Love Letter Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⢦⣼⢳⡀⠀⠀⠀⢀⡴⠋⠁⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⣸⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡴⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡇⣈⠵⠃
⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠈⢧⣡⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣯⠤⠤⠤⠤⠤⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣺⣿
⠀⠀⠀⠀⠀⠀⢸⠛⢦⣄⠠⠤⠤⠤⠤⠄⠀⠀⠀⠀⢀⡀⢀⡀⢒⡒⣒⠂⠀⣀⡴⠚⠁⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⢦⡀⠀⠀⣤⣀⡄⠀⠀⠈⠯⠟⠀⠘⢭⢟⡤⠞⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠶⣄⠈⠳⠁⠀⠢⠄⠀⠀⢄⡠⠖⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⣠⠴⠶⢤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡟⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣙⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣟⣛⣟⣛⣻⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠑⠲⠋⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠦⡀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠚⠙⡆
⠀⢀⡤⢄⣾⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣤⠴⠊⠁
⠀⣏⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠖⠒⠒⠒⠛⠳⢤⡀
⠀⠘⠦⠤⠤⣴⠇⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠖⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⢀⣠⡤⠤⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⡷
⠀⠀⠀⠀⠀⣀⣉⣳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠃
⠻⣏⠉⠉⠉⠉⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢸
⠀⠈⢳⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢦⣀⣀⡀
⠀⠀⠀⢳⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡠⠚⠉⢧
⠀⠀⠀⢸⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⠊⠀⠀⠀⢸⡀
⠀⢀⣠⠋⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠸⡇
⢰⠋⠁⠈⠁⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠸⣆⠁⠀⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠶⠶⠛⠓⠋
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠶⠒⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⣰⡥⠤⠖⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡋⠀⠀⠀⣀⡤⠤⠤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠑⢦⡀⠀⠀⢀⡤⠚⠁⠀⠙⢦⠔⠋⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠳⠔⠋⠀⠀⠀⠀⣰⠃⢠⠴⠒⠲⢄⡤⠖⠒⢦⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠳⡄⠀⠀⠀⠀⠀⠀⣠⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣴⢋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⠀⠀⠈⠢⣀⠀⠀⣠⠞⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⣄⠀⠀⠈⠳⠚⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠤⠴⠖⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣶⡶⠤⠤⠤⢤⣄⣀⡀⠀⠀⣠⣤⡀⠀⠀⠀⣿⣿⣿⠛⠛⣛⣛⣛⣻⣿⠿⠿⣿⣿⡿⠛⠻⣿⣿
⠀⠀⠘⠻⢿⠀⠀⠀⠀⠀⠀⠈⡆⠀⣿⣿⣷⠀⠀⠀⣿⣿⣿⣤⣀⣿⣿⣿⣿⣿⣿⣿⡜⣿⡇⠀⠀⢿⣿
⠀⠀⠀⠀⡾⠀⢴⣶⣦⣶⣦⠀⡇⠀⢹⣿⣿⠀⠀⠀⣿⣿⣿⣿⡏⣿⡟⠉⠙⠋⠉⣿⡇⣿⣷⠀⠀⢸⣿
⠀⠀⠀⢠⡇⠀⠈⠻⣿⠿⠃⢰⠃⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⢳⣿⣿⣦⡀⢀⣴⣿⢸⣿⣿⠀⠀⣾⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⣠⣿⣿
⠀⠀⠀⠸⡄⠀⢠⣤⣤⣤⣶⣾⣷⡆⠸⠃⠀⠀⠀⠀⣿⣿⣿⣿⡬⣷⣿⠿⠛⠛⠛⠋⠈⢙⣿⣴⣿⣿⣿
⠀⠀⠀⠀⠙⠤⠴⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣝⣛⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⠶⠶⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣶⠶⠶⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⢰⣿⠁⠀⢀⣴⣶⡶⠾⠿⠿⣷⡀⠀⠀⠀⢠⣤⠀⠀⣿⡀⠀⢠⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠸⣿⡀⠀⠛⠃⢸⣿⠀⠀⠀⢹⣧⠀⠀⠀⠛⠻⠷⠾⠟⠿⠾⠟⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠙⠿⣦⣤⣶⣿⠷⠶⠾⠿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⡄⠀⢀⣀⣀⣀⣀⣀⣴⠶⣦⣤⣤⣤⣴⠟⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣶⠟⠋⠿⠋⠉⠛⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢀⠀⢀⣤⣄⣀⣤⣄⣠⣤⡄⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠾⠋⠙⢿⣦⡾⠛⠻⠟⠁⠙⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢠⣿⣆⣴⣶⣄⣠⡤⠀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠏⠻⠋⠀⠉⠉⠀⢰⡟⠻⣷⣠⡾⠛⣿⡇⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠹⠿⢁⣾⠏⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⡟⠁⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣀⣀⣠⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠋⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣤⠾⠻⣶⡀⢀⣿⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⠁⠀⣠⣾⠃⣸⡇⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢸⡇⠀⠀⠉⠀⢀⣿⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⣄⠀⠀⠀⣸⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⢶⣾⣧⣀⠀⠀⠀⠙⠻⠶⢶⣿⠟⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣼⡏⠛⢷⣄⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣴⣟⠛⢷⡄⠀⣠⣶⠀⠀⢀⣶⣶⠀⢠⡶⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⢻⡿⠶⣴⣿⡾⠛⣿⠀⢀⣾⠋⣿⣠⡿⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠃⢸⣇⠀⢀⡿⠀⠀⣿⡄⣼⠏⠀⠈⣿⠟⠛⠁⢀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣸⠏⠀⠀⠻⣶⠿⠁⠀⠀⢸⣿⡏⠀⠀⠀⢿⡄⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⣀⣴⠟⠁⠀⣶⠀⠀⢀⡄⠀⠀⠀⠀⢿⡄⢰⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠸⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⢿⡀⠀⣸⡇⠀⠀⠀⠀⠈⢷⡿⠁⠀⢺⡟⠛⢻⡆⠀⠀⣰⡶⣦⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠻⣶⠟⠀⣶⢷⣆⠀⢶⡄⢀⡶⠀⢹⡷⢿⣟⠁⠀⣰⠏⠀⢸⡇⠀⢀⣠⡶⠟⠋⠉⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣶⠟⠀⠈⠻⠟⠃⠀⠘⠃⠀⠛⠀⢰⡟⠀⠀⣾⣡⣴⠟⠉⠀⠀⠀⢰⡟⠃⠀⣿
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⠀⠀⢸⡇⠀⠀⣿⠇⠀⣼⡿⠋⠀⠀⠀⣀⣤⡀⠘⢷⣤⣼⠏
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⣀⣤⡀⠀⢀⣠⣄⢠⡾⠋⠀⠀⢰⡟⠀⢀⣀⠀⠀⢠⣿⠀⠘⠋⠀⠀⠀⣰⡟⠋⣹⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠚⠋⠀⢀⣴⡾⠛⣿⡄⣠⡿⠉⣿⣿⠁⠀⠀⢠⡿⠁⢀⣾⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⣸⡿⠿⠿⠋⠀⠀⢀⣤⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣀⣴⠟⠁⠀⠀⢹⣧⡿⠀⠀⣿⠇⠀⠀⢠⡿⠁⠀⣼⠿⣿⠀⢠⣿⣿⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡁⠀⠀⠀⠀⠸⣿⡇⠀⠀⠟⠀⠀⠀⣾⠃⠀⣰⡟⠀⢿⣤⡾⢹⣿⠀⠀⠀⢠⡿⠙⣿⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠉⢿⣄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢰⡿⠀⢰⡟⠀⠀⠀⠉⠀⠈⣿⠀⠀⢠⣿⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡿⠁⠀⠀⠀⠀⠀⠀⢻⣇⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣿⡿⠿⠿⠛⠛⠋⠉⠉⠁⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⡿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⣠⣶⣿⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠟⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣾⡟⠉⠈⠙⢿⣿⠏⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⣴⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⣿⣇⠀⠀⠀⠈⠁⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⠶⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠴⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⢿⣦⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣿⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠠⠶⠿⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⠶⠶⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⠶⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⡶⠾⠟⠃⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⣾⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⣾⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⢠⣾⢿⡆⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠿⡿⠏⠸⠃⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣠⣤⣴⣶⣿⡿⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣾⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣐⡂
⠀⠀⠀⠀⠰⣀⠨⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⡰⠐⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠐⠒⠀⠈⠉⠁⠀⠀⡠⢋⡔⠫⠐⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠑⠂⠀⠀⠔⠀⠀⠀⠀⢔⡠⠤⢀⣈⡉⠂⠀⠀⠀⡄⠒⠉⢀⡀⠜⠀⢸⢇⡀⠒⢘⡀⠀⠀⣀⣀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠀⣀⠀⢠⠞⠀⡆⠀⠀⠀⢠⠃⠈⠀⡠⠇⠀⠀⠉⠖⠳⣄⢀⠎⠑⠄⡀⠀⠀⠀⠈⠀⠁⠀⢨⠂⠀⠤⢤⠆⡀
⠀⠀⡀⠀⢀⣄⠀⠠⡖⠂⠈⠁⠀⠀⠊⡠⠊⢰⠀⠀⠀⠀⠙⣀⡁⠔⢳⢀⠔⠁⠀⠀⢀⣁⣀⡀⠀⠤⠙⠀⠀⠀⠀⠀⠀⠀⠡⣀⡆⠀⢁⠄
⠀⢍⠀⠑⠋⡰⠀⠀⠃⠁⡰⠂⡴⠒⠈⠁⠢⣀⡆⠀⠀⠀⠈⠂⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁
⠀⠀⠁⠢⠔⠁⠀⠀⢨⡔⠡⠤⠡⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⡢⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠐⡄⠀⠀⠀⠀⠀⠀⠀⢍⠈⠀⠀⠈⠁⠀⠀⠁⡩⠂
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠤⠀⠴⠮⠑⠦⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢀⠔⠈⢉⣁⠢⢅⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⡄⠀⠠⡒⠉⡆⠀⠠⢦⠀⠀⠀⠌⠀⠑⠂⠉⠁⠔⢄⠀⢀⠤⠠⡀⠀⠀⠀⠀⠃⠃⡠⠁⣀⣍⠁⡸⠤⢀⡼⢦
⠀⠀⠀⠀⠸⠀⠀⠀⠘⠣⢄⠀⢈⡊⢀⡠⠊⠉⡇⠀⠈⠀⠀⠀⠀⠀⡔⠈⠉⠑⠃⠀⠉⠊⡄⠀⠀⠀⠀⢸⠛⠃⠄⠀⢉⠀⣠⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠈⠣⠀⠢⠀⡃⠀⢠⠀⠀⠀⠀⠐⠹⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡀⠀⠀⢸⠁⠀⠐⠤⢀⡀⢀
⠀⠀⠀⠀⠺⣹⠀⠀⢀⡠⠊⠀⠀⠀⠀⠈⢀⠀⡆⠀⠈⠄⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢁⢀⡠⠃⣀⡀⠠⠤⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠒⠀⠀⠀⠑⠃⠀⠀⠈⢆⠀⢠⠞⠁⠀⠂⢄⠀⠀⠀⡐⠀⠀⠀⣀⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡠⠢⠄⠄⠀⠀⠀⣀⡀⢀⠄⠠⡀⠀⠀⢈⡉⢱⠀⠀⠀⠀⠀⠈⠒⠞⢣⠀⠀⠀⡟⠠⢀⡠⠄⣣⡠⠘⠁⠀⠀⡎⠑⠄
⠀⠀⠀⠀⡠⢂⠨⠥⣀⡠⣂⠀⠀⢂⢆⠀⠁⢠⠐⢧⠀⠄⢰⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠀⠀⡇⢠⠈⠉⠴⠉⢢⠀⠀⠀⠀⠑⠐⠁
⠀⠀⠀⠈⡐⡡⡂⠍⠁⢬⠞⢣⠀⠀⠑⠠⣀⠔⠣⣀⡘⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠠⠵⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣧⣀⣐⣀⡤⠐⠚⠠⢀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢀⡀⣀⣤⣀⡤⠁⠀⡆
⠀⠀⠀⠩⠀⠀⡘⠀⠀⢀⡀⠄⠘⠁⠀⢠⠒⡆⠀⠀⠀⠀⠀⠀⠀⠈⢢⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⢸⡄⠈⠁⠀⢸⡋⡤⠒⠁
⠀⠀⠀⠀⠡⠴⠅⠒⠈⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⢠⠀⠀⠁⠐⠂⠓⢄⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣐⣚⣛⠂⠂⢢⢀⡀⠀⠀⠀⢠⠃⠀⠀⢀⠃⢤⠠⠌⣏⢘⣦⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⢹⠀⢀⣀⣀⣀⡂⡨⠍⢱⠀⠀⠀⠚⠄⠀⡄⠘⡀⠀⣶⡨⠄⠑⢌⠀⠀⠀⠀⠀⠀⠀⠤⢀⠠⢠
⠀⠀⠀⠀⠀⡠⠔⠲⠀⠀⠀⠀⠀⠉⠂⢠⠄⣀⠄⠪⣀⠀⠀⠀⠀⠀⠀⠘⠲⠀⠀⢥⡬⠮⣴⠒⠈⠉⡇⠀⠀⠀⢀⠀⠗⠀⢆⠀⠸
⠀⠀⠀⠀⠀⠈⠢⠎⠀⠀⠀⠀⡆⠀⡠⠁⢀⣀⣀⡀⠀⠁⠴⠂⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠑⢤⠀⡇⠀⠀⠀⠐⢤⡀⠀⠮⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⣀⣀⣀⠀⠀⣀⣀⣱⡄⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⢀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⣠⠤⠆⠒⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠑⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠕⠀⠄⠁⡠
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢀⢠⠌⣄⠐⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⡰⠃⠀⠈⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠠⠁⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠔⠁⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠐⠀⠡⠀⢪⠀⠐⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠢⠊⠀⠀⠀⠀⠀⠂⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠘⠈⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⢠⢀⠖⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢠⠀⢐⡰⠛⠀⢅⢄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠢⠌⣌⡈⠌⠀⠈⢐⡠⠂⠉⠀⠀⠉⠁⠚⠂⠦⠤⡠⣀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢚⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠰⠤⠄⣌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠘⠲⢄⡇⣠
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⢄⡄⡰⣢⢦⠒⢂⣠⡾⣽⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀⢄⡄⡠⣠⣠⠄⠌⠑⣁⡤⡶⣿⡵⠻⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢄⢊⠆⠁⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⡀⠀⠀⡠⢂⠌⠔⡡⢁⠊⠀⠀⢁⣀⡤⠔⠚⠀⠄⠐
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠈⡐⠁⠀⠀⠀⠀⠀⠠⢀⠌⡐⡡⠁⠌⡐⢁⠔⡠⠂⠊⠀⣀⠀⠴⡰⠃⠉⠊⠈⠀⠈
⠀⠀⠀⠀⠀⢂⠀⠔⢠⠎⠀⠀⠄⠄⠄⠔⡐⠁⢀⠊⠔⡀⠂⠔⠀⠂⣀⠄⠖⡐⡡⢁⠈⠄⠐⠁
⠀⠀⠀⠀⠀⠀⡀⢵⠃⡠⡀⠠⠂⢂⢂⠌⠰⠁⠁⣈⣀⡤⠴⠒⠛⠡⢀⢂⠊
⠀⠀⠀⠀⠀⠀⠳⣀⢐⡀⣀⢁⠅⡤⠰⠂⠂⠘⡡⠊⢊⠊⠄⠀⠐⠀⠁
⠀⠀⠀⠀⠄⡨⢐⠁⢊⠔⠀⠠⢊⠄⠐⠁⢊⠄⠀⠁⠁
⠀⠀⠀⠀⠊⠐⠁⠀⡁⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠀⠀⠈⠙⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣷⣶⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣿⠟⢻⣿⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⣾⣶⣶⣶⣤⡀⠀⠀⠀⣤⣄⠀⠀⢀⣶⡆⠀⠀⣴⣶⡄⠀⠀⠀⠀⢰⣿⡿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⠏⠉⠉⠻⣿⡄⠀⠀⢻⣿⠀⠀⣼⣿⠃⠀⣼⣿⣿⠃⠀⠀⠀⠀⣿⣿⠁⠀⠉⢿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠃⠙⢿⣿⣿⡇⠀⠀⠘⣿⡇⢀⣠⣾⣿⣿⣇⠀⢀⣴⡿⠃⠀⠀⠈⣿⣧⣼⡿⠃⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⠀⠀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⣼⡿⠀⣀⠀⠉⠻⣿⣦⡀⠀⢿⡿⠿⠋⠁⠀⠙⠿⠿⠟⠋⠁⠀⠀⠀⠀⠈⠿⠿⠁⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⣿⣯⣤⣾⢿⣿⣿
⠀⠀⠀⠀⠀⣿⣧⣼⠟⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠟⢡⣾⣿⡏
⠀⠀⠀⠀⠀⣿⣿⢫⣶⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⡀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠀⠠⡿⣻⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠸⣿⣿⣷⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⢃⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠙⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⢉⣸⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠘⣿⡿⠋⠀⢀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢩⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠇⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⣀⣀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⣾⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⣿⡟
⠀⠀⠀⠀⠀⣿⣿⠟⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⣿⡇
⠀⠀⠀⠀⠀⣿⣏⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⣸⣿⡇
⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣀⣾⠇⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠐⠛⣁⣼⣿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⢠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣟⣻⣿
⠀⠀⠀⠀⠀⢸⣿⣯⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿
⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢒⣩⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣤⢄⡀⠤⣒⠨⠅⢒⡉⠤⠲⣇⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣿⡏⣒⠨⠅⡐⠨⠍⠐⠂⠉⠹⠟⡄⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠽⠾⢾⣿⠋⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠞⡰⠈⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠉⠉⠀⠀⠀⠀⢧⣿⠀⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⢰⢀⢃⠘⡀
⠀⠀⠀⠀⠀⠀⢋⠀⠀⢀⠤⠀⢂⠀⠀⡠⠤⡀⠘⣿⡄⠀⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠎⡌⡆⠱⡀
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠒⠊⠁⠀⠀⠱⣄⠈⠢⣹⣇⣠⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠰⠘⡀⠱
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢿⣿⣿⡃⠀⠀⣀⡠⠤⠔⠊⠁⠀⠀⡆⢃⢱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⣧⠀⠉⠢⡀⠠⠔⠒⠈⢉⡀⠀⠰⠈⡆⢣⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠸⢛⣆⠀⠘⠁⠠⠔⠒⠈⠀⠀⠀⠀⠇⢘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡆⡎⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡌⢧⣀⡀⠠⠄⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣀⠠⠤⠄⠒⠂⠙⠽⠬⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠴⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠁⢀⣨⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠚⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣠⠴⠒⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣼
⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣤⣤⣤⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⢯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⢀⣀⡀⠙⠁⣀⣀⠀⠀⠀⠀⠀⣾⣿⡶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣠⡀⠉⠉⠀⠀⠀⠀⣼⡏⠹⣷⡀⠉⠙⠛⠿⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⢰⡿⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣦⣤⣀⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠶⣦⣤⣀
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀
⠛⠛⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣶⣤⣀⡀
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠉⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣤⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣀⣤⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⢸⣿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣹⣿⣿⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⢸⡇⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣿⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⣼⠏
⠀⢸⡇⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⣿⣄⡀⠀⠀⠀⠀⠈⢿⡄⠀⠀⢰⡟
⠀⢸⡇⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⠂⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣿⠉⠛⠻⠶⣦⣤⣀⡈⢻⣆⢀⣿⠁⠀⠀⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠛⢿⡿⠟⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⠃⠀⠀⠘⠛
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠻⣦⣤⣀⣀⣀⣀⣠⣴⡾⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢸⡇⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⢸⡇⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠿⠂⠀⠀⠻⠗
⠀⢸⣧⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⢀⣴⣿⡗
⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⢠⣾⢂⣤⣶⣾⣿⣶⣦⡤⠤⠤⢽⣿⣿⣾⣿⡯⠧⠤⠤⠤⠤⠤⠤⢿⣶⣶⡦
⠀⠀⠀⣠⠞⠋⣿⡇⠀⠀⠀⣾⡇⠀⠈⠉⠛⠛⠉⣹⡶⠀⠀⠈⢿⣿⣿⠋⠀⠀⣀⡀⠀⠀⠀⠀⠈⠉
⠀⢀⣾⠃⠀⢠⣿⠁⠀⠀⢠⣿⠀⠀⠲⣶⡄⣤⠀⣿⠁⣴⢶⡆⠀⠛⠁⢰⡗⢠⣿⠁⠒⣶⡆⢠⡤⢀⣶
⠀⠈⠛⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⣾⡇⣿⡇⣿⠀⣿⢸⣟⡾⠁⡄⠀⠀⣿⡇⣸⣿⢸⣿⢸⡇⣾⡇⢸⡿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⢠⣿⡇⣿⠁⢿⡄⡟⢹⣏⠀⣸⠀⠀⠀⣿⣇⣿⣿⢸⡇⢸⡇⣿⠃⣿⡇⡸
⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠛⠚⣹⡓⠋⠀⠈⠛⠃⠈⠛⠛⠁⠀⠀⣀⣉⣫⣼⡟⠈⠛⠛⠀⠙⠟⠈⠛⠁
⠀⠀⢠⣀⣀⣤⠶⠶⠶⠶⠶⠤⢄⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣟⣿⣿⠇⠐⠒⠚⠛⠛⠛⠶⠤⠔
⠀⠀⢠⣤⣭⠀⠀⠀⠀⢠⣤⣤⠀⣠⣄⠀⣠⣴⡄⠀⢠⣴⣤⠀⠀⣠⣤⣬⣭⡁⠀⠀⣶⣦⠀⣀⠀⣴⣶⡄
⠀⠀⢠⣿⡅⠀⠀⠀⠀⢸⣿⣿⣾⠟⠁⠀⢹⣿⣿⡀⢸⣿⣿⠀⣾⣿⠇⠈⣿⣿⡄⢸⣿⣿⢠⣿⡆⣿⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠻⣿⣦⠀⢸⣿⣿⣧⢸⣿⡿⢰⣿⣿⠀⠀⣿⣿⡇⢸⣿⣿⣾⠟⣿⣿⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⢿⣿⣿⡇⠈⣿⣿⠀⠀⣿⣿⡇⢸⣿⣿⡟⠀⢹⣿⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠈⣿⣿⡇⠀⠹⣿⣧⣠⣿⡟⠀⢸⣿⣿⠁⠀⠀⣿⣿⡇
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠉⠉⠀⠈⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⣠⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⣶⡆⢀⣠⣤⣶⣶⣤⣤⣀⠀⠀⠀⢘⣿⣿⣿⣴⣿⣿⢟⣎⣀⣀⣀⣀⣀⣀⣀⣐⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣠⡴⢾⣿⡇⠀⠀⠀⠀⣿⡟⠀⠛⠿⠿⣿⣿⡿⠿⢟⣉⠉⠉⠉⢻⣿⣿⣿⣿⠯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠉⠁
⠀⠀⠀⣠⡾⠋⠀⢸⣿⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢀⡀⠀⠻⣿⡿⠋⢀⡀⠀⣴⡦
⠀⠀⣼⡏⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⣿⠀⠀⡋⢻⣿⡄⣶⡆⢸⣿⢀⣾⡟⣿⠀⠀⠙⠀⢀⣿⡏⢀⣿⠇⠘⡉⢿⣷⠀⣶⡇⢠⣿⡇
⠀⠀⠙⠛⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡿⠀⣸⣿⠈⣿⡇⣿⡇⢸⡇⣼⣿⣰⠏⢠⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡏⢸⣿⢸⣿⠁⢸⣿⠀⢠
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⢿⣇⠀⣿⣿⠀⣿⠀⢿⡇⢸⡇⣿⣟⠉⠀⡼⠀⠀⠀⢸⣿⠀⣿⣿⠀⣿⡇⢸⡟⢸⣿⠀⣿⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠸⣿⣼⠻⣿⣸⠏⠀⠘⢧⣼⠃⠘⢿⣤⡴⠁⠀⠀⠀⠘⠿⡼⢹⣿⠀⢿⣇⣼⠃⠸⣿⣸⠻⢿⡼
⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⣀⠀⠀⠀⠈⠀⢰⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣿⡿⠀⠀⢀⣀⣀⣀⣈⣁
⠀⠀⠀⠦⣤⣤⣴⠾⠛⠛⠛⠛⠛⠛⠒⠦⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⢿⣭⣿⣿⠃⠀⠉⠉⠉⠉⠉⠉⠉⠛⠲⠚⠁
⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⢠⣴⣶⡄⠀⣠⣦⡀⠀⣴⣶⣦⠀⠀⢠⣶⣶⡄⠀⠀⣠⣴⣶⣮⣭⡁⠀⠀⢰⣶⣶⠀⢀⡀⠀⣶⣶⡆
⠀⠀⠀⣨⣯⣍⠀⠀⠀⠀⠀⢸⣿⣿⣧⣾⡿⠋⠀⠀⣿⣿⣿⣆⠀⢸⣿⣿⡇⢀⣾⣿⡟⠀⠹⣿⣿⡄⠀⢸⣿⣿⠀⣾⣷⠀⣿⣿⣷
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣄⠀⠀⢸⣿⣿⣿⡄⢸⣿⣿⠁⢸⣿⣿⠇⠀⠀⣿⣿⣇⠀⣼⣿⣿⣸⣿⣿⣇⣿⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⣿⣿⣧⠀⢸⣿⣿⣿⣷⣸⣿⣿⠀⢸⣿⣿⡀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⢸⣿⣿⠀⢸⣿⣿⡏⣿⣿⣿⣿⠀⠸⣿⣿⡇⠀⢀⣿⣿⡇⠀⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿
⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⢸⣿⣿⡇⠘⣿⣿⣿⠀⠀⠻⣿⣷⣄⣼⣿⠟⠀⠀⣿⣿⣿⠃⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠈⠉⠉⠀⠀⠙⠋⠁⠀⠈⠙⠁⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⢺⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⠏⢜⢆⢇⠇⢞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠺⡫⡑⡜⡸⡘⡌⡌⡜⡌⡌⡷⣄
⠀⠀⠀⠀⢰⠒⠀⠤⠤⠤⠤⠾⢯⣦⣧⣣⣳⣰⣱⣰⡸⢰⡑⡘⡜⡜⡜⣷⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠓⠻⠾⠼⠼⢼⣦⣀
⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⡆
⠀⣴⣮⣧⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠙⠀⡇
⠀⡇⠈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⡇⠀⠀⠀⠙⢯⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡫⠳⡀
⠀⠇⠀⠀⠀⠀⠀⠉⠲⣭⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⡿⢷
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡪⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⠯⠓⠉⠀⡆⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣒⠥⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⡃⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣕⣢⣄⣠⣀⠄⣠⣶⠽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡇
⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠈⠉⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡇
⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡇⠅⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠅⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠄⠀⠀⠀⠀⠀⠀⠀⡈
⢷⡠⠒⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡔⡀⠀⠀⠀⠀⠀⡇
⠀⠉⠙⠒⠯⠬⢔⣐⣢⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠢⠥⢰⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣥⠀⠀⢰
⠀⠰⠤⢀⢤⡢⡶⢔⠦⡲⠔⡢⣔⠤⡂⢄⡢⡈⢉⣐⡲⢢⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠈⠀⠁⠉⠘⠑⠃⠊⠚⠱⠫⠟⠵⠲⢶⠦⡤⣤⣽⣯⢔⢔⣴⣖⢔⡠⣠⢄⣤⣀⢀

⠀⠀⠀⠀⢀⣠⣤⢶⠶⠒⠶⢶⡶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣦⣀
⠀⠀⢀⣴⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣰⡿⠋⠀⠀⠀⠀⠠⠀⠀⠀⡄⢀⢤⠀⢿⣿⣧⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢰⡿⠀⠀⠀⠀⠀⠀⠀⡁⠠⣴⢟⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⠃⠀⠀⠀⠀⠐⠄⠈⢠⣼⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡄⠀⠀⠀⠀⠆⠀⢸⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣁⠀⠀⠀⠰⠶⢸⣾⣽⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⣷⠀⠀⠀⠀⠀⢽⡿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠘⣧⡀⠀⠀⠀⢘⡿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢷⣤⡠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠹⣷⣩⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣧⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⣘⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠈⠉⠉⠉⠉⠁⠒⠢⠤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠉⢀⡀⠀⡇⠀⠀⢀⢴⠀⡘⠯⠀⠙⡆⠀⡠⠊⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠐⡫⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠂⠁⠀⠀⠀⢤⢰⣎⡇⠀⠇⠀⠀⠀⠸⠰⠀⠒⡈⠴⠁⢠⡃⠀⣼⣧⡾⣸⢿⠋⣴⠂⠀⡴⠀⠀⣠⣤⠀⣀⠣⠀⠈⠁
⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⡄⡾⢳⡜⠿⠉⢁⢴⠃⠀⠀⠀⢐⠂⠐⠐⢀⡜⠀⢸⠳⡀⠉⠀⠁⠙⠛⠚⠷⠶⠸⠧⠤⢾⣥⣽⢐⠃⠀⠀⢄
⠀⠀⠀⢀⠀⡀⠀⢰⡄⣧⣿⠙⠋⠀⢀⠔⠁⠀⠀⠀⠀⠈⠓⠂⠮⠕⠁⠀⠀⠀⠑⢌⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢄⡀⠀⢢
⠀⠀⠀⠈⠄⠰⠀⠀⠛⠁⠀⠀⢀⡴⠃⡠⠊⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠬⣉⡒⠒⠀⠲⠖⠀⠒⠐⣒⡨⠅⠢⣌⢦⡀⢡
⠀⠀⠀⠀⠐⠀⢃⠀⠀⠀⠀⡠⢊⠔⠊⠀⠀⢀⠔⡒⠒⠐⠊⠀⠀⠈⠐⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠢⠱⡀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⢊⠔⠁⠀⠀⡠⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⠡⠀⠐⠐⠂⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠱⣱⡀
⠀⠀⠀⠀⠀⠘⡀⢁⠀⠗⠁⠀⠀⠀⢀⠇⠀⠀⣀⢤⡀⢤⡀⢶⡀⢰⢲⠀⢹⠂⠀⠀⡡⠀⠀⠀⠀⠠⡄⢦⢰⣖⠐⣶⠂⠀⠀⠀⠀⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠡⠀⠄⠀⠀⠀⠀⢠⠁⠀⠀⠀⣿⠀⡇⢠⡗⣦⠳⠸⠏⠇⢰⡄⠀⠐⡅⠀⠀⠀⠇⠀⡅⠸⠀⠻⠄⠘⠀⠸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠑⠲⠀⠀⠈⠘⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠂⠀⠀⠄⣀⠀⠄⣀
⠀⠀⠀⣀⠀⠀⠀⠰⠀⠳⠀⠀⠠⠀⠀⠡⢈⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠠⡀⡂⠀⠀⠀⠀⢀⠀⠀⠀⡌⠀⣤⢠⡄⠀⠀⠀⠀⡑⠠⠁
⠀⠀⠀⣀⠈⠢⡀⠀⠡⠁⠀⠀⠈⠐⠁⠀⠀⠀⠀⠉⠂⠂⠁⠂⠐⠉⠈⠉⠁⠀⠀⠀⠀⠙⠈⠀⠀⠀⠚⠁⠀⠀⢠⠁⢀⠌⣸⢇⠗⡷⠀⡐⠀⠁
⠀⠀⠠⢀⡈⠀⠐⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⠀⠀⠀⣀⠄⠀⠄⡀⠀⠀⠁⠈⠘⠁⢠
⠀⠀⠐⠀⠀⠙⠂⠀⠀⡠⠈⠀⣀⠀⢀⡄⣠⡠⣤⡤⢤⠀⢠⣄⣤⣠⠄⢀⡤⣠⢄⡄⠀⠠⠀⠀⡇⠀⠈⠔⣢⢀⠀⠀⠈⠀⠀⠄⠄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢄⣀⠀⠀⠈⠁⠉⠀⠉⠁⠈⠀⠀⠁⠉⠉⠁⠀⠉⢉⣀⣀⣀⠠⠤⠔⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⡀⣀⠤⠒⠒⠒⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⡀⠤⠁⠀⠐⠒⠂⠈⠉⠉⠨⠀⠀⠀⠀⠀⠀⠀⠠⠔⣊⠜⠉⠢⠤⠤⠰
⠀⠀⠀⠀⡚⣡⠊⠁⠀⠀⠀⣀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠇⣠⠀⢀⡀⣀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢐⡃⠀⠀⡖⢺⠋⠙⣺⠁⠀⠠⢆⠀⠀⠀⠀⢰⠀⠥⡖⠫⠚⠥⠓⡜⠀⡘⠀⠀⠀⠀⠀⡄⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠆
⠀⠀⠀⠀⡼⠁⠀⢀⣁⡈⢀⢀⢁⣀⠀⠀⠀⢳⠀⠀⠀⡈⠀⠂⢰⢰⠶⢱⡄⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠡⠄⠒⢀⠀⣀⠀⠀⡎
⠀⠀⠀⠰⠁⠀⠀⠾⠂⠇⠾⠾⠿⠧⠀⠀⠀⡰⠀⠀⠀⠇⠀⠓⠙⠃⠘⠘⠓⠈⠀⠐⢄⠀⠀⠀⠠⡁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠠⡀
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⣀⡀⠀⠀⠤⠤⠄⠀⠐⠁⠑⠄⠆⠀⠀⠀⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠒⠉⠁
⠀⠀⠀⠀⠀⠉⠒⠶⢤⠄⢀⠰⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⡘⠀⠀⠀⠀⠀⠁⠀⠐⢠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⡤⠒⠂⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠐⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣤⣀⣀⣤⡶⠶⢶⣤⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠈⠻⠛⠁⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⣀⣤⣴⠾⠛⢻⡇⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢸⡟⠛⠷⣦⣤⣀
⣤⣶⣿⣯⣭⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣬⣽⣿⣶
⣿⠙⠻⢷⣤⣀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣀⣤⡾⠟⠋
⣿⠀⠀⠀⠈⠙⠻⢶⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡶⠟⠋⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⣏⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠈⠙⠻⢶⣤⣀⣀⣤⡶⠟⠋⠁⠀⠀⠙⢷⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⣿⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⣿⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⣿⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⣿⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⣠⣴⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣤⡀
⠀⠀⠀⠀⠀⣿⠉⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠉⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⣀⣀⣀⡀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⠋⠉⠉⠻⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣶⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣷⣾⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣿⠿⡿⠿⡿⡟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣻⣿⣛⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠋⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣤⡶⠿⣶⡀⢀⣿⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⠃⠀⣠⣾⠃⣸⡇⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢸⡇⠀⠀⠉⠀⢀⣿⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⢿⣄⠀⠀⠀⣸⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⢶⣾⣧⣀⠀⠀⠀⠙⠻⠶⢶⣿⠟⠋⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣼⡏⠛⢷⣄⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣴⣟⠛⢷⡄⠀⢀⣴⠀⠀⢀⣴⣶⠀⢀⣶⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⣾⢿⡿⠷⣴⣿⡾⠛⣿⠀⠀⣾⠟⣿⣠⡿⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠃⢸⣇⠀⢀⡿⠀⠀⢿⡆⣼⠏⠀⠈⣿⠟⠛⠉⠀⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣸⠏⠀⠀⠻⣶⡿⠃⠀⠀⢸⣿⡟⠀⠀⠀⢿⡅⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⣀⣴⠟⠁⠀⣶⠀⠀⢀⣄⠀⠀⠀⠀⢿⡆⢰⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠸⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⢿⡀⠀⣸⡇⠀⠀⠀⠀⠈⢷⡿⠁⠀⢸⡟⠛⢻⡆⠀⠀⣠⡶⣦⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠻⣶⠟⠀⣶⢶⣆⠀⢶⡄⢀⣶⠀⢸⡷⢾⣟⠁⠀⣰⡟⠀⢸⡇⠀⠀⣠⡶⠟⠋⠉⠀⠈⢹⣧
⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣶⠟⠀⠈⠻⠿⠃⠀⠘⠃⠀⠛⠂⢰⡿⠀⠀⣾⣃⣴⠟⠉⠀⠀⠀⢰⡿⠃⠀⣿
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣠⡶⠶⠶⣦⠀⠀⢰⡇⠀⠀⣾⠇⠀⣼⡿⠋⠁⠀⠀⣀⣠⡀⠘⢷⣤⣴⠟
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⣀⣤⡀⠀⢀⣠⣄⢀⡾⠋⠀⠀⢠⡟⠀⠀⣀⠀⠀⢀⣿⠀⠘⠛⠀⠀⠀⣠⡿⠋⣹⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠺⠋⠀⢀⣴⡾⠛⣿⡄⢠⡿⠋⣿⣿⠁⠀⠀⢠⡿⠁⠀⣼⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⣰⡿⠿⠿⠋⠀⠀⢀⣤⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣀⣴⠟⠉⠀⠀⢹⣧⡿⠀⠀⣿⡇⠀⠀⢠⡿⠁⠀⣼⡿⣿⠀⢠⣿⣿⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡁⠀⠀⠀⠀⠸⣿⡇⠀⠀⠿⠀⠀⠀⣾⠃⠀⣰⡟⠀⢿⣤⡾⢻⣿⠀⠀⠀⢠⣿⠉⣿⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠙⢿⣄⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢰⣿⠀⢠⡿⠀⠀⠀⠉⠀⠀⣿⠀⠀⢀⣿⠃⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡿⠁⠀⠀⠀⠀⠀⠀⢻⣇⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣶⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⢶⣤⣴⠢⢔⣄⡠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⡸⠆⡼⠙⢄⣠⢴⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⢿⠾⠃⠁⠈⠁⠀⠀⠉⠙⠻⢀⢀
⠀⠀⠀⠀⠀⠈⢢⣄⣀⠟⢄⠴⠋⠒⠁⠀⠀⣾⣋⣀⢸⣼⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠀⠀⡀⠀⠠⠈⠂⠐⡀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢀⡅⠀⢀⣴⠶⠿⣟⣻⡆⣶⣤⡽⢿⡾⣿⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⢤⠐⠦⠀⣀⠱⠀⣠⠈⣅⠃⠀⢼⣄
⠀⠀⠀⠀⠀⠈⠉⠲⠀⢸⣇⠀⢀⣿⠛⢶⡟⣙⢆⣘⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡆⠀⠐⢦⡀⠑⡄⣀⡠⠧⠈⣀⠄⢀⡃⣾⡉⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡠⠤⡝⠛⠛⡍⡠⣨⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡅⠀⠓⠄⠔⠒⠡⠀⠠⠈⠘⠁⢀⡀⠛⠛⠓⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠋⠱⢿⠟⠠⠀⠹⠇⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣳⡦⡀⢀⣀⡀⠀⢀⣤⡤⡀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠊⠩⣝⠞⠋⠀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣸⠋⠉⢲⣆⠆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼⡃⠀⠈⠿⠀⠀⠘⠇⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⡴⠛⠛⠷⠀⠀⠤⠠⠒⠔⠦⣠⡌⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢱⣟⣷⠄⠀⠀⠀⠀⠀⠀⠙⠆⠀⠻⡄⠀⠀⠀⠸⢧⡀⡀⠀⠐⡄⠀⠐⠊⠂⠙⠉⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡔⠈⠉⠱⢞⡴⣀⡀⢀⡀⡀⠀⠈⢦⠀⠀⠀⠀⠀⠀⡼⠛⠃⠀⠁⠀⢰⣄⣠⣄⣦⣤⢋⠉⠀⢀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠐⠚⣷⣛⡾⣳⢱⡆⣦⢈⠀⠀⠀⠀⠀⠀⢧⡀⢈⣤⢨⣷⠿⠿⣿⡟⣉⠻⠀⢡⣆⠈⠀⠈
⠀⠀⠿⣇⡀⠀⠈⢱⡀⠀⠀⠀⠁⠈⠁⠉⠘⠀⢣⡏⠀⠀⠀⠀⠀⠀⠀⠉⠋⣏⠀⠁⣾⡇⠙⠀⣿⢆⠀⣆
⠀⠀⠀⠙⠷⠀⠀⠀⠛⠦⣄⢄⠀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠙⡟⢒⢚⠑⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠒⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⠆⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⣀⡐⠀⠀⠀⠀⠀⠰⠶⢐⡄⢀⣠⠞⠛⠉⠉⠉⠙⠲⢦⣀
⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⠟⠉⠉⠈⠉⠙⠆⠀⠀⠀⠀⠀⠀⠈⢀⣿⠁⠀⠀⠀⠀⠀⣀⢀⠀⠙⢠
⠀⢄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡽⠃⠀⠀⠀⣠⣄⣦⣶⡳⠀⣿⠤⠀⠀⠀⠀⠀⠘⡄⠀⠀⣤⣲⣀⡤⠀⠀⠂⠈⢱⡃
⠀⠘⠀⠀⠘⡈⣿⣷⣶⣄⠀⠀⣈⠤⠀⠀⠀⠀⠀⠀⠈⠇⢰⣶⡾⠽⠛⠋⠈⠀⢀⡶⠯⠤⠄⠀⠀⠀⠀⠀⠳⣀⠁⠈⢀⡠⢤⠀⠀⡶⠒⢋
⠀⠀⠀⠀⠐⠀⠙⠿⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠁⠀⠀⡀⢀⣴⠴⠚⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠁⠀⠀⠃⣄⣧⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠶⠞⠃⠏⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂⠀⠀⠀⠰⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠶⣤⡈⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡴⠋⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⣼⡁⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢆⡀⠀⠀⢠⡏⠀⠾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⣼⠇⢀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⢸⣿⣿⣿⠟⠀⠀⣠⠤⠤⣴⣄⡀⣠⣻⣦⣤⡴⠾⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢠⣾⣿⣿⠋⠀⣠⣾⣷⣤⣤⣬⡿⠷⠛⠉⠁⣀⣤⣶⣾⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⢸⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⡟⠁⠀⠀⢀⣶⣾⡿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⠃⢀⠜⢿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⡏⠀⠀⠠⡿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⢙⣿⣇⡀⠀⣿⣿⣿⣿⣿⠦⠀⢀⣻⣿⠅⠀⠀⠀⣠⣤⣿⣤⡀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠇⠀⠀⠉⢹⣿⣿⡧⢼⣿⣿⣿⣿⣿⡟⠻⣾⣿⣿⡄⠀⠀⠀⣿⣏⠙⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣼⣷⣿⣯⠁⠀⠀⠙⠛⠿⣿⣿⠀⠰⣿⣿⣿⣷⣦⣴⣶⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡆⠀⠀⠀⠀⠀⠸⠛⢦⣄⢺⣿⣿⣿⣿⡟⠻⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⠟⠀⠀⠀⠀⠀⠳⡀⠀⠉⠣⠈⢿⣿⣿⡦⠀⣻⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣿⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣀⠀⠀⠀⢀⣦⣀⣀⣀⣤⣾⠟⢻⣦⣺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⠀⠀⣀⠴⠛⠉⢁⣿⡏⠀⠠⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢊⠏⠀⠀⠀⣼⡿⠀⢠⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⠀⠀⣠⡟⠁⣠⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣰⣿⠀⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣸⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠁⠂⠄⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⡀⠀⠀⢀⡀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⢂⡐⠁⠀⠀⠀⠀⠈⢂
⠀⣀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡗⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄
⡇⢰⠀⠉⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠁
⡇⢀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⡇
⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠠⠀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡀⠀⠀⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡇⠀⠠⠤⠄⠀⠤⠄⠀⠠⠤⠀⠠⠤⠀⠀⠤⠄⠀⠤⠤⠀⠠⠤⠀⠀⠤⠄⠀⠤⠤⠀⠠⠤⠀⠠⠤⠄⠀⠤⠄⠀⠠⠤⠀⠐⠁
⣬⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴
⣿⣿⣡⣭⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣿⠿⠋⠀⠀⠀⢀⠀⠒⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠲⣄⢀⠀⢀⣾⣿⡿⠏⠈⠀⠀⢀⡠⠄⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣧⣿⣿⡗⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⠛⢁⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣆⢠
⠀⠀⠀⠀⢸⣿⣿⣿⣏⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠿⠛⠛⣿⣿⡿
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠰⠞⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠾⠝⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⣮⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠣⡀
⠀⠀⠀⠀⠘⢿⠹⡌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⡔
⠀⠀⠀⠀⠀⠘⡅⠁⠄⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠛⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠙⠢⢤⣭⣤⣤⣶⣶⣿⣿⠉⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣷⣠⡢⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠻⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠟⠋⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣶⣾⡧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠋⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣇⠀⠀⠀⠀⢀⣠⣶⣿⣟⠉⠀⠀⠀⠀⠀⣠⣾⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣻⠂⠀⠲⣿⣿⣿⣿⣅⡀⠀⣀⣠⣶⣾⢿⠁⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⡾⠛⠻⡛⢁⣀⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢦⣀⡿⢻⡄⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠻⡧⢸⡇⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣾⠁⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⣷⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸⡅⠀⣡⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡶⢶⡟⡆⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠳⣌⢠⠇⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣄⡀⠀⣠⣀⣀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠂⠴⠖⠒⠂⠀⠀⣠⣴⠟⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠻⣦⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠶⣾⠇⠀⢸⠶⢶⡿⠀⢀⣤⠾⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠙⢷⣄⡐⠀⠀⠰⣶⣤⣶⠆⠀⠀⠀⠀⠙⠞⠃⠀⠀⠈⠷⢞⣡⠾⠋⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠙⢶⠟⠀⠀⠶⢤⠄⠀⠀⠀⠤⠄⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⣀⣀⡀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣶⠶⠛⠛⠉⠛⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣈⣿⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣠⣴⡾⠋⠉⠉⠉⠙⢿⠶⢦⣄⠀⠀⠀⠀⣠⣴⣾⡟⠋⠉⠉⠉⠉⠉⠉⠛⣲⣤⡀
⠀⠀⠀⢀⣾⠟⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⣸⡟⠈⢻⣄⣷⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣿⠇⠀⢻⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠋⠀⠀⠈⠻⢶⣶⠶⠾⠿⢿⣦⠀⣰⠟⠛⠋⠁
⠀⠀⠀⠀⠙⠷⢶⣶⠒⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⣁⣴⠏
⠀⠀⠀⠀⠀⢀⣸⣿⠿⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠛⠉
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠿⠿⠿⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣦⣄
⠀⠀⠀⢠⣾⣯⡅⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⣿⣦⠀⠀⠀⠀⠀⢠⣿⣯⣀⡀⠀⠈⠹⣿⣶⣦⣄
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠇⠀⢻⣇⠀⠀⢠⣾⠟⠉⠉⠈⠉⠀⠀⢀⡿⠀⠈⢿⡆
⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡿⠀⠀⣿⡇⠀⣀⣀⠄⠀⠀⠀⠈⠀⢀⠀⣸⡇
⠀⠀⠀⠀⠙⠿⣶⣶⡶⡞⠀⢸⣷⣦⣄⣠⣴⣦⣾⠃⠀⠀⠘⢿⣾⡟⠀⠀⠀⠀⠀⠀⢀⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⣾⠃⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠹⣿⣤⣀⢀⣀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⣴⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠾⠧⠿⠿⠶⠽⠦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣍⣩⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠦⣀⠀⠀⣠⠴⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⢁⡔⡰⢣⢆⠈⢦⡼⠁⡴⢣⢎⡔⡘⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⡇⢨⢎⡔⣡⢫⢆⠌⣁⡜⣡⢃⢎⠜⡄⡿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡿⠀⠀⠀⠀⠀⠀⢷⠠⢎⡜⡡⣣⢊⢞⠟⡴⣡⢫⢊⠞⣰⠃⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠻⣴⣀⠀⠀⠀⠀⠈⢣⡊⡜⡵⣡⢪⢏⠞⡰⡡⢣⢊⡴⠁⠀⠀⠀⠀⠀⠀⠀⢸⡿⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢾⣡⢂⡀⠀⠀⠙⠮⣐⠱⢣⢎⣜⡜⣱⠷⠋⠀⠀⠀⠀⠀⠀⢀⣰⠖⠋⠤⡂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠻⣴⣡⠄⡀⠀⠈⠑⠮⣎⣼⠞⠁⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠨⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⡴⣡⠄⠀⠀⢀⣀⡀⢀⠀⠀⢀⡰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⠾⠒⠉⠉⠉⠉⠓⠾⣖⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠅⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⣃⡀⡀⠀⠀⠀⠀⠀⠨⡗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡂⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠧⣤⣀⢀⠀⠀⠈⠁⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡈⠁⠀⠠⢠⢀⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠦⠤⠤⠭⢌⣘⣈⣐⡀⠂⠒⠠⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠔⠋⡴⢪⠔⢋⠴⢣⠔⣡⠞⡠⠚⡤⠊⡴⠋⡤⢂⡴⣠⠔⣠⠆⡠⢂⡤⢂⠔⢢⠔⡤⢂⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⢰⡆
⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣤⠦⣼⠃⠀⠀⣿
⠀⠀⠀⠀⣠⣽⣇⠀⠀⠀⠀⢀⢀⣴⣿⡿⠃⠀⠈⣷
⠀⠀⠀⠀⠈⠙⠿⣷⣶⣧⠀⢨⣿⡿⠋⠀⠀⣀⣠⡟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⠀⠀⠈⠀⣀⣴⣿⣽⡿⠗⠀⠀⠀⣰⡶⠛⠉⢀⠀⣲⣤⣾⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣰⣿⣿⣿⣿⠖⡀⠀⠀⣾⣿⠀⠀⠀⣼⣛⠯⠛⠁⠀⠀⠀⠤⠔
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⠌⠁⠀⠀⣿⣿⠂⠀⠈⠙⠁⠀⠀⢀⣴
⠀⠀⠠⢴⣶⣿⣿⣿⣿⣿⡇⡄⠀⣿⣿⣿⣿⡿⠀⠀⠀⢈⣿⣿⣩⠀⢀⠀⠀⠀⠀⣼⣿⡆
⣾⣖⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣑⠀⠀⡜⢂⣻⣿⣿⣔⡄⠀⠀⠀⠀⢿⣿⣿⣦⣀
⢹⣿⣿⣿⣿⠿⠻⣿⣿⣿⣽⣷⡀⢿⣿⣿⣿⣿⣟⣄⣤⣿⣿⣿⣿⣿⡏⢰⠀⠀⠐⢸⣿⣿⣿⠟⠋⠁
⠀⠉⠉⠀⠀⠀⣠⣿⣿⣿⣿⡛⠻⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣇⠀⠀⠀⠘⣿⣿⡟⢷⣀⣀
⠀⠀⣶⠟⣻⣿⣿⣿⣿⣿⣿⣴⣀⣴⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⡣⠀⠀⠂⠀⢹⣿⣷⡊⢿⡟⠒
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⠟⠀⢀⣿⣿⣿⣿⣿⣿⢏⣵⢿⣤⣀⡌⢠⡀⠀⠈⢿⣿⣏⠀⢻
⠀⠀⣨⣤⣴⣶⣿⣿⣿⣿⣿⣿⣟⠗⠀⢀⣾⣿⣿⣿⣿⣿⠿⢏⠀⢄⠜⠻⠿⣷⠛⠆⢠⡞⢽⣿⣆⢼
⠀⠀⣳⣷⣿⣿⣿⣿⣿⣿⣟⣿⣽⣶⣷⣿⣿⣿⢛⣿⣿⡿⣤⣀⡐⢄⠘⠀⡷⣿⣷⣿⠞⠁⠀⢹⡻⡏
⠀⠀⠻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡟⠁⣼⣿⣏⠥⠈⣹⣿⣶⣆⣠⡿⣿⡟⣿⡆⠀⢁⢀⠃⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠘⢿⣿⣯⣤⢦⣻⣿⣟⣿⣧⣨⣿⣿⣿⡇⢀⠀⠒⠈
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⢻⣽⣷⣷⡷⣌⢿⣿⣍⣿⣿⣷⣿⡿⣏⣿⣿⣿⣯⠀⠸⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣶⣹⡯⣿⣯⡇⣻⣤⣍⣿⣿⣿⠟⠛⠣⠀⣻⣿⣿⡟⠀⢢⠀⠀⠁⡐
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡌⣺⣟⡻⣿⣿⠛⠁⠀⠀⢻⣷⣿⡇⣈⠀⢷⣆⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣧⡿⡅⣿⢻⣱⣟⠛⠦⠀⠰⢦⣬⣿⣿⠁⡃⠀⢸⡍⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣾⣿⢿⣶⢶⣮⠆⢀⠬⣿⣷⡞⣇⣄⠸⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣿⣷⢏⣲⣿⣿⡧⣮⡇⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠾⣿⣿⢡⡴⣾⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣷⣍⣡⡿⠉⣆⣛⡿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣼⣿⣷⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠴⠒⠒⠂⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣭⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠤⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠶⢦⣄⡀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣴⣶⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢿⡀
⠀⡀⢀⠀⢀⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠃⠎⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⣼⣿⠁⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀
⠀⠀⢠⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⣼
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⢃
⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠖⠁
⠀⠐⡀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⢣⡑⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⡀⣠
⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠦⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⠛⠛⢻⣦⣀⠀⠀⠀⢻⣆⢆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⢷⣦⣀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠻⢷⣦⣙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⣄⠀⠀⣟⠉⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻⣿⠀⠀⣿⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⢶⣶⡀⠀⢸⠀⢸⣿⡇⢰⠇⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⣿⣇⠀⢸⡆⢸⣿⣇⣼⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠄⢻⣿⡄⢸⠀⢠⣿⣿⠇⢰⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠀⢻⣿⡞⠛⠠⢿⡯⠀⠘⠋⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣤⠀⠀⢱⠦⠘⠋⠀⠀⢀⣀⢤⣀⣴⣅⢶⣶⣤⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣭⢹⣿⣿⡄⢀⠞⠀⠀⢀⣠⣴⣿⣿⠿⠋⢻⠁⠜⢋⠻⣷⣇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⣿⣧⡎⠀⠀⠀⣿⣿⢧⣾⣿⣾⣷⡬⣿⣿⣷⣧⣬⠛⣇⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⠀⣿⣿⡟⠀⠀⠀⢠⣿⢏⣿⣽⣿⣛⣿⠇⠹⠿⠿⠿⠻⠿⠷⠴⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠠⣿⣿⢱⠁⠀⠠⣿⠋⢰⣿⠿⣿⡟⠋⠀⠀⠀⠀⣠⣤⣤⣤⠄⣀⠈⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢧⣈⢻⡟⡿⠀⠀⣽⣟⣷⣿⣇⣰⡟⠀⢠⢐⣼⣾⠛⠈⣩⠹⣝⣓⡈⢫⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠄⠀⠈⠙⢿⣇⠀⢸⣿⣿⣿⣿⣧⣻⠇⠀⣠⣿⣿⡍⣠⣶⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣴⡉⠀⠀⠀⠀⢸⣿⣄⣿⣿⣛⣿⣿⣼⣟⠁⢐⣷⣿⠟⢰⣿⠟⣧⣽⡿⢷⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣺⣦⣀⣠⣄⣀⣠⣿⣿⣿⣿⣿⡿⢿⣧⡾⠁⠀⢸⣿⣿⡆⢸⣿⣀⡼⠋⣴⣟⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣼⣿⣿⡿⡟⠹⢛⣿⣿⣿⣿⡿⠋⠀⠘⠛⠁⣤⣴⣿⣿⣿⣷⢼⣿⠿⣷⡄⠛⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⣿⡿⠋⠀⠱⢁⡼⣿⣿⢏⣤⠀⢠⣄⣀⣄⣤⣤⣬⣍⣙⠻⠟⠻⣿⣧⡈⠛⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⣃⠠⠀⣦⣸⣿⣿⠃⡼⣷⣄⡘⠋⣿⠿⢿⢿⣽⣿⣽⣶⣿⡄⢿⣿⣿⣟⡛⠛⡄
⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣿⣿⢏⡲⣾⣿⠋⠐⣦⠄⠀⠉⠀⠀⠀⠳⢻⡟⠫⡝⢼⢏⣧⡉⠢⠙⠛⠉⡛⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠁⣭⣼⣿⣿⠟⠛⠂⠰⡥⠂⣀⣀⡀⢑⠄⢠⢄⡀⠀⠺⠁⠀⣽⣧⡀⣠⣶⣧⣴⣦⣄⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⣿⡿⢛⠁⠀⢀⣠⡟⢰⣾⡿⣿⣿⣿⣿⡛⢦⡜⢀⢦⠀⢰⢾⡇⣰⡇⣾⣿⣿⣿⣿⣇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⣾⠟⣅⠛⣥⠛⣔⡿⣿⢻⡟⣦⠱⡉⣤⠒⠀⣴⠿⠟⢠⡏⠳⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀⡞⠀⠐⠇⠘⢠⣤⠙⢿⣤⣿⣯⢥⣟⣷⠖⠁⣆⡠⠂⣀⡴⢃⢾⣵⣛⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢰⡏⠀⠈⠃⠰⢸⣿⣦⣹⡡⢍⣆⠢⠺⣅⠶⠚⣩⡴⣻⡏⠰⡿⢻⣿⡛⣹⢾⣿⣏⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣺⣿⣄⡀⢡⣽⣬⣿⣿⡟⠀⠈⡁⠔⢠⢞⠐⠁⠈⢳⠉⣰⡇⢀⠎⣹⣶⢫⣟⡿⡏⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⢻⣿⣟⣸⢣⣿⣿⢿⣧⠈⢀⠀⠀⡄⡘⠃⢀⠐⠏⢰⠏⡼⢛⣴⠣⣯⡛⢼⠱⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⡻⣿⣢⡱⠆⡉⠘⠹⡀⢀⣴⢞⣷⣦⠎⣀⠁⠠⠏⠾⣁⡾⣯⡾⢃⡔⠠⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡟⣴⣸⣟⡇⢸⣇⢻⣿⣿⣯⡥⠀⠌⠀⡞⢻⡿⣿⣁⡿⢧⣸⠄⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡛⣿⣷⣭⣿⣿⡟⠻⠋⠀⠀⠔⠁⢨⡏⣱⠾⣏⢘⢻⣅⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣽⣻⡅⣹⢿⢀⣠⢂⣏⣠⡑⢲⣤⣉⣾⣥⠟⣲⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣟⣧⣶⡜⢁⡎⢡⣜⣁⡛⣯⣼⠧⢾⡻⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣧⣾⣟⡻⢿⣿⠁⣿⢃⣶⠜⣥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⢿⣍⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⠿⠿⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠒⣻⡿⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠖⠛⠉⠉⠀⠀⠀⠀⣠⡾⠋⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⢀⣀⣠⡤⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⢠⣶⣿⣟⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠸⣇⠀⠉⠉⠙⠛⠻⠷⠶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣠⣤⣤⣤⠞⠉⠉⣿⣃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡀⠀⠀⠀⠀⢠⡟⠉⠙⠛⠻⠷⠶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠟⠓⠢⢤⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⣦⣿⡇
⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠾⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠾⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢀⣴⠟⠋⠀⠀⠀⢀⣀⣠⣤⣴⠶⠾⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⣟⣡⣤⣴⠶⠾⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉



⣀⣀⣀⢀⡀⣀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠘⢦⠎⠀⠀⠀⡷⠒⠖⠲⠗⠤⠤⠤⠤⠤⠤⠤⣀⢀⣭⡉⢸⠀⣸⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⡠⠤⠧⣼
⣤⣄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡟⠖⠁⢸⢸⠹⡀⠀⠀⠀⠈⠓⠤⢤⣤⣴⠃⠀⠀⠀⠈⢧⣠⣤
⠀⠀⡇⠀⠀⠀⣀⠞⠀⢀⠔⠊⠉⠉⠙⠒⠚⢡⠇⠀⠀⡇⠀⠀⢸⢸⠀⠉⠉⠉⡏⠉⢳⢰⣋⣁⣸⠀⠀⠀⠀⠀⣸⡇
⠀⠀⡧⠤⡀⢎⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇⠀⠀⢸⠾⣄⣀⣀⣀⣧⠖⠹⡎⠀⠀⢸⡣⢄⣀⣠⠔⠁⡇
⠀⠀⢧⣄⠉⠛⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡧⣤⠤⠞⠀⠀⢧⣈⠁⡇⠀⠀⠁⠀⠀⠈⠀⠀⠀⢸⠀⠀⡇
⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠧⣇⠀⠀⠀⠀⡔⡩⠖⠚⠦⣄⡀⠀⠀⠀⠀⠀⡴⠓⢦⠀⡇
⠀⠀⡧⠤⠤⠤⠤⠤⠵⠤⣤⣀⣀⡀⠀⠀⢀⠞⠀⠀⠀⣠⡴⠃⠀⠲⢖⡛⠁⠀⠀⠀⢀⣉⣉⣉⠉⠉⠒⡡⢄⢀⠧⡇
⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠚⠁⠀⠀⠀⢠⠁⡆⠀⠀⠀⠀⡟⡆⠀⠀⠀⡏⠀⠀⠀⢹⡀⠀⠑⠋⡇⠀⣇⣀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡥⠤⠤⠤⠤⠔⡣⠊⣧⠀⠀⠀⠀⡿⡇⠀⢲⠲⠃⠀⠀⠀⢸⡇⠀⠀⠀⡄⠀⠀⠈
⠀⣠⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⠤⠎⣠⡀⠰⣶⠲⠒⠁⠀⠻⠤⠤⠤⠤⠇⡇⠀⠀⠙⡆⠀⠀⠀⢸⠇⢠⠚⠉⠳⠤⣤⢤
⠔⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⣀⡰⠃⠙⣄⢈⣙⣢⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢠
⠤⠤⣄⡀⡎⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⢆⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⡇⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣄⡀⠀⠀⠀⣠⠔⠓⠒⠺⡇⠀⠀⠀⢸⠤⠧⣄⠀⠀⡠⠚⠁
⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠀⠀⠀⣠⠔⣇⠀⠀⠀⡸⠀⠀⢸⠀⡜⠀⣀⣠
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢱⠀⠰⠁⠀⠀⠉⠉⠉⢣⠀⠀⢸⠀⡅⠀⡇
⠤⠤⠤⠤⢤⠭⠟⡹⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⢣⡀⠳⠤
⣀⣀⡤⠖⠁⠀⠀⢇⠀⠀⠀⠀⠘⠤⠤⠤⠤⠤⠤⢤⠤⡤⠤⢄⠀⡤⠤⠜⠀⠀⠱⢄⡀⠀⣀⡠⠋⠀⠀⠸⣄⠀⠑⢤
⠛⠒⠲⠤⣔⠒⠋⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠲⡇⠀⠀⠻⠀⢠⠖⠒⠒⠒⠒⢧⠟⠳⢦⡀⠀⠀⢀⡤⠛⢀⣼⣀
⠀⠀⠀⠀⠈⢣⠀⠀⠈⠓⠦⠤⠤⡠⠤⢄⠀⡞⠁⠀⠀⣇⠀⠀⣀⡤⠼⠶⠶⠦⣄⠀⠈⠀⠀⠀⡇⠀⠀⡸⠀⠀⡇⠘⠁
⣀⣀⣀⣠⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠂⠀⠀⡨⠖⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡗⠒⡎⠀⠀⠀⠙⣆⣀
⠀⠀⠀⠀⠙⠒⠒⢲⠄⢠⠖⠒⠒⠒⠒⠒⠒⠒⠒⡲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣀⣀⣠⠗⣏⣁⠀⠀⠀⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠺⢲⠁⠀⠀⡰⠒⠒⠒⠒⠒⠚⡃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⡴⠋⠁⠀⠀⠀⠀⠉⢢
⠤⠤⣄⠀⠀⡤⠤⠴⡊⠘⠯⣉⠁⠀⠀⠀⠀⠀⠀⠙⠦⢤⡀⢀⣤⠔⢺⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⡤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣻⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⡄⠀⠀⢠⣿⣿⡏⠀⠀⠀⣿⣿⣛⣛⣋⣉⣻
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⡇⠀⠀⠘⣿⣼⣷⠀⠀⣾⣧⣾⠁⠀⠀⠀⣿⣿⣿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⢹⣿⠽⣇⣸⡟⣽⠇⠀⠀⠀⠀⣿⣷⢿⠶⠶⡶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⢿⣯⠽⡿⣼⡿⠀⠀⠀⠀⠀⣿⡿⣿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡾⠶⡶⢶⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⣿⣵⠿⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠾⠃⠀⠀⠀⠙⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠺⠿⠿⠷⠶⠶⠶⠇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢿⣇⠀⠀⠀⢠⣿⣿⣯⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⣠⣾⣿⣿⡏⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣟⣿⣿⠟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⣿⣏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠉⣿⡟⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⡼⣿⣿⣿⣿⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁

⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⠻⢿⣿⣿⠿⠛⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⠟⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠈⠑⢄⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠐⢄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡠⠤⡄⠀⢣⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠥⠀⠀⠬⠆⠈⡄⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⣍⠀⠂⠀⠄⠂⡘⠀⡇⠀⠀⠀⢸⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠈⢢⡀⠫⢃⡠⠃⡠⠃⠀⠀⠀⠗⠊⠁⠀⠑⢄⣀⠀⣀⡠⠞⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣤⠞⠀⠉⠹⠦⣒⠛⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠈⠂⠤⠤⠤⠒⠁⠉⠢⡀⠀⠀⢀⠛⠉⢙⠏
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢀⣤⡤⡤⡄⠀⠀⠀⠘⡄⢀⠼⣀⡠⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡆⢀⠎⠀⠈⣿⠇⠀⢰⠀⠀⢈⠎⠀⠀⡏
⠀⠀⠀⠀⠀⠀⡘⠀⠀⡠⠋⠁⠑⢢⠎⠁⠀⠀⢸⡄⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠇⠀⠊⠀⠀⠀⡠⠊⠀⠀⠀⠀⢸⠈⠒⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠸⢄⣀⣀⡴⠊⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣀⣀⣀⣀⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠸⠆⠀⠀⢹⣄⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢠⣦⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠛⠿⣿⣷⠈⡟⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⠶⠋⣀⣤⣬⣟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⢀⡏⠀⠀⣼⠃⡀⠈⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢋⣶⠀⠀⢸⠇⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⢀⣿⢯⡀⢀⣾⣧⠼⠟⠀⠀⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣸⣿⣮⣽⠟⠛⠁⠀⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⠀⠀⢀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⣹⣿⣿⠃⠀⠀⠀⢀⣴⠴⢶⣿⣴⣿⣿⣿⣷⣴⣶⡶⠿⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡄⣸⣿⣿⡏⠁⠀⢀⣼⡛⠓⠶⠶⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⡀⣸⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣥⣿⣿⣿⠇⠀⠀⣼⣿⣧⣤⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠉⠙⠁⢸⣿⡿⠂⠀⠀⣿⣿⣿⠥⠀⠀⠀⠀⢠⠛⠋⠙⠛⠻⢿⣿⣯⣤⣽⣟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⣁⣤⣿⣷⣤⠀⠀⣿⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⠻⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠀⣠⢥⣼⣿⣿⣶⣾⣿⠏⢹⡀⠀⠀⠀⢀⠎⠀⢀⣠⡖⢠⡀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢷⣄⢿⣷⠾⠋⠉⠉⢻⣰⠚⣲⠟⠁⠀⠀⠀⣾⣠⣾⣟⠃⠀⠀⠐⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣷⣶⡿⠛⣿⠀⠀⠀⠀⠀⠀⠙⣅⠀⠀⠀⠀⢸⣿⣿⡔⢉⠀⠀⠀⠀⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣯⡘⣠⢼⡏⠀⠘⠀⠀⠀⠀⠰⠀⠐⠛⠂⠀⠘⡿⣿⣆⠺⠃⠀⠀⢀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⠿⣄⣦⣾⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡇⠀⠈⠋⠛⠛⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⠠⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣾⠋⠳⣄⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆⠈⠁⠀⠀⠀⠀⢀⢀⡠⠜⠋⠁⣙⠁⠀⠀⠉⡀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡟⠀⠀⠀⠀⡇⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⣠⠛⢁⠀⠀⠀⠀⠁⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⠠⠄⠀⠀⠀⠀⣸⠃⠀⠀⠆⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣮⣦⡀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⢛⣯⠇⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⣿⣻⡶⣄⠀⠀⠀⠀⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣦⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⡿⠟⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠆⢿⣦⠄⠀⠀⠀⠤⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣟⢻⡟⣿⣿⡀⠉⣿
⠀⠀⠘⠿⠀⢴⡇⠀⠀⣈⣤⣤⣤⣄⠀⠀⠀⣀⣤⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡏⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣴⣾⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠠⠄⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⢤⡀⢸⣿⣿⣿⣿⣿⣿⠀⠸⠮⠛⠀⠀⠀⠉⠁⠀⠀⣿
⡆⠀⠀⠀⠖⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣤⣼⣧⣀⣀⣀⣠⣤⣤⣤⣀⣿
⣿⡟⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡤⢠⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿
⣏⡀⠀⠀⠀⠀⠐⠓⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣤⣤⣀⠀⠀⠀⠘⠃⠉⠙⠛⣿
⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠂⠃⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠉⠉⠉⠀⠺⡆⠐⠆⠀⢀⣠⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣄⡂⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⠛⠿⠿⠟⠻⠿⠿⠿⠿⠿⠿⠛⢻⣿⣿⠿
⠀⠆⠀⣠⡄⠀⠀⠀⠀⣠⣤⡀⠀⠀⢠⣤⠀⣤⡄⠀⠀⢀⣄⣠⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣴⣶⣷⣷⣶⣶⣶⣶⣶⣧⣉⠆
⠀⠀⠀⣾⡇⠀⠀⠀⢰⣿⠉⣷⠀⠀⠘⣿⡄⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⣼⠿⠿⠟⠻⠿⠿⣿⣿⣿⠶
⣶⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⣿⠶⠄⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⣿⡿⣷⣀⣀⣀⣀⠀⠀⢻⣿⣿
⢸⠁⠀⣿⡇⠀⠀⠀⠀⣿⣤⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠰⣿⢠⡄⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠻⣷⣾⣿⣿⣿⢿⠿⣿⣿⣿⠟
⠻⠀⠀⠻⠿⠟⠀⠀⠀⠙⠛⠉⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠿⠿⠗⠀⠀⠀⠀⠀⠛⠋⠀⠀⡀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⣿⣿
⣿⣿⣿⡛⢿⣿⡏⣿⠏⣿⠏⣿⣟⣿⠙⣿⠙⣿⠹⣿⣻⡟⢻⣛⣿⢻⣟⣻⣿⣿⠁⡾⢶⣴⡖⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠆
⣿⣿⣽⣷⣬⣿⣇⣿⣇⣽⣆⣿⣟⣿⣀⣿⣠⣟⣠⣿⣻⣇⣠⣿⣧⣸⣏⣹⣿⣿⠈⢧⡌⠁⠐⢨⣿⡿⠿⣿⣿⠿⣿⣷⣾⣿⣿⡆
⣿⣿⡇⢸⡇⢹⣏⢸⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣟⠿⡟⢹⣿⠛⣿⣻⣿⣿⠀⠘⢥⡐⠆⠘⠛⠛⠚⠿⠿⠿⠿⠿⠿⠿⠟
⣿⣿⣧⣾⣧⣼⣯⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣸⣟⣷⣌⣻⣿⣿⠀⠐⠸⠇⠠⡆
⣿⣿⠁⢾⡇⢻⡅⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠉⣯⣿⠉⣿⡏⣿⡿
⣿⣿⣷⣾⣷⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣤⣿⣿⣄⣿⣧⣿⡿⠀⢠⣶⣶⣄⣠⣶⣤⡀⠀⢠⣾⣷⣦⣠⣶⣦⡀
⣿⣿⣧⠸⣇⣿⡇⢹⡇⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡼⢋⣿⡇⣿⣯⣯⣽⣿⣿⣷⠀⢺⣿⣿⣿⣿⣿⣿⠇⠀⠸⣿⣿⣿⣿⣿⣿⠇
⣿⣿⣿⣦⢿⣿⣿⣼⣷⣼⣿⣯⣿⣿⣿⣿⣿⣿⣿⣥⣯⣽⣧⣽⣯⣭⣿⣿⣿⡏⠀⠈⢻⣿⣿⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⡿⠋
⣿⣿⠷⣿⠸⣿⢿⡇⣿⣷⡖⣿⠁⣟⢿⣿⠶⣾⠇⣿⠈⣿⣸⡏⢹⡏⢹⡍⣿⡇⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⠀⢿⣾⡿⠀⠀⠀⢀
⣿⣿⣷⣿⣾⣿⣿⣷⣿⣾⣷⣿⣷⣷⣾⣿⣶⣿⣦⣿⣤⣿⣽⣧⣾⣷⣼⣴⣿⡇⠀⠀⠀⠈⢿⠇⠀⠀⠀⠀⠀⠀⠸⣿⢁⡤⠀⠈⠻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠻⢹⣧⡄
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣷⣶⣾⣾⣿⣷⣾⣿⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⣄⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣧⢸⣿⣿⣤⣾⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⣶⣿⣿⣿⣿⣿⣋⣀⣀⣀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡺⣠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢃⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠠⠀⣴⣾⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢤⣉⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⣦⣶⣼⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣆⣼⣿⣷⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣾⣿⣿⠉⠉⠉⠉⠉⠉⠛⠿⢿⣿⣿⢿⣿⣿⣷⣫⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢿⡌⣿⣿⣿⣿⣞⣿⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢻⣿⣿⣿⡾⣻⡮⢝⡷⣄⢀⠀⠀⠀⢀⣀⣠⣿⡸⣿⣿⣿⣿⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡟⣾⡝⢎⠀⠈⢈⠁⠳⠚⡟⢩⣿⣿⡿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⣿⣿⣿⠷⣯⡖⠁⠐⠐⠏⠀⠼⣓⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣹⡮⠄⠁⠀⠀⠀⠐⠀⠀⣻⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⡒⠂⠈⠀⠀⠂⠀⠔⢸⣿⣿⣿⣾⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣛⡤⠈⠁⠠⠀⠨⢴⣾⣿⣿⣿⣏⣸⡏⣧⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠴⢖⡤⠀⠀⣀⣾⣿⣿⣽⡿⢸⣿⣧⢹⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⣈⢀⣐⣾⣿⣿⣿⣹⣿⠗⢂⢚⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⢣⣉⠉⠹⣻⣿⣿⣿⡌⠀⡁⣸⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣛⣾⣆⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠋⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣸⣿⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣛⣡⡾⠋⠀⠀⠀⠀⠀⠀⢸⡿⣶⡀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠋⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣧⣠⣤⣤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠸⠟⠃⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⣤⡴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣾⡏⠈⣿⠀⠀⠀⣠⣶⣄⣴⠞⢻⣧⠀⠈⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠻⠇⣰⡏⠀⣀⣠⣿⡏⠻⠇⠀⢰⡟⠀⣤⣤⣤⠀⣠⣴⣤⠀⠀⠀⠀⣼⠃⣿⡷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣠⣾⣫⣴⡿⠿⠟⠛⠷⣦⣤⣴⠟⠁⠀⣿⡏⢿⣿⡟⣹⡿⠀⠀⢀⣼⣇⣀⣩⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠟⠉⠀⢀⣀⠀⣰⣿⠟⢷⣆⠀⠀⠘⣷⣈⣹⣾⠟⠀⠀⠀⠈⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⢠⣾⡿⢿⣿⡇⠀⣸⡏⠀⠀⠀⠼⠟⠋
⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠸⣿⡇⠈⢿⣧⣠⣿⠇⠀⢠⣶⣶⡄⠀⢀⣤⣄
⠀⠀⠀⢀⣴⡿⠏⠀⠀⠀⢀⣴⣶⣄⠀⠀⠘⢿⣄⡀⠉⣿⡏⠀⠀⣿⡏⠘⣿⣶⡿⠋⠙⣿
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿⠉⣿⣄⣤⣤⡀⠈⠿⣶⣿⠁⠀⠀⠘⣿⡀⠘⠿⠀⢀⡾⠋⢠⣄
⢰⣿⣏⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⣿⠟⠁⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠟⠁⠀⠈⠙⢷⣤
⢸⡟⠻⣶⣀⠀⠀⠀⠀⠀⢸⣧⢈⣡⣴⠾⠋⠀⠀⣠⡿⠿⣶⣄⠀⠀⢀⣠⣬⣍⡀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣄
⢸⡿⠀⠈⠙⢷⣤⡀⠀⠀⠼⠿⠟⠋⠁⠀⠀⠀⢸⣿⠃⠀⠘⣿⣤⣴⠟⠉⠀⢹⣧⠀⠀⠀⠀⣠⣶⣿⢿⣿⡿
⢸⣿⠀⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠃⠀⠀⠀⣼⡏⠀⣠⣴⡿⠟⠛⠁⠰⣿⣷
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣴⣿⠟⠋⠀⠀⠀⠀⠀⣿⣷
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣠⣴⣶⣶⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⠋⠁⠀⠉⠛⠻⣶⣤⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⣿⡿⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠰⣿⡇
⣿⡷⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠰⣿⡇
⣿⣇⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⢰⣿⠇
⣿⣿⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⣸⣿
⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⣿
⢿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠈⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣾⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣦⣄⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣿⡟⠛⠛⠛⠟⠛⢛⡛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠛⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏
⠀⠀⠀⠀⢀⣤⣾⠋⢻⣇⠀⠀⢸⣿⠋⠀⠀⣼⣿⠿⣶⣦⠀⠀⢠⣦⠀⠀⣰⡷⠀⢠⣶⡦⠀⠀⠀⢰⣿⠟⢿⣶⣤⡀
⠀⠀⠀⠀⢸⣿⠿⣷⣼⣿⠀⠀⢸⡏⠀⢀⣴⣿⡇⠀⠀⣿⡇⠀⠈⣿⡆⢠⡿⠃⢀⣿⣿⠃⠀⠀⠀⣸⣿⠀⠀⣽⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠈⠻⣿⣄⡀⠸⣿⡶⠟⠋⠙⢿⣶⠾⠋⠀⠀⠀⠘⢿⡿⠁⠀⠘⠻⠿⠆⠀⠀⠀⣿⣇⣠⣾⣿⣿
⠀⠀⠀⠀⣿⣧⡞⠁⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣼⣿⡇
⠀⠀⠀⠀⣿⣯⣾⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⣶⣦⡀⣠⣶⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠘⣻⣿⡇
⠀⠀⠀⠀⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠸⠛⣿⡇
⠀⠀⠀⠀⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⢹⣿⡟⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⣰⠞⣿⡇
⠀⠀⠀⠀⣿⡿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⣀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣿⡇
⠀⠀⠀⠀⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢃⣿⡇
⠀⠀⠀⠀⣿⡏⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠐⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣿⡇
⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⠀⠀⠀⠀⠀⠈⣠⣾⣿⡇
⠀⠀⠀⠀⢿⣯⣼⠇⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⢋⣴⣿⠁
⠀⠀⠀⠀⢸⣿⠏⠀⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢿⣽⣿
⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⠿⠿⠿⠿⠿⠛⠛⣛⡛⠛⡛⢛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣿⠿⠿⠿⠟⠛⢛⣛⡉⠉⢩⡭⠁⠠⠴⠆⠀⠐⠒⠀⠀⠙⠉⠁⠈⠉⣁⢀⣵⠟⡅⣿⡇
⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⠿⠿⢛⡛⢛⡭⠭⠀⠐⠓⠀⠛⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢌⣵⠟⠁⠀⣁⢿⣿
⠀⠀⠀⠀⢺⣿⣟⡛⢭⡉⠐⠒⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⣴⠟⠁⠀⠀⠀⢀⢸⣿
⠀⠀⠀⠀⢸⣿⡍⠛⠷⣦⣜⡃⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣴⠟⠁⠀⠀⠀⠀⠀⠘⠸⣿⡇
⠀⠀⠀⠀⠈⣿⡇⠓⠀⠀⠉⠛⢷⣬⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⡇
⠀⠀⠀⠀⠀⣿⣧⠺⠀⠀⠀⠀⠀⠈⠙⠻⣦⣔⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣍⡀⢤⡀⢀⣴⠶⠾⠷⣦⣤⡾⠛⠛⠻⣦⣘⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣧
⠀⠀⠀⠀⠀⢸⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⣦⣾⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⣿⠋⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡀⠁⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠠⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⢤⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠸⠁⠀⠀⠀⠀⠈⠻⣦⣄⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⢷⣄⠀⠀⠀⠀⠀⢈⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⡇⢧⠀⠀⠀⠀⠀⠀⠀⣴⠏⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡝⢿⣄⡀⠀⠀⠸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⢀⠀⠀⠀⠀⠀⢀⣼⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠝⠻⣦⡀⠐⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⠃⠀⠀⠀⢀⣾⢃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⡻⣦⣄⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠻⠀⠀⢀⣾⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⡄⠀⠠⠤⠀⠶⣒⣙⣀⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⡄⢠⡾⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢠⠤⠀⠀⠶⠆⢀⣘⣛⣁⣀⣩⣤⣤⣤⣴⣶⣶⣶⣿⠿⠿⠿⠟⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢡⡿⠱⠇⠀⠴⠀⠐⢒⣀⣀⣩⣭⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣶⣿⣿⠿⠿⠿⠟⠛⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠛⠋⠉⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠉⢡⠀⠀⠀⠀⢠⣿⣥⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⡏⠀⠝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠺⠂⠀⠐⡸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⣿⡟⠀⠀⠀⠀⠁⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⢀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢾⣿⣅⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⡔⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠸⣿⣿⡟⠛⠻⠶⠶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠁⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠹⣿⡟⠆⠀⠀⠀⠀⠘⠉⠋⠙⠛⠛⠶⠶⣦⣤⣌⣀⣀⠀⠀⠀⠀⣴⡞⠋⡉⣤⣈⣿⡟⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠆⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢿⣇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠻⠷⠶⣾⣿⠠⠟⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠘⣿⣆⠘⡄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⢀⠔⢀⠄⠀⠀⠀⠀⢀⣀⣤⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⣁⣤⡶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⡄⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡷⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⢀⠎⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠈⣠⠂⠀⠀⠀⠀⠘⡀⠀⠀⠀⡰⠀⠎⠀⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⡰⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠀⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠈⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣠⡧⢂⣀⣤⡶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⠿⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⢆⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⢠⡏
⠀⠀⠀⠀⠀⠀⣀⡨⣷⠄⠀⠀⠀⢐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⠴⡄⠐⠋⣿
⠀⠀⠀⢀⠴⠋⠁⠰⡇⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠠⠀⠀⠀⠻⡀⠈⠀⡃⠁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠴⣧
⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠇⠀⠈⣢⠀⠀⠀⠀⢺⡙⠂⢨⠄⠀⠀⣠⡶⠶⢦⣄⠀⠀⢀⣤⠶⠶⠷⣤⡀⠀⠁⠀⡠⢃⡆
⠀⢠⡇⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠱⡀⠀⠀⠸⣀⠆⠀⠐⠒⠁⠀⠀⠀⠊⠦⠑⠄⠀⠀⠀⣾⠋⠀⠀⠀⠈⢳⡼⠋⠀⠀⠒⣦⠈⣷⠀⠀⠈
⠀⢸⡗⠤⣴⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣸⠀⣿
⠀⠈⢯⡐⢻⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠒⠒⢤⣀⠀⠀⢀⣴⣾⠟⠃⠀⠀⠀⠀⠀⠀⣷⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠏
⠀⠀⠀⠙⠂⠈⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣝⢆⠀⠀⠀⠀⠀⠀⠐⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣥⡀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⡠⠀⣿⡀⠤⠄⠒⠙⠀⠀⠀⠀⠀⠀⢄⣴⠟⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠹⣆⣠⠞⠁⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠒⠛⡯⠉⣹⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠋⠁⠀⢀⠔⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⢀⣖⡟⢀⠁⠀⠘⠋⠀⠀⢱⠀⠀⠀⠀⠈⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠛⠉⠉⠉⢩⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠒⠙⢲⡀⠀⠀⢊⠜⢁⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⡇⠀⠀⠀⠀⠀⠀⠰⠊⠉⠙⢦⠀⠀⠀⠀⣧⠀⠀⠉⣰⠷⠶⠚⠛⠋⠉⠉⠉⠉⠛⣶⡀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠘⠄⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⣑⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⢄⠀⠀⠦⢤⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢹⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠢⢄⡇⠀⠀⠀⠀⠀⠀⡏⠀⠙⠀⠙⠀⠀⢀⡤⣤⠀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠇⠀⠈⠲⣔⡀⠀⠀⠀⠀⣠⡞⠀⣾⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠑⠒⠊⠀⢳⠀⠀⠀⠀⠀⠈⠲⣄⠐⠁⣀⠔⠉⠀⠈⡗⠄⠀⠀⠀⠀⠘⡄⠀⠀⠆⠀⠀⢠⠊⠉⠓⠢⠴⠊⠀⠈⢄⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠋⡠⠚⠁⠀⠀⠀⠀⡇⠈⢦⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠳⠤⣤⣤⣤⡤⠤⠶⠖⠋⡴⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⣰⠚⠝⢦⣀⡇⠀⠀⢣⠀⠀⠀⠀⠀⣠⠤⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣀⣀⣧⠀⠀⠀⡿⠉⠀⠀⢀⣣⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠉⠈⠁⠀⠒⢲⡦⣄
⠀⡠⠀⠀⠀⢀⡴⠋⠉⠁⠁⠀⣰⠋⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⡇⠀⠀⡠⣢⠃⠀⠀⠀⡇⠀⢂⠀⢠⠖⠲⣄⣤⣄⠀⠀⢀⢏⣼
⢰⠁⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠻⡤⢄⣀⣀⣈⣢⣤⣤⠤⠤⠼⠀⠠⣪⠞⠁⠀⠀⠀⢠⠃⢀⡠⠓⢴⡄⠀⠉⠀⡸⠃⣀⡴⢋⡟⠀⠀⢀⡀
⠸⣆⠀⠀⠀⠀⠙⢢⠄⠀⠀⠀⠀⠑⢄⠀⠀⠘⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⢸⠔⠁⠀⠀⠀⢹⡶⠞⠛⠒⠉⠃⢀⡞⠀⠀⢀⠞⡇⠀⠀⢀
⠀⠈⠲⠤⣄⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠳⣄⠀⡄⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⢐⠒⠤⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⡞⢀⡧⢒⡸⠃
⠀⠀⠀⠀⣟⠀⠀⠀⠙⠒⢺⡀⠀⠀⠐⠀⠈⠦⣧⣤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⠀⠀⠈⢱⠾⠡⠎
⠀⠀⠀⠀⠘⠦⣀⣀⣠⡀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠀⠀⠀⠀⣀⠴⠒⣒⢦⠀⠀⠀⠀⠀⢀⡴⠓⠂⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⣀⡀⠤⢂⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠔⠋⠁⠀⠀⠀⠀⠀⢠⡴⠚⠁⠀⠀⣨⣞⡀⠀⠠⠀⠈⠁⠀⡠⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢒⠁⠀⠀⠀⠐⠲⠤⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠈⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋
⣶⠒⠒⣶⠶⠶⣶⠶⢶⣶⠶⣶⠶⠶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⠶⠶⢶⣶⠶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠈⠓⢤⣀⠔⢶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠑⢍⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠑⢮⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠢⡀
⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡈⢢⡀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⢼⡁
⠀⠀⢰⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⡴⠃⠀⣱⡄
⠀⠀⢸⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡠⠊⣀⠔⠊⠁⡇
⠀⠀⡎⠀⠀⠀⠀⠉⠲⢄⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣼⠕⠊⠀⠀⠀⠀⠇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⠔⠋⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡢⠔⠋⠉⠒⠶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⡇
⠀⠀⠀⡆⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⡇
⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢺⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⡆⡄⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠀⡠⠂⠀⠀⠈⠃⠰⡶⠂
⠀⠀⠀⣀⢖⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠌⡄⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠠⠄⠀⠁⠀⠈⠁
⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠐⠀⠀⠘⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠠⡄⡀⢀⡆⠀⠀⠐
⠀⠀⣠⣤⡤⠐⠂⠀⠐⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⢠⠚⠐⠀⠈⠇
⠀⠃⠙⠿⠋⠀⢀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠂⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⡀⠑⢀⣀⢪⡀⠀⠀⠀⡐⠀⠀⠀⠌⡍⠀⠀⠀⡀⠂⠀⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠈⠚⠛⠁⠀⠀⠀⠀⠀⠐⢿⠗⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢠
⠀⡀⠀⠀⠐⠁⠂⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⢀⠐⠐⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢀⡀⠀⢤⡄⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉⡄⠀⠠⠄⠀⡀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠈⠏⠀⠀⠀⠀⢀⠶⡀⠐
⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⣀⠀⡀⠐⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠟⠉⠉⠉⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⠤⣤⣀⣀⣀⡠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⣀⣠⢊⣽⠥⡿⠭⠧⣀⡀⠀⠀⠀⠀⢠⠂⠀⠀⡆⠀⠀⠀⠀⠀⠀⡞⠁⠐⡍⠓⠲⠤⠤⠤⠤⠤⠤⠒⠚⠉⠁
⠀⠀⠀⠀⢀⣰⡅⠚⡀⠙⠄⠓⠀⠀⠀⠈⠑⢦⡀⠀⠀⢓⠶⠚⠁⠀⠀⠀⠀⠀⠀⢙⠒⠒⠁
⠀⠀⠀⠀⣷⠁⠑⠄⠈⠀⠀⢀⡀⠀⠀⡀⠀⠀⠙⢆⠀⠓⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠔⠀⠀⣦⣔⣪⣅⡠⠈⠀⡐⠤⣀⠀⠀⠔⠀⠉⠒⡄
⠀⠀⠀⢰⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠈⡎⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡔⠁⠀⠈⠁⠀⠀⠀⡌⡆⠈⠳⣍⣿⢍⠙⡄⢸
⠀⠀⠀⢸⢠⠤⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⠀⢀⡀⠀⠱⡘⣄⠀⣈⢧⠈⠀⣇⡇
⠀⠀⠀⠘⣌⠉⠀⠀⠀⠀⠀⠈⠢⡄⠠⠈⠀⠀⠀⣠⠃⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠐⠇⠀⠈⠀⠀⠀⠘⢮⡓⠬⡎⡄⠀⡟
⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⣀⠔⠁⠀⢈⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠈⠁⠐⡇⠀⣇⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⢄⢀⣀⠠⠤⡔⠊⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠉⠒⠛⠁⠀⠀⠀⠀⠀⠀⠬⠇⡸⢌⠂⠈⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠖⠃⡇⠳⠤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢓⠀⠀⠀⠉⠢⢀⠀⠀⠀⢀⣀⠀⣐⡠⠊⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡿⠀⠐⠒⠃⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⡴⠐⢄⠜⢹⠏⠣⡉⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠁⢸⡇⠀⠈⠉⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠉⠀⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⣤⣀⠔⠋⠀⠀⠀⢹⡏⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⢀⡞
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⡿⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠳⡎⠙⢞⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⡀⠀⠀⢹⡀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣠⠇⠀⠀⠉⢿⠄
⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠲⣤⣽⠆⠀⠀⠒⠲⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠙⠋⠁⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠋⠉⠛⠲⢦⣄⠀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢀⡀⠀⠀⢀⣀⡤⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢤⣠⣇⡴⠋⠉⠉⠉⠉⠁⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠿⢿⣿⣷⣠⠶⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣭⣭⣭⣭⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠬⠭⠭⠥⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿

⠀⠀⠀⠀⠀⠀⡇⠀⣾⠀⠀⠀⠀⠀⠀⡗⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⢰⡆⠀⠀⣗⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣿⠀⠀⢸⡆⠀⠀⣇⠀⣿
⠀⡀⠀⠀⠀⠀⠙⠒⣿⠀⠀⢸⡇⠀⠀⣿⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡇⠀⠀⢸⡇⠀⠀⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣸⣇⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣼⣧⣤⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠄⣀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣂⡠⠤⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣡⠠⠄⠂⠊⠉⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠀⠂⠀⠉⠀⠀⢀⠀⠤⠤⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀
⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠖⠰⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌⠀⠀⠀⠀⠀⠀⣀⠄
⠀⢀⠜⡄⠀⡀⠀⠀⠀⠀⠈⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⡀⠀⡰⠃
⢠⠀⣤⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠑⠐⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢐⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠰⠀⣀⠈⠀⠀⠀⠀⠀⢀⠀⡀⠔⠐⠂⠼⠄⣐⡁⣐
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠠⠤⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠤⢔⡁⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⠄⢄⡀⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⠠⠀⢊⠈⠄⠀⢀⠄⢊⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠨⠢⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠄⢀⠀⠐⡀⠡⢂⠈⠄⠐⠀⢁⢀⠤⠂⠋⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡕⠁⠀⠀⠀⠀⠀⠀⡠⠁⢈⠈⡐⠡⠂⡀⠁⢊⠈⠐⠀⢁⡠⠰⠐⠊⠁⠀⠀⠂
⠀⠀⠀⠀⠈⠀⠀⠢⣢⠎⠀⢀⠀⠀⠀⢂⠌⠐⡐⠡⢀⠄⡐⠁⠊⢀⡁⡄⡰⡠⢁⠀⠄⠐
⠀⠀⠀⠀⠀⠐⠈⡠⠃⠀⠀⠁⠁⡁⠡⢂⠈⠀⠀⠀⡀⠠⠠⠖⠃⢋⢈⠄⠐
⠀⠀⠀⠀⠀⠀⢇⣀⢈⡈⡀⡈⢀⠄⠄⠒⠀⢋⠌⠕⠔⠐⠁⠀⠁
⠀⠀⠀⠀⠀⡈⢀⠄⡡⢀⠄⠠⠠⠊⠊⠐⡠⠡⠂⠂
⠀⠀⠀⠀⢊⠀⠁⢈⠔⡡⠊⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⠻⢿⣿⣿⣿⠿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠙⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠋⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⣠⣀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⡿⢆⣴⣾⣿⣿⣷⣄⠺⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣮⡛⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡙⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡋⢙⣿⠉⢹⣿⠉⢹⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⣶⡦⠀⣶⡆⠠⣶⡆⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢦⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡹⣿⣿⣿
⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⢈⡇⠀⠀⢸⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡷⣹⣿⣿
⠀⠀⠀⢀⡴⠿⠋⠁⠐⢤⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢸⣿⣿⣿⣿⢋⣠⣴⣿⣏⡻⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠦⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣭⣧⣙⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⠒⠋⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠦⡀
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⢙⡆
⠀⣠⠤⠤⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠖⠉
⠀⣇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠚⠛⠉⠉⠙⠲⣄
⠀⠈⠓⠒⠠⠞⠀⠀⠀⣀⣀⣤⠤⠤⠶⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⣀
⠀⠀⠀⠀⠠⠶⣖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢩⡇
⣀⣀⣀⣠⣤⡤⠴⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸
⠉⠢⡀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢸
⠀⠀⠹⡄⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠓⣶⠶⡀
⠀⠀⠀⢹⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡠⠊⠀⠀⣇
⠀⠀⢀⡞⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⢹
⢠⠖⠛⠀⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠂⠀⠀⠀⠉⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⢀
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠤⠴⠶⠒⠒⠛⠋⠉
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⠒⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠸⡄⠀⠀⣀⣀⡴⠧⠖⠚⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠷⣦⣀⣴⠾⠛⠟⢷⣦⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⣾⠋⠀⠀⠀⠀⠀⠈⠛⠁⠀⠐⠠⡱⡙⣷⣤⣤⣤⣤⣀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠻⠹⠱⡱⡹⢙⢷⣄⠈⠆
⠀⢀⡤⠖⠂⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠡⠁⠁⢃⠜⣻⡆
⠰⠁⣠⡶⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠛⠟⡷⣦⡀
⠁⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡐⠠⠊⣻
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣽
⠀⠀⠻⣦⡄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⢠⡟⠁⢠⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠸⣧⣸⣟⣗⣴⣼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠙⠿⣾⣮⣿⣧⣿⣮⡵⣡⡖⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣵⣟⣼⣱⣳⣷⣆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⢻⡆⠀⠀⠀⠀⣰⠟⠳⠶⠶⠶⠞⠉⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠋⢀⠴⠤⠤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⣤⡾⠋⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠁⣀⠔⠉
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶