷⣷⣦⣤⣤⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡧
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠑⠓⠒⠚⠿⠛⠛⠛⠛⠛⠻⠟⣻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⠛⠛⠛⠛⢿⣿⣶⣶⣶⣷⣤⣤⣤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠺⠂⠀⠈⠀⠀⣠⠂⠀⠀⠀⠖⠀⠀⠀⠀⠈⠉⠉⠉⠁⠃⠂⠐⠀⠀⠀⠀⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⣀⣤⡀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠿⠏⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆⣀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠿⠀⠙⠉⠻⠶⠟⢳⣤⡀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠟⠀⢀⠀⠀⠀⠀⣠⣦⠀⠸⢧⣤⠶⠟⣻⢄⣴⡄⣠⠾⣆⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⡟⠙⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⢼⠿⠞⠁⠛⠃⠀⠙⠉⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣁⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠶⠶⠂⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠤⢤⢤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⠤⠤⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢳⣤⣷⣤⣤⣴⠋⢀⣤⣀⠙⣧⣤⣤⣤⣤⡾⠉⣠⣤⡈⢻⣦⣤⣤⣾⣴⠞⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣀⣀⣠⣿⠀⢿⣤⡿⠀⣿⠀⣀⣀⣸⡇⠸⣧⣼⠇⢠⡟⠀⣀⣀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠁⠉⠙⢷⣤⣀⣤⡾⠋⠀⠀⠁⠉⠻⢦⣄⣀⣤⠞⠁⠀⠈⠁⠉⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⡤⢤⠀⢠⡀⡇⠀⡿⡄⡰⡇⣤⢠⠤⡀⡅⡤⢤⢠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠂⠳⠚⠘⠝⠃⠃⠀⠃⠙⠃⠃⠛⠘⠀⠃⠃⠃⠘⢸⢛⠄

⠀⠀⣀⢀⣀⡀⠀⣀⣀⢀⣀⣀⣀⡀⣀⠀⢀⡀⣀⣀⢀⢀⣀⣀⣀⢀⣀⢀⣀⢀⠀⢀⣀⣀⠀⣀⣀⠀⢀⣀⡀⠀⢀⡀⠀⡀⢀
⠀⢰⠉⠀⠀⠀⠀⣀⠁⠉⢁⡉⠉⢀⡀⠀⠀⣄⢈⠀⣀⠈⣩⡀⠉⠀⣀⠈⠁⣀⡈⠉⡉⢁⢈⣁⣀⣈⣁⡀⢉⣉⠁⠉⢉⣀⡠⢘
⠀⠀⠦⠀⢻⠗⠛⠉⠁⠛⠋⠁⠛⠋⠉⠋⠋⠉⠛⠋⠉⠉⠉⠉⠉⠙⠉⠉⠋⠉⠁⠉⠉⠈⠈⠉⠉⠁⠉⠉⠉⠁⠈⠂⠙⣿⠃⣼
⠀⠀⡆⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘
⠀⢠⠑⠀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢄⠀⠀⠀⡀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣮⠀⠘
⠀⠀⡆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠈⠠⠀⡇⠀⠀⠘⠛⠀⠀⡹⠀⠀⢀⡴⣉⠀⠀⠀⠁⢀⠀⠀⠀⠈⡀⢸
⠀⠀⡀⠀⢺⠁⠀⠀⠄⠈⠃⠀⠀⠐⠀⢸⡆⡀⢲⢵⡆⠼⠤⢁⡞⠀⠀⠀⠀⠀⠠⠁⠀⠀⢈⡄⠀⠰⡄⡂⠀⠀⡀⠀⠀⣿⠀⢸
⠀⠀⣷⠀⣰⠆⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠈⣤⡁⢊⠤⠂⠀⠀⠘⠀⢒⠀⡐⠖⢀⠁⠀⠄⠠⣀⠀⡀⠀⢁⠀⡠⠀⠀⠀⣿⠀⢈
⠀⠀⡧⠀⢹⠀⠀⠀⠂⠀⠐⠀⠆⢀⠀⠀⠀⢈⠘⠳⠂⠀⠐⢀⠃⡄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⡷⠶⠐⡂⠂⠀⠀⠀⠀⣿⠆⠈
⠀⠀⡇⠀⢻⡀⠀⠀⠀⠁⠀⡂⠀⡇⠀⠀⠂⠘⠁⠐⠀⡁⠀⠐⠂⠀⡝⢀⠄⠀⠀⠀⠀⠀⢠⠌⠀⠀⠀⣀⠀⠀⠀⠀⠀⣭⡀⠘
⠀⠀⡟⠀⢼⠂⠀⠀⠀⠀⠀⠀⠀⢁⠀⠸⠅⠀⠂⠀⠒⡇⢀⠀⡅⢸⠋⠡⠠⠀⠀⠀⡀⢂⠏⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⣏⠀⠸⠄
⠀⢀⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⣄⠀⠀⠀⢀⡇⠈⠄⣃⠈⠄⡠⠴⠀⠁⠀⡠⠋⠀⠁⡠⠔⠀⠀⠀⠀⠀⠀⠀⢿⠃⢀⠁
⠀⠀⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⠆⠀⠠⠀⠱⢄⠋⢹⠀⢨⠃⢀⢀⡀⠀⠀⣠⣤⡎⠀⠀⠁⠀⠀⠀⠀⠀⠀⣟⠀⠈
⠀⠈⡅⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠲⠆⠀⠳⠃⠀⠸⠄⠊⡤⠀⠐⣼⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠸
⠀⠀⡧⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⡟⢀⡾⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠟⠀⢀
⠀⠀⣧⡀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠠⣈⡉⠳⡀⠀⡀⢡⣶⠶⢶⢤⣵⣀⣃⠀⢐⣠⠞⠁⠈⢳⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⢚
⠀⠀⢋⠀⢹⡆⠀⠀⠀⠀⠆⠀⠀⠢⡀⠓⠠⠈⠋⠀⡀⢠⠀⠀⠀⠩⡿⠉⠉⠉⠀⠀⠐⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢠
⠀⠀⡏⠐⢾⠃⠀⠀⠀⠀⡙⠀⠀⢦⠠⠀⠀⠀⠀⠸⠁⠰⠇⠒⢀⣈⣁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⡟⠀⢠
⠀⠀⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⣠⡶⠿⠛⠉⣯⠀⢀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⡿⠀⢸
⠀⠀⣿⠀⢸⡃⠀⠀⠀⢚⠒⠂⠀⢀⠈⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠘⢀⠀⠀⠀⠀⠘⢂⠀⠈⠀⠀⠀⠀⠀⠀⠰⣇⠀⢘
⠀⠀⠇⠈⢻⡇⠀⠀⠀⠈⡖⠁⠀⠀⢀⡼⠁⠀⠀⠀⠀⠢⠀⠀⠀⠀⣐⠁⠀⠈⠁⠀⠀⠀⠀⢀⡓⡀⠂⠀⠀⠀⠀⠀⢀⣯⠀⢠
⠀⠀⡎⠀⢼⠇⠀⠀⠀⠀⠛⠀⢀⠶⠡⠀⠉⠀⠀⠀⠀⠄⡀⢀⣀⣠⣤⠀⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡀⠀⠀⠀⠀⠀⠷⠀⢸⠂
⠀⠀⣷⡀⠐⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠠⠀⠀⠀⠀⠀⠛⠛⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠈
⠀⠀⣃⠀⢻⡅⠀⠀⠀⠀⠀⠀⠘⣦⢣⡀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢸
⠀⠀⡏⠀⢾⡃⠀⠀⠀⠀⠀⠒⠢⠙⢦⡑⢴⡄⠀⡠⠀⡁⠀⠀⠀⠀⠀⠙⡂⠁⠀⠐⠀⠐⠀⠁⠀⠠⠆⠤⠀⠀⠀⠀⢀⡄⠀⢸⠂
⠀⠀⣿⠀⣸⡇⠀⠀⢀⠀⠠⠀⠀⠀⠀⠁⠒⠙⠒⢤⡤⠦⠀⠀⠠⡀⠈⠀⠉⠀⠀⠰⢀⠀⠀⠠⢀⡄⠂⠀⠠⠀⡀⠀⠘⣧⠀⢩
⠀⠀⡿⠀⣸⠀⠀⠀⠀⠠⠀⠀⠂⠠⠃⠴⣄⡠⠤⠠⢄⡀⠀⡨⠀⠀⡀⠄⠉⠀⠀⠠⠀⢐⠘⠂⠈⠠⠀⢄⠀⠀⠀⠀⠸⣇⠀⢺
⠀⠀⣇⠀⢹⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⡀⠈⠒⠚⢀⠕⠂⠀⠚⠂⠠⢀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠰⡗⠀⠼
⠀⠘⡏⠁⢼⡃⠀⠀⠀⠀⢀⠀⠀⠐⠑⠂⠀⡠⠀⡀⠀⠀⠀⠈⠐⠀⠀⠒⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠀⢠
⠀⢰⠓⢀⣸⣧⣬⣤⣠⣤⣀⣠⣤⣄⢤⠤⣄⣀⣀⣀⣠⣀⣀⣠⣀⣀⣀⣄⣀⣀⣀⡀⠀⣀⣀⠀⡀⡠⠄⡠⠄⠀⡀⠀⡺⣇⡀⠦⡀
⠀⠈⠀⣸⠟⢯⡁⠀⠀⣀⠀⠁⣉⠀⠀⢀⠀⠈⢉⠀⠈⢀⠀⠉⢀⣀⠈⢡⡀⠈⢁⡀⠀⠀⣀⠀⠀⣀⠀⢑⡀⠀⠑⣀⠀⠹⣇⣀⠂
⠀⠀⠀⠈⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠉⠉⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠁⠉⠁⠀⠉⠉⠉⠉⠉⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠋⠛⠻⡛⠓⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠐⠀⢢⡏⠀⠀⠀⠀⠙⣆⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠭⣀⡀⢀⣠⠼⠷⠶⠦⣄⠀⠀⠈⢆⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣼⢤⣄⠜⢋⠀⠀⠀⣠⠖⣻⡶⠶⠦⣤⣥⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠈⢿⠉⠙⡶⠛⣶⠞⠁⠀⠀⠀⠀⠀⠉⠛⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣀⣈⣧⣬⣦⣤⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡖⠒⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⢻⡀⣀⣀⣤⣤⠶⠶⠦⣿⣸⣇⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢧⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⡀⢸⠟⠉⠉⠀⠀⠀⠀⠀⠈⢻⡈⠳⣄⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠈⢻⠒⠒⠒⠻⣄⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⢹⣧⠶⣄⢀⣠⣤⣤⣄⣀⠀⠀⡇⠀⠙⢷⡤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠒⠲⠤⣄⣸⣄⠀⠀⠀⠙⢲⠤⣤⣧⣠⣤⠶⠶⠚⠛⠛⢷⣄⡟⠋⠀⠀⠀⠀⠉⠛⢶⣇⡠⠤⢄⣡⣤⡾⠁⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⡴⠞⠛⠛⠓⠶⢤⣜⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣠⠼⢧⣤⠃⠀⠀⡌⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠚⠳⢤⡼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠋⠓⠦⣄⠀⠀⢀⣠⣄⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠻⣆⣠⠋⠓⢻⡀
⠀⠀⠀⣀⣤⣄⣀⣰⢀⠤⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⣿⠀⠀⠀⣸⠛⣹⠋⠀⠀⠈⠉⠉⠻⣄⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢸⣇⠤⠤⢼⣇
⠀⢀⡾⠁⠈⠢⡀⠀⠈⠉⡟⠀⠀⢰⡋⢉⣲⣀⣀⣀⣠⣥⣬⣷⡤⠤⠷⢤⣿⡀⠀⠀⠀⠈⠀⠀⢹⣆⣤⣤⡴⠶⠿⢧⣄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢷
⠀⣼⠁⠀⠀⠀⠈⡳⢤⣄⠳⣴⠛⠉⠉⠉⠉⠉⡴⠛⠋⠉⠉⠙⠲⢦⣄⣀⣈⣙⣷⣄⡀⣀⣤⡶⠏⠀⠀⠀⠀⠀⠀⠀⣸⠧⣤⣠⡴⠋⠀⠀⠊⠀⠀⢸⡆
⢀⡟⠀⠀⠀⠀⠈⠀⢀⣬⠷⠟⠒⠒⠶⠶⠶⠶⢦⣀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⠈⢿⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⣼⠧⣄⡀
⢸⡇⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣸⠁⠘⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣤⣿⣤⣤⣤⡤⠖⣋⡥⠴⠚⢻
⠘⣇⠀⠀⠀⠀⢰⡟⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⠛⠛⠲⠶⠶⢿⡀⠀⠀⠀⠀⡟⠀⠀⣽⡀⠀⢠⠔⠢⡄⠀⣸⢃⡞⠉⠀⠀⠀⠀⠀⠹⣯⠁⠀⠀⠀⣸
⠀⠉⠓⠶⢤⡤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⣠⠾⢧⣤⣾⣥⣈⣭⠿⠖⠛⠛⢻⡇⡼⠀⠀⠀⠀⠀⠀⠀⢀⡿⠤⠴⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⣸⠗⠉⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⣄⡀⠀⠀⠀⣀⣴⣾⠓⠛⣛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠶⠶⠶⠶⠞⠛⠧⣀⣀⣀⣀⣀⣀⣠⡴⠋⠀⠀⠀⢧⡀⢀⣤⣤⠤⠶⠶⠶⠶⠶⣯⡁⠀⣨⠽⢿⡙⠋⠉⠀⢹⡀⠀⠀⣠⡿
⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠶⠯⣭⣭⣉⠉⢀⡤⠴⠖⠲⣦⠀⠉⡟⠳⣄⣀⣀⣀⡀⠀⠀⠀⠙⢦⡙⠶⠞⠁⠀⠀⠀⠀⠉⠉⠉⠁
⢠⠞⠉⠉⠉⠉⠉⠛⢶⡄⠀⠀⠀⠀⠐⡯⢄⣀⡀⢀⠀⠀⠀⣿⠀⢸⣄⣀⣀⣤⠞⠀⠸⡇⠀⠀⠈⠉⠉⠉⠉⠛⠉⠉⠉⣿
⣟⠀⠀⠀⠂⠤⠤⠤⠀⣿⠀⠀⠀⠀⠀⠈⢤⣬⣉⣥⣤⣤⠞⠋⠀⠀⠈⠉⠉⠀⠀⠀⠀⠙⠲⣄⣀⠀⡀⠀⠀⠀⠀⠀⣠⠏
⠈⠓⠶⣦⣄⣤⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠀⠀⠉⠁⠀⠂⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠐⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠙
⠀⢀⢀⠠⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠄⠀⠠⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⡊⢉⣹⣿⠛⢉⣉⡁⠈⢉⡉⠉⠉⣡⣿⠟⠃⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣉⣷⠟⠉⠀⠀⠈⠙⢿⣄⠈⢈⣱⡾⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠏⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⣉⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣋⠵⡀⠀⠀⠀⠀⠀⠢⡀⠀⠀⡰⢆⣉⡱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⣰⠦⣾⣽⡤⣶⠀⠀⠀⠀⠀⠀⠈⢄⢐⡦⣼⣽⡦⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⢀⣏⠉⠛⡦⢤⣶⠤⡞⠃⠀⠀⠀⠀⠀⠀⠀⢻⡧⢤⣧⠤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⢻⣸⠶⡶⢿⣖⡒⣾⣤⣤⣄⣠⣄⣀⣀⠀⠀⠀⣫⡖⡒⣎⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠰⡀⡸⠁⣠⠠⠄⠤⢳⠨⡠⢋⠛⠉⢉⣁⣀⣷⠋⠄⠠⢡⡀⠘
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠄⠇⠠⠧⠴⠀⠀⠀⠀⠀⠹⠀⡔⢰⠐⠒⠒⢺⡀⠁⠆⠀⠀⠀⢿⠇⢿⡆⠒⠒⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣨⣤⣀⣀⣼⠀⠂⠀⠀⠀⠀⢸⡇⣸⣇⣠⣠⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣾⠉⠁⠉⠉⠉⡀⠀⠀⠀⠀⠀⣼⡖⡍⠈⠉⠉⠉⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢸⠀⢆⠀⠠⠀⠀⢰⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡜⠀⠀⠀⠀⠀⣀⠼⡆⡈⡀⠀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠼⣈⠂⢠⠀⠀⠀⠀⢀⠈⢀⡇⢊⡹⠜⣁⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣮⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠤⠈⠱⠒⠒⠴⣀⠀⠐⣠⡀⡄⠙⠕⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣰⣄⠀⢀⠀⢉⣥⣤⠶⠀⢀⣼⢀⣉⣶⡀⠁⠀⠉⠂⡐⡄⠐⠺⠷⣄
⠀⠀⠀⠀⠀⠈⢮⡃⣷⢂⣵⡶⠟⢠⠤⣀⠀⡉⠀⠀⠀⠈⡅⠀⠒⢠⡁⠙⠺⡄⠀⠀⢸⣾
⠀⠀⠀⠀⠀⡸⠀⣻⡿⠻⢋⣀⠤⠀⠊⠐⠆⠉⠀⠀⠀⠀⠘⢣⡆⡘⡄⠐⠀⣇⢱⣄⠠⢻⣀⢶⡄
⠀⠀⢸⡀⢀⠀⡸⢻⡷⡟⣉⢀⢠⣠⡸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡗⠴⣥⡄⣏⢢⡨⣿⣼⠃
⠀⠀⡄⢧⡊⢲⡟⡿⣼⠛⠁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠗⠙⢦⣉⠘⠻⣷⣇⣿⡇⡤
⠀⢣⠘⠎⣧⣟⡿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⣄⢸⣯⢻⡗⣖
⠀⠈⢷⡀⢸⣿⢵⣿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣹⣿⠸⣷⡺
⢳⡀⣏⢿⣾⣿⣾⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⣿⡻⣿⡿
⠀⢻⣸⡎⣿⣿⠋⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⣿⣿⡟
⠀⠈⢿⡧⣿⣿⣸⠟⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⢄⠙⢧⣿⣿⣷
⠐⢾⣼⣧⣿⣿⡅⠀⣿⣟⡄⠀⢠⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣗⡾⠷⣿⣿⢀⡇
⠀⠹⣟⠹⣿⣿⣧⠀⠂⣿⣇⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⠁⢸⣿⣿⢨⠁⡐
⠀⠀⠱⡪⡸⣿⣿⣧⡘⣻⠇⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⣿⣿⢲⣿⣿⣿⡎⠀⠁
⠀⠀⠀⠘⣦⣿⣿⣿⣷⣜⣾⣿⣭⣶⣾⣄⠀⠀⠀⠀⠀⠈⡿⡷⡄⠀⠀⣶⡦⣿⣳⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⣶⣄⣟⣹⣿⣿⣖⠀⠐⣀⠀⢈⡬⠷⠿⠾⢾⣷⣵⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠉⠹⠳⢤⣀⣹⣿⣉⣀⢀⣀⠈⠉⠙⢻⢄⠁⢠⡐⣻⣡⣼⣿⣿⣿⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠙⢿⣶⣛⣙⣷⣤⣂⡠⠞⣟⡟⠋⠁⠀⣀⡭⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠻⡏⠠⠋⠀⠂⡜⠀⠀⠐⠉
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠉⠉⠉⠉⠉⠉⠀⠉⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⢀⢀⠀⠀⠀⠀⠀⠀⠀⡪⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⠒⠒⠒⠒⠖⠒⠲⠒⠫⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⡠⠠⡀⡀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠤⠤⢤⢬⢬⠤⠥⠮⡤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠄⠄⠄⢀⢄⣀⣀⣀⡀⣀⡀⠀⢀⣀⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠒⠒⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣐⡑⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠉⠀⠀⠈⠀⠉⠉⠽⢻⡒⡶⡲⡢⡍⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠐⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠈⠀⢁⢳
⠀⠀⠀⡀⠤⠀⢐⠀⠄⢀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠄⠀⠀⠀⠐⠀⠀⣢
⡀⡰⢡⠀⠐⠐⠁⠰⠁⠀⠢⢀⠀⠹⠶⠤⣀⣀⠀⠔⠄⠄⠔⠤⠀⠀⠀⠄⢄⣀⣂⣂⣠⡥⢥⢤⣖⡇⠚⢥⠐⠪⠐⢄⠀⡁⢀
⠁⠡⠰⡀⢌⠢⡁⠢⠄⡀⠐⠠⠀⡀⠈⠀⠀⠈⠉⠘⠛⢛⠿⠴⠸⠭⠉⠩⠍⠉⠍⠀⠀⠀⠉⠀⠂⢂⠈⠡⠄⡊⠔⠃⣀⠆⡠
⠈⠢⡐⠌⡀⠑⠠⢀⠀⠀⠄⠀⠒⠤⠄⢁⡀⠀⠀⠀⠀⠒⠀⠠⠠⠡⠁⠄⡀⠀⠐⠀⠁⣀⡁⠈⠁⠀⠀⠈⠄⢐⡀⠥⠂⠀⢀⠠⠊
⠀⠀⠈⠐⠈⠐⠠⠄⠀⠁⠒⠀⠀⠀⠂⠀⠄⠈⠀⠉⣀⣀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠄⠀⠂⣉⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠒⠠⠄⠀⣀⡀⠀⠈⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠤⠀⠐⠀⢀⡀⠀⠠⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡠⡐⠀⠀⠀⠑⢄⠀⠘⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⣿⣜⠆⣤⠀⠀⠀⠂⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣽⣶⣿⡄⠹⣧⠀⠀⠀⠐⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣇⣻⣿⣿⠀⢣⡣⠀⠀⠀⣠⠀⠉⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢯⣻⣿⣇⠀⠱⡀⠀⠀⡸⡆⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠈⢹⣿⣿⡄⠀⠀⠀⢀⣾⣇⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠾⠟⢸⣿⣿⣿⣤⣀⡀⠈⠛⠿⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⣿⣿⣿⣷⣽⣿⣷⣶⣄⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⢀⣻⣿⣿⣿⣕⣿⢿⣿⣿⣧⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢀⠀⠰⣿⣿⣿⣿⣿⣯⡑⢵⣝⢿⣷⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠟⠛⠛⠻⠿⣿⠦⠀⢹⢷⡿⣧⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠰⠀⠑⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠋⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣄⠀⢀⠀⣼⠃⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⣏⣶⣯⣰⠃⠀⠀⠀⠀⠐⠈⡆⠀⠀⠀⠀⠀⠀⡎⠉⠉⠉⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠏⠉⠉⠉⠀⠀⡿⣄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠈⣇⣰⠆⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⠀⠀⠀⢀⡼⠋⠉⠳⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⢀⣀⣀⣀⣀⣀⢹⣏⠴⡪⠟⠁
⠀⠀⠀⢀⠀⠀⣌⢳⣾⠧⢄⡀⠀⠀⠳⣌⢠⡞⠁⠀⠀⢁⡵⠖⠒⢲⢦⡀⡔⠳⡀⠀⣠⠞⠙⣭⠉⢉⠉⠉⠛⠳⣼⡷⣫
⠀⠀⠀⠀⠙⢷⢼⣷⣿⠀⠀⠈⠉⠉⣽⣻⡛⠛⢲⣤⠞⠉⠳⡔⢚⡷⠚⠻⣤⠞⡟⣿⠃⠀⠀⠈⠳⡄⠀⠀⠀⠀⠈⠻⡇
⠀⠀⠀⠀⠶⣲⡿⠛⣟⠓⠲⠶⣤⣸⣇⠀⠱⢀⠎⠹⡄⢀⣀⣙⣼⡇⠀⢁⣸⠧⣷⠏⢆⠀⠀⠀⠀⡜⠓⢄⡀⠠⠀⠀⢻⡀
⠀⠀⠀⠀⢴⡋⠤⠤⠼⠦⢄⣠⡏⢧⠉⠉⢻⡏⢀⡾⠯⣉⣉⣁⣀⡩⢷⣯⡀⠀⠸⣆⠈⢢⡴⢶⣾⠶⡖⠶⣤⡙⢢⠤⢼⡇
⠀⠀⠀⠀⠈⠳⠤⣤⣤⣤⠶⠾⢧⣼⣀⣀⣨⠷⡾⠀⠀⠐⢨⠃⢣⠀⣸⡧⠷⢤⣴⠛⣳⠋⠀⢸⡬⠿⣧⢊⡤⡷⢼⣤⠞⠁
⠀⠀⠀⢉⣤⣬⣄⠀⢾⣁⠀⠀⠐⣸⠏⠭⠅⠈⠳⠚⠓⠒⠾⣤⡼⠖⠛⢯⣉⣉⣉⡿⢳⣄⣀⣸⣠⣤⠏⠻⣖⣁⣼⠃⠐⠲
⠀⠀⠀⠘⠿⠶⠞⠁⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⠒⠒⡶⢤⡀⠀⠀⠀⠈⠩⠥⠀⢀⣬⢤⡈⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠶⠯⠴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡔⠀⠀⠀⡄⠀⠀⢡⠀⠀⠀⢢⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠈⠃⠀⠀⢠⣾⣿⣿⣿⣿⣶⡄⠀⠀⠘⠁⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣿⣿⣃⠰⠄⣘⣿⣿⡄⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⣠⣿⠟⢩⠙⠁⠈⠛⡉⠻⣿⣄⠀⠀⠜
⠀⠀⠀⢠⣀⠀⠠⠀⢀⠀⠀⠀⠀⢀⠠⣶⠓⣠⣾⣿⣯⠀⠂⠄⠈⠀⠠⠐⠀⣽⣿⣷⣄⠂⣖⠄⡀⠀⠀⠀⠀⡀⠀⠄⠠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⠀⠠⠊⠙⣾⢸⣿⣿⡟⠟⢧⣀⣤⡄⣠⣄⣀⡼⠻⢿⣿⣿⡃⣷⠋⠑⠄⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠀⢢⠤⢇⡏⠈⢿⣫⠃⣠⣄⠨⢹⡎⢱⠏⠁⣠⡄⢘⣝⡿⠁⢹⡰⡦⡔⠀⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣄⠈⢿⣄⠀⠹⠻⣄⡞⠁⠰⣏⣩⡮⠀⢻⣡⠿⠏⠀⣠⡟⠃⣠⠃⠀⠘⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⢀⣈⣙⣛⢻⠇⠀⢠⡸⡍⠃⠈⢫⡍⠁⠐⢩⣆⡄⠀⠰⡟⣛⣋⣁⡀⠀⠀⠀⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⢤⣷⡎⠀⢀⠈⠻⠺⠇⠐⠀⠀⠃⠸⠗⠟⠁⡀⠀⢱⣾⡤⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠏⠤⠾⠛⠹⠶⣦⣤⣤⠄⠀⠀⠀⠀⠠⣤⣤⣴⠶⡏⠛⠷⠦⠹⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠄⣀⣀⠀⢀⠞⢻⣷⣧⠀⠀⠀⠀⠀⠀⣼⣾⡟⠳⡀⠒⡐⣀⠠⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠡⠀⡀⣿⣿⣷⡲⠶⠶⢖⣾⣿⣿⢀⠀⠍⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣧⡞⢿⣼⣿⣿⣿⡀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⢻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⢀⡀⠛⠿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⢸⠉⠈⢹⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠠⠅⢒⠚⠢⠆⠚⢒⠂⠵⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠀⠰⠄⠀⠀⠀⠆⠀⠀⢸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡤⠤⠤⠤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠰⠀⠀⠀⠀⡴⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⢀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⢰⠂⠀⠀⠀⠀⢣⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡴⠋⠀⢸⣷⡀⣠⠴⠂⡈⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠁⠀⣀⠚⢿⣧⡀⠀⢠⠄⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠛⠦⣤⣤⢬⣷⡴⠀⠀⢠⡿⠄⡄⠠⠄⢠⡀⠠⠀⠠⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠬⠤⠤⠥⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠁⠀⡠⠐⠀⠀⠴⠁⠀⠀⠀⣀⡀⣀⠀⡐⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢀⣄⠘⠢⠄⠀⠀⠀⢰⡁⠀⠀⠀⢰⠁⠀⠁⠛⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⢁⠂⠸⢦⠤⢤⡇⣀⠀⠀⢀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠈⠂⠌⠀⠂⠀⠀⠀⠀⣂⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠶⠶⠶⠶⠦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠾⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠤⣝⠓⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣿⠀⠀⠀⠉⠳⢦⡀⠀⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠢⠤⠀⣸⠆⠀⠀⠉⠙⠛⠛⠺⠶⢶⠞⠋⠉⠉⢳⡤⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠒⠊⠁⠀⠀⣀⣤⣤⣤⣄⣀⠀⡏⠀⠑⠆⠀⠀⣷⠻⣦⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⣀⠀⠀⠨⠻⣮⡲⢤⣀⣠⡴⠏⠀⠈⠛⠦⣤⣄⣠⣃⣀⣀⣀⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠳⣄⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠈⠃⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⢤⣄⣀⣠⡴⠞⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠶⡧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⡀⠀⢠⡀⢡⠀⣤⠀⠀⠐⠀⠀⠀⠀⠀⡌⠀⠀⠀⠼⠁⠂⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⢂⠀⢀⠒⢛⠀⠂⠓⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠴⠄⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⣄⠈⡅⠦⠀⠀⢀⠀⠐⠀⠈⡃⠀⡐⠗⠀⠀⠀⠀⠠⠀⣦⡀⠀⡀⠀⠀⣀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠑⢠⠄⠀⠀⠀⠀⠆⡠⠀⢠⠈⠀⠀⠀⠠⠆⠀⠁⢀⠀⠉⡤⢤⡀⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠠⡔⢁⠀⠀⡀⠰⡆⠀⢀⠠⠴⠀⠀⠠⡄⠂⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠇⠀⠘⢀⠇⠀⢀⠀⠰⡀⠒⠀⠀⠀⠀⠀⣜⢠⠔⠀⠀⠀⠀⠀⠁⠀⡠⠓⠤⠤⠤⣀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⣸⠀⠀⠈⠀⠀⢉⢁⠀⢀⠀⣇⠀⡋⠀⠄⠆⠀⠀⠀⠀⡀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠋⠡⡀⠂⠀⠀⠀⠀⢹⠀⢸⠀⣇⠀⠣⠀⠠⠤⢠⠀⠀⠊⡀⠊⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠘⣄⠀⠀⠀⢈⠐⡀⢈⠔⠹⠀⠀⣸⠀⠀⠀⠀⠄⠠⠁⠀⣀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠐⠈⠂⠠⢇⣀⠀⠈⠰⣀⠎⠀⠀⡇⢀⡀⠐⠃⣀⠀⢠⡟⠙⡧
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠠⡈⠉⠀⠀⠋⠀⠀⠀⠋⠀⠀⠞⠁⠀⠀⣼⠀⢀⡟⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡏⠀⡼⠁⠀⠀⠄⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⢉⠙⢦⠆⠀⠀⠀⢠⣴⡶⣶⣦⣄⣤⡀⠰⠁⠀⠀⠀⣠⠞⠀⠀⠓⣄⠀⠀⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠀⠈⡄⠀⠑⠲⠊⠉⠁⢆⡀⠀⠀⠈⠙⢻⡷⠲⠶⠒⠊⠁⠀⠀⠀⠀⣇⡀
⠀⠀⠀⠀⠀⠀⢀⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠁⠰⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⢀⠀⠀⡀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠈⠀⠀⢠⡶⠟⠛⠉⠉⢸⡄⠀⢠⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣒⠲⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠁⠀⠀⠀⠀⠀⠳⠄⠂
⠀⠀⠀⠀⠀⠀⠠⢦⠄⠀⠀⠀⠀⠀⣺⠁⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⢀⠄⠚⠁⡤⠀⠠⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠆⠀⠑
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⢤⣤⠶⠶⢦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡙⠋⠁⠀⠀⠀⠐⠁⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠠⡈⠀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢚⣄⠹⣆⢂⠀⠂⠀⢊⡀⠂⠀⠀⠀⢀⡀⠂⠐⠦⠤⠖⠐⠀⢀⠀⢀⣀⠰⠀⠀⠀⢀⢀
⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠈⠳⠈⠙⢣⠄⠀⠊⠀⠃⠀⠀⠀⠀⠀⠁⢀⢀⣠⠀⠀⠀⡁⠀⠀⠀⠐⠂⡀⠸⠃⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠊⠁⠐⠛⠀⠶⠄⢰⡀⠄⢀⠰⢀⠀⠀⠀⠀⣀⣀⠀⠃⠀⠄⠀⡄⠐⢠⡎⠰⠀⠈⠠⠄⡀⡀
⠀⢠⠀⠀⠀⠀⠀⡀⠀⠠⠂⠠⠊⡀⢤⡀⠀⠤⠄⠰⠄⠀⠀⢈⡄⠀⠀⠂⠠⠀⡁⠀⠀⠀⠄⠀⠈⡄⠁⠀⠀⠀⠀⠀⠀⠥⠰⠀⠁
⠀⠼⠀⠀⠀⠀⠀⠄⠀⠁⠀⡔⠀⠀⠀⠀⠀⠀⠈⠡⡄⠈⠐⠢⠤⠴⠀⢓⠠⠄⠀⠬⠤⠊⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⣴⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠕⠃⠀⡀⠀⠀⠀⠄⠀⢀⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠉⠉⠛⠲⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⣀⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠋⠉⠀⠀⠀⠀⠈⠙⠶⣤⣄⡀
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⡠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠈⢷⡴⠶⠶⠶⠶⠶⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢀⣀⣼⠃⠀⠀⠀⠀⠀⠙⠒⠒⠂⠀⠀⡷
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠈⢧⠘⡏⠉⠙⠛⠒⠒⠒⠒⠒⢲⡾⠛⠳⠶⠶⠦⠤⠤⢤⣤⣴⣶⡚⠋⠹⣆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠳⣷⣀⠀⠀⠀⣀⣠⣤⠶⠋⠀⢀⣤⠶⠚⠛⠋⠙⠉⠉⠉⡼⠙⣦⠀⠙⢶⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⡏⠈⠓⠢⠤⣤⣤⣤⣤⣼⠃⠀⣿⠀⠀⠀⠈⠉⠉⠙⠓⠒⠚⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠀⠀⢸⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⠶⠖⠛⠁



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

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠟⠛⠉⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠋⠁⠐⠈⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠉⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣏⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠋⠁⠀⠀⣀⣠⣤⣶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⢉⡀⠀⣀⣤⣴⡶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠸⣿⣄⣀⣀⣠⣴⡾⠟⠋⠁⢀⣀⣤⣵⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡟⠿⠻⣿⡋⣁⣠⣤⣶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣷⡀⢠⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡷⢾⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣌⢿⣆⢀⣠⣶⠾⣿⠿⠿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣦⣿⣿⣋⣀⡴⠃⠰⠆⣀⣿⣷⣶⡿⠟⣿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣼⡿⡛⠻⠟⢻⡿⣾⣶⣾⠛⠉⠀⣩⡴⣾⠋⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⣸⠏⠙⢧⠀⢿⣌⠳⣤⣉⠋⢀⣀⣴⣋⣀⣿⠀⠀⠁⠸⣿
⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⢻⡟⠃⣿⡶⠀⠈⠃⠠⢶⡆⢈⣿⠿⠛⠛⠋⠙⠛⠻⣧⣆⣄⣠⣿⡄
⠀⠀⠀⠀⠀⣼⣟⣿⣼⣿⣤⣽⣶⣇⢶⣤⡀⡀⠀⣴⡶⠿⢿⣦⣤⡀⠀⠀⠀⠀⠉⢻⡏⡀⠙⠻⣷⣶⣆
⠀⠀⠀⠀⠀⠈⠿⢷⣾⣿⡙⢻⣭⣿⣦⣬⣴⣷⣾⣿⣧⣀⣸⠟⢹⣿⣶⣆⢺⣂⣀⣸⣇⠛⠂⣀⣿⣾⠟⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠘⠓⠆⠹⡻⣿⣿⣠⣤⣬⣿⢉⡷⠛⠛⠻⢦⡞⠋⠁⢸⣿⢿⡿⠛⠙⢿⣿⣶⡿⠁⣠⡾⠷⣦⡙
⠀⠀⠀⠀⠀⠀⢠⣴⡿⢷⣄⠈⠉⣩⣭⣉⣿⣾⣇⣀⠻⠷⣾⠀⣤⣾⣼⡿⠸⠷⢶⣶⠿⢋⡀⠀⠀⠻⣷⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠿⠷⠾⠟⠀⡀⢿⣿⣙⣿⠟⡛⢻⠿⠿⠿⠛⢛⡉⣁⠀⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠘⠛⠋⠀⠁⠉⠙⠁⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⢠⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⢠⢀⡀⡆⢠⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢡⠀⠀⢀⠀⢀⡧⢠⡃⢘⡄⢼⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢇⢀⣠⣦⡏⡤⠃⠙⠋⠘⢄⢹⣤⣄⠀⡘⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠠⠀⣨⣿⢟⡋⢀⠀⠀⠀⠀⠀⠈⢸⢻⣛⢝⠁⠀⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠙⣄⠀⣱⣿⣟⣽⣿⡈⠀⠄⠀⠀⣀⠔⢁⣯⡻⡛⠦⢫⠄⡠⠋⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠂⡐⢌⣷⣿⣽⢛⡿⢻⣻⣦⣀⣀⡀⣀⡴⣿⣮⡳⡜⠀⠘⡞⠁⡀⠈⠀⢀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⣄⠈⢲⣿⣿⡇⣫⣾⣿⣿⠟⠃⡀⡀⠀⠙⠦⡹⣇⣻⡄⠈⣿⣦⡐⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⡀⠀⠁⠢⢁⠪⠑⢾⣟⣿⣿⣿⣿⣯⣤⣄⠀⠙⠁⠀⣠⣤⣴⣿⣿⡇⣆⠙⢿⠿⡅⠀⢔⡀⠀⢀⣀⠤⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⡈⠐⣿⣿⣿⣿⡟⣿⠉⠓⠛⣁⠠⠤⢈⡙⠛⣿⢻⣿⣿⠘⢮⣦⠀⠀⠀⡈⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠌⣀⠦⢙⡽⠻⣻⡟⣹⣷⣿⡒⠊⠉⠀⠀⠀⠀⠈⠋⣼⣿⠹⣯⡀⠀⠉⠻⢄⠀⠀⠸⡂⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠂⠠⠞⣠⠞⢁⠴⢞⣩⣾⣿⣿⣿⡇⠀⠀⠀⠀⡀⠀⠀⢰⣿⡿⡀⢿⡏⠲⣤⣀⠀⠀⡀⣸⡧⠐⠒⠒⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⢇⣾⢃⣶⣶⡿⠋⣙⣿⣿⣿⢻⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣷⣄⢸⡇⠀⠈⣿⣳⡹⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⢳⢋⡿⠁⠐⢸⡿⠋⠈⢃⡿⣽⣿⣷⣤⣀⣀⣤⣾⣿⣿⣿⣮⠈⡳⠀⠀⠈⠃⣥⢸⡯⣭⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⡟⣧⡾⡼⠀⢰⠛⣀⠀⢀⡾⠻⢛⢩⣿⣿⣿⠟⠿⠻⣿⣿⣿⡞⣷⠁⠀⢀⣴⡆⠟⠀⡗⢆⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢳⣽⡗⠃⠀⢢⠏⠁⢠⠟⠀⠀⠎⠸⣿⡏⠁⠀⠀⠀⣿⠁⣿⣷⠏⠀⠜⠋⡉⠀⠀⢠⠙⡄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡤⡠⠁⢻⣿⣏⠀⡟⣠⣾⡿⡀⢀⡴⠀⢀⣿⡃⡆⠠⠀⣠⣧⡴⢋⣡⣠⠴⠞⢋⣁⠀⠀⢸⡄⠈⢄⢠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡄⡐⠁⠀⢠⠓⢉⡻⢋⡵⠋⢀⣤⣞⡡⣠⠋⢻⣵⣇⠀⠀⡸⡏⣮⣿⣿⣵⣾⡻⠭⠖⢀⠀⡋⠁⠀⠈⢂⢠⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡜⠀⠀⠀⢨⢀⠜⢠⣿⣷⣿⡿⠿⡿⣾⡥⠀⡹⠋⡟⢢⣠⠏⢹⢹⣿⣿⣿⣍⠉⠳⠔⠤⠊⠀⠀⠀⠀⠀⢣⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡈⢘⡀⠂⣀⠒⢊⣟⡴⠿⢿⠏⠕⣴⣿⡿⠛⠉⢁⣴⡖⠳⢸⠿⠳⣄⣷⣿⡟⢯⠛⠳⣆⠀⣒⠀⢐⡒⠀⣀⠀⢂⡃⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠉⠁⠈⣿⠇⢠⠇⡆⠀⣿⣿⣷⠀⣰⡈⠁⠁⣤⢆⠀⢀⣿⡿⠹⠀⠘⡇⠀⠈⠙⢍⠁⠈⠁⠀⠉⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⢷⣇⠉⠁⠀⡴⠛⠛⠻⠸⠿⠟⠊⠉⠁⠀⢀⠄⣸⡃⠀⡀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠘⠿⠶⠟⢰⢠⠇⠀⡂⣼⠿⠥⠴⠶⣶⣯⡴⠾⠿⠞⠋⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢈⠟⠛⡓⠛⠁⠐⠤⠀⣤⠌⠋⠁⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⠈⠳⠏⢀⠀⡶⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⣐⡠⠔⠒⠉⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠘⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⢀⣴⠎⠁⠀⠲⣋⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢆⠡⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠀⠀⡀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠈⢇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⡄⠣⠄⠐⠄⠒⣀⠀⢀⠀⠀⠀⠀⠈⢧⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⠀⠀⢼⡏⢸⢳⡀⠘⢧⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠤⠟⠀⢻⠁⠈⡎⠑⡄⢘⣆⠥⠈⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠃⢀⡀⠦⠄⠠⠈⠁⠀⡡⠚⡋⠀⠐⡤⡗⡀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⠀⠴⠞⠁⡠⠏⠀⠀⠀⡤⢎⠀⠀⠂⠀⠐⠀⡴⠳⠀⡀⡀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠐⠉⠀⠀⠀⠀⣐⠀⠀⠉⠇⠀⠀⠀⠛⠣⢄⢇⠠⠈⠢⣄⠀⠀⠀⠀⠀⠈⠾⠤⠂
⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠁⢠⠄⠀⠀⢣⠀⢀⡄⠀⠀⠀⠀⠀⠼⡃⠀⠙⡄⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡃⠀⠠⠀⠁⠀⠀⠀⠀⠀⢸⠄⢸⠀⠀⠠⢀⡀⢔⠀⠀⠀⠀⠡⠀⠈⢠⡑⠄⡀
⠀⠀⠀⠈⢩⡀⠈⠁⡅⠇⠀⠀⡄⠀⠀⢃⠀⠀⠀⠀⡧⢠⠀⠀⠀⠀⢹⠈⡆⠀⠘⠀⠘⣮⡊⡀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⠀⠈⠒⢤⣡⡀⠀⠄⠀⠀⠀⠀⢀⡀⠄⠂⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠳⡈⢦⡀⠀⠀⡀⠇⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠄⡀⠀⠀⠀⠨⡄⣀⣀⠀⡠⠤⣅⣀⣀⣘⣤⣥⣤⣇⠤⠤⠤⠿⢛⡈⠉⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠒⠊⠁⠀⠀⠀⠨⠴⠀⡀⠀⠱⠄⠘⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠉⠙⢏⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡁⢀⡸⠤⢤⡀⠀⠣⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠞⠲⣌⢥⣀⣠⣢⠝⠒⠒⠶⢼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⣘⣄⣏⣸⡁⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠈⢢⡀⠀⠀⢀⣀⢀⢿⠋⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⡀⠀⠀⡏⠀⠀⠀⢀⣀⣀⣀⠀⡷⠚⠋⠉⠉⠉⢾⠱⡄⠀⠳⡄
⠀⠀⠀⠀⠀⢀⣴⣋⠀⠙⠋⠁⠳⣄⠀⠜⠉⢀⣀⣀⣽⠒⣤⠴⠲⠤⢤⣀⠇⠈⠲⠒⡿⠤⡀
⠀⠀⠀⠀⠀⢸⠀⠀⣩⠽⠷⠦⢤⣼⠉⡟⠋⠉⠁⠀⠈⠹⡅⠀⠀⠀⠀⠉⢳⣉⣿⣹⠃⠀⡸⡄
⠀⠀⠀⠀⠀⠊⠓⡾⠁⠀⠀⠀⠀⢸⣤⠏⠑⢢⣤⡤⠦⠤⠧⣄⠀⠀⠀⠀⠈⡧⠀⠈⠳⡔⠉⢻
⠀⣰⠋⠫⡚⠒⢳⠃⠀⡔⢢⣀⣀⣀⣈⣣⣄⣬⣰⡁⠀⠀⠀⠈⣧⣀⣤⣤⢾⣁⠀⠀⢀⡏⠉⠉⢳⡀
⢠⠇⠀⠀⠈⠒⢌⣲⣉⣉⣉⣀⠚⠉⠁⠉⠓⢦⠤⠭⠷⣤⡤⠞⠁⠀⠀⠀⠀⣸⠲⢴⡊⠀⠀⠀⠈⡇
⢸⠀⠀⠀⢀⡖⠉⠁⠀⠈⠉⠉⠙⢦⠀⠀⠀⢸⠀⠀⠀⢸⠈⣦⠀⠀⠀⠀⠀⣿⢀⣠⣿⣧⣬⣴⣞⡭⠿
⠸⣄⡀⠀⣼⠓⠂⠀⠀⠀⠀⠀⠀⣾⠉⠙⠛⠻⡄⠀⢀⡞⢀⡼⠄⣰⣒⣆⣠⢳⠋⠀⠀⠀⠉⣿⠁⣀⡴
⠀⠀⠉⠉⠻⡀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣿⠒⢉⠜⠉⠉⠋⠉⠀⠀⢹⢿⣀⠀⠀⣀⣴⠿⠿⠢⡀
⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠛⠉⣣⣤⢤⠤⠤⠞⢁⣀⠘⠄⣤⠖⠒⠒⠒⠒⠧⡀⣜⣻⠉⠁⠀⠄⣠⠴⠃
⣠⠖⠒⠒⠒⢦⡀⠀⠀⠀⣞⣉⠉⠉⠉⣳⠀⣏⣁⣨⠗⠰⡁⠉⠒⠒⠒⠒⠒⠘⡆
⢇⡀⠀⠒⠂⢀⡇⠀⠀⠀⠐⠢⠄⠶⠚⠁⠀⠀⠀⠀⠀⠀⠙⠢⠤⣤⣄⣀⣠⡴⠁

⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠶⠶⠶⢶⣶⠀⠀⠀⠀⠀⣀⣤⣾⣶⣤⡀⠀⠀⠀⠀⠀⢰⣛⡄⠀⠉⠳⣤
⠀⢀⣴⣴⣿⣿⣷⣴⣄⠀⠀⠀⠀⢸⡇⢸⢛⠛⢻⠁⣿⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⢦⡠⠋⠈⠳
⢠⣾⣿⣿⣿⣻⣿⣿⣿⣧⠀⠀⠀⢸⡇⣸⠆⠀⢸⡀⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⠊⣹⣾⣷⡄
⠀⠀⠀⠘⡆⠑⠲⠄⣄⡀⠀⠀⠀⠘⠟⠁⠀⠐⠀⠙⠛⠀⠀⠀⠀⠀⠘⠛⠉⠙⠟⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⣀⣯⣹⢀⠛⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠉⢹⣿⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⡶⠶⠆⠀⠀⠀⠀⠀⠀⢠⣶⣶⣠⣤⣶⠄
⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⡖⡖⢖⣀⣿⣇⡀⠀⠀⠀⠀⢀⣯⣽⣻⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠉⣾⣀
⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣛⣻⠧⠀⠀⠀⠀⠸⣿⣿⠏⠉⢿⣿⡿⠀⠀⠀⠀⠈⢻⣯⣯⣯⣯⣷⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⠀⠴⠦⣟⠀⠀⣾⣿⠀⠀⠀⠀⢠⡾⣅⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡃
⠁⠀⠀⠀⣹⡆⠀⣿⣿⠀⠀⠀⠀⢸⣧⠈⠉⠀⣬⣤⡀⠀⠀⠀⠀⢀⡾⣷⠉⠃⢠⣤⣤⡀⠀⠀⠀⠀⣻⣿⠉⠃⢼⣥⣾⣷⡄
⠀⠀⠀⠴⠣⠇⠠⠿⠿⠀⠀⠀⠰⠋⠘⠃⠀⠛⠻⠿⠛⠂⠀⠀⠀⠋⠀⠛⠀⠀⠛⠻⠟⠛⠂⠀⠀⠰⠃⠸⠀⠀⠘⠿⠛⠟⠁


⠀⠀⠀⠀⡇⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠋⣽⣿⡍⠻⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃
⠈⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣷⣶⡄⣀⡀
⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢿⡅
⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠠⢀⠃⠀⢀⠔⠀⠀⠀⠀⠰⡎⠀⠀⢀⡷⠀⠀⠀⣠⣟⣰⠿⣦⡀⠀⠀⠀⠀⢀
⠀⣠⢠⠌⣦⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⡓⠀⠐⣆⣉⣦⣸⡄⠒⡣⠆⠀⠀⠀⠀⠰⣌⠉⠋⢁⠜⠀⠀⢾⣷⡦⢭⠿⢿⣛⠷⠀⢠⣀⣿⣤⡤
⠀⠉⢘⠀⢹⠀⠀⠀⠀⡄⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⣈⣱⠖⠉⠁⠀⠈⠋⢳⣖⠰⡦⠎⠀⠀⠀⣠⠫⡝⣣⡀⠀⠀⠀⣿⠈⠉⠉⢰⡏⠀⠀⢠⡽⣿⢧⣄
⠀⡿⠀⠄⢽⠀⢰⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⢉⣂⡓⢤⡏⠰⠶⠆⠀⠐⠿⠆⡹⠂⠢⠤⠤⡄⠀⠉⠀⡇⠈⠁⠀⠀⢀⠇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠸⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⠈⠀⣪⣥⡄⠀⠀⠀⠀⠀⠀⠀⠸⠯⣑⣀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠈⠓⠠⢀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠘⠀⠠⡇⠀⠀⠰⠎⠐⡦⠼⠦⣀⠈⠀⠁⣀⣴⡃⠲⠤⠊⠓⠀⠀⠀⠀⣀⡴⠟⠈⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢢⡀
⠀⠀⠀⡄⠀⠀⡂⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢀⡜⠕⠂⠒⢯⠹⢏⠉⢻⠤⠤⣵⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠐⠀⠈⠃⠀⠺⣭⣼⣯⠽⠆⠀⠀⠀⠀⠈⠉⠀⠀⢀⡾⠔⢈⡔⠋⠀⠀⠈⠀⠀⠀⠀⢀⢾⠃⠀⠀⠀⠐⠈⢧⣀⠀⠀⠀⠀⣠⡟⠐⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠀⠀⢀⢀⡀⠀⠀⣾⠇⠀⠀⠀⠀⠘⡇⢀⡙⣿⣷⣾⡟⣉⠀⡼⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⣾⣷⠀⠀⠀⠀⠠⡁⢈⣿⠂⢠⣿⠀⠀⠐⠂⠀⠀⠸⣄⣁⣼⣿⣿⣧⢈⡴⠁⠀⠀⣤⡄⠀⠀⢻
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣿⢹⡀⣿⣹⡇⢠⣖⡆⠀⠈⠈⠁⠀⢸⣿⠀⠀⠈⠁⠀⠀⠀⣸⢿⢟⣻⣟⠻⡿⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⡴⠒⠒⠀⠀⡷⠄⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣿⣾⡇⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⣏⡆⠀⠀⠀⠀⠀⢠⣃⡇⠓⢿⡷⠋⣆⡱⡀⠀⠀⠀⠀⠀⠀⣾
⠀⣹⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⣾⣇⠋⠉⠁⢸⣿⣧⠀⣤⡀⠀⠀⠀⠹⡜⡄⠀⠀⠀⠀⡎⢻⠇⠀⢸⡇⠀⢿⡏⢣⠀⠀⠀⠀⠀⢰⠏
⠀⠘⢦⣀⣤⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠹⣌⢦⡀⠀⠀⠃⠘⡧⣄⣸⣇⡠⣞⠀⠸⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⠀⠀⢸⡆⠀⠀⡇⠀⢀⠸⠿⠇⠀⢠⠀⠀⠀⠈⠳⣕⠢⠀⠂⠀⢁⠀⠀⠀⢀⠇⠀⠔⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⡍⠉⠉⠉⠉⠉⠉⣡⣤⣄⠀⠀⢈⠀⠀⠸⠇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⡀⠤⠤⠤⢌⡛⠦⣄⣀⡀⠈⠁⠈⠃⣀⣀⣤⠴⠋⠁
⠀⠀⠀⠐⡒⢶⠒⠀⣦⡠⠄⠀⠀⠀⠸⣧⠘⣷⠀⢸⠀⣲⡴⠀⠄⠂⠀⡀⠘⠃⠀⠅⠀⠀⠨⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁⠀⠀⣀⣀⡀
⠀⠀⣈⠋⣨⡋⣚⣁⠶⢠⡀⡆⠀⠀⠀⠹⣿⣿⣧⡈⠠⠀⠀⠀⠀⠶⢀⠀⠀⢸⠆⡁⠀⠀⠦⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢼⣭⣨⡽⢀⠤
⠀⠀⣀⠛⣬⠾⠱⠵⠎⣴⠨⡕⠀⠀⠀⠀⢩⠁⠀⠃⡀⠀⠀⠄⢲⣖⠦⠀⠀⠀⠄⠉⠀⠀⡛⠿⠟⣤⠻⠿⠗⠀⠀⢀⡴⢄⠀⠀⠀⠀⠀⣸⢲⢿⡧⣷⣾
⠀⠀⠀⢠⠄⠎⠃⠙⠳⢶⠑⠉⠀⠀⠀⠀⠸⠀⢀⢠⡈⠀⠀⠐⠲⠂⢀⠀⠀⢠⡄⠀⠀⠀⠐⢶⡀⠉⠁⣶⠊⠀⢀⠞⠀⠈⢆⠀⠀⠀⠀⣙⠟⠀⠃⠐⣏
⠀⠀⠀⠀⠀⠈⠉⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠉⠁⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⡁⠀⠀⠀⠈⡉⠉⠉⠩⠂⢠⠎⣠⣤⣤⣌⢣⠀⠀⠘⡯⠁⠀⠀⠀⢽⡆
⠀⠀⢀⡀⢰⠻⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢣⡀⢀⠠⠄⠀⠀⠀⠀⢰⣲⡦⢀⠇⠀⠀⠀⠀⠈⠀⠉⠀⢠⠃⢎⠀⢟⡾⠈⠀⢳⡀⠀⢫⠀⠀⠀⠀⣸
⠀⠀⠀⠁⢸⢸⠀⠀⠀⢀⡴⠚⠉⠁⢪⣍⠲⣄⠀⠹⣄⠀⠀⠠⠄⠄⠀⠘⠛⢉⠜⠀⠀⢀⠄⠀⢄⠀⠀⣰⠃⠀⠀⠙⠒⠒⠁⠀⠀⠱⡀⠸⡧⠀⠠⢠⡏
⠀⠀⠐⠃⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣥⠈⣆⠀⢸⠓⠤⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠆⠀⡿⢀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣷⠀⠀⢸⠁
⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⣆⠼⢠⠀⢿⠀⢸⠀⡀⠀⠂⠀⠂⠀⢸⠀⠀⠀⠀⠘⠒⠒⠈⠀⠀⠀⠀⠀⠐⠀⣀⣀⡀⠀⢀⠀⠀⠀⠘⣦⢰⠏
⠀⠀⠀⠰⠾⡿⠆⢀⠀⠱⣀⠀⠀⠀⡘⡀⠂⣠⠃⠀⢸⠀⠀⠀⠎⠑⠀⠀⢸⠀⠰⢡⠬⠙⣀⢀⣴⡿⢿⣦⠀⠀⠀⠰⡇⣶⣾⠄⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⢦⣤⣥⡤⠜⠀⠀⠈⠳⢂⣤⣭⠤⠚⠁⠀⠀⣼⠀⠀⠀⣀⡁⡀⠀⢸⡄⠐⠌⠋⠠⠋⠀⠻⣷⣾⠟⠀⠐⠀⠈⠙⠉⠊⠀⡀⠀⠀⡤⠶⣿⣒⣒⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⣀⣁⣀⣈⣁⣀⣤⡸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢤⣿⣿⣩⠭⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠛⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠙⣧
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠹⣇
⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⡇
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣀⣸⣧⣤⣤⣤⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠁⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠐⢤⣀⡀
⠀⠈⣷⠟⠛⠛⠉⠉⠉⠉⠉⠉⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⣠⣤⠴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠉⠁⠀⠀⠀⡇
⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⢻⡀⢸⡗⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⣤⣤⡿⠶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠶⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠈⢷⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣀⣉⣭⣭⣭⢭⠽⠿⠿⠟⢻⢶⣄⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠙⠻⢦⣤⣀⣀⣠⣤⠶⠞⠛⠋⠀⠀⢀⡴⢟⡉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⢹⡆⠀⠈⠙⠶⠦⣤⣤⣄⣀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠙⠒⠶⠶⠤⠦⡤⠶⡞⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⣀⣀⣀⣤⣴⠶⠟⠋