Hurry Emojis & Symbols

⠀⠀⠀⠔⡀⢤⡤⢀⡀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠀⡀
⠀⠀⠀⠀⢁⠀⠀⠀⠈⢁⢅⣇⣀⡠⠔⠀⠀⠀⠀⠐⠢⠴⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣂⠎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣤⡀⣀⣠⠀⠀⠀⠀⠀⢀⣤⡤⠞⠑⠴⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠉⢱⠀⠀⠀⠀⣆⠀⠀⠀⣼⡷⣋⡀⠉⠁⠀⠀⠀⠀⠀⢀⡊⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠑⠠⠤⠀⠀⠀⠀⠉⠲⣄⢀⠀⢰⠟⠉⠠⡴⠋⠂
⠀⠀⠀⠀⠰⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⡶⠀⠀⣤⣤⣄⡷⠀⠀⢠⣾⢻⡍⡇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⢍⠇⠀⠙⣡⢙⣧⣤⡴⣯⡟⣫⣭⡥⣾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠤⣄⠀⣩⣼⣿⣿⣿⣿⣹⠷⠿⠴⢟⣋⣡⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⢯⣾⣿⡎⠀⣠⢿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣶⣾⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⢀⡠⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢿⣿⡟⠉⢹⣿⣿⣿⣿⣿⣿⣟⣉⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡀⣀⣀⣤⣴⣾⣷
⠀⢠⢎⣠⣄⡬⠳⡄⡀⠀⠀⢰⠋⠈⠙⠦⣴⣿⣄⡼⢻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿
⠀⡞⣸⣜⣀⣀⠀⡇⢹⣶⣤⡿⠀⠀⠀⠀⠈⠙⠳⡴⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠻⠾⢇⣿⡿
⠀⣿⣙⡌⠑⡌⡸⢁⣿⣿⣿⠇⠈⢦⣦⡀⠀⠀⠀⠙⣤⢶⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣴⡿⠛⠁
⠀⠿⣶⠶⠞⠉⠓⠿⣿⣿⡏⠀⠀⠀⣿⣿⣷⢤⣀⠀⠈⢳⣶⣤⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⣿⠇⠀⠈⠛⠢⣄⣉⠓⠤⣄⡀⠈⠉⠉⠉⠉⠉⠙⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⢄⡀⠀⢦⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠱⣄
⢠⣴⣲⣶⣿⡉⠉⠓⢤⣀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠳⡄
⠙⠛⠻⠿⠿⣿⣿⢶⣠⣤⡬⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣄⣁⣀⣀⣀⣀⣠⡤⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠒⠒⠶⡤⠔⠁⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣧⣤⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣾⢿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠁⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠰⠀⠀⠀⠀⡠⠂⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⠾⠀⠢⠰⠀⠀⢠⣴⡞⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠋⣉⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠀⠸⠏⠅⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠦⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠸⣀⠀⣠⣶⣿⡶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣠⣿⡿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡱⠀⢀⡀⣀⣤⣴⡾⠋⠁⠀⠀⠈⠑⠒⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢸⡇⠀⠈⠉⠉⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⢉⠏⠀⣿⡇⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠁⠀⠀⢀⠏⠀⢰⣿⡇⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠈⠉⠉⠣⡀⠉⠁⠒⠤⣄⠀⡸⠃⠠⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠒⠒⢒⡏⠀⠀⣿⣿⣇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠹⡅⠀⠀⠀⣠⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠀⠈⡇⠀⠀⠈⠦⣀⣀⣀⡀⠀⣤⠶⠇⠀⠀⢀⣀⣀⣤⣤⣤⠧⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⣠⣶⣾⣿⣿⣿⣿⣿⣦⣤⣤⣴⣶⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣾⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣷⣝⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⢿⣿⣿⡟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣭⣼⣥⣭⣧⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⣽⣭⣭⣽⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣄⣀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⣿⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣸⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠟⠛⠋⠉⠉⢉⣽⣿⣿⣿⡿⠃⣼⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣄⣴⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡀⠀⢀⣠⣀⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⢁⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣭⢿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⣠⣿⡿⠉⠙⠻⠿⠿⢿⣿⡿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣦⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡿⠸⠟⣽⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢠⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠟⠋⠁⢀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣿⠿⠛⠉⠀⣤⣶⣾⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠻⣿⣿⡟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⢀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⢀⢀⣠⡝⢄⢢⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⡘⣇⠜⡌⣎⣷⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣈⠤⢤⠈⠁⠢⡉⠁⠱⡙⠧⠘⢸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠤⠀⠟⢳⠁⠇⠀⠀⠈⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠈⡂⣄⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣐⡡⢶⢆⢜⡼⠁⠀⠑⡄⠃⠘⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠈⡆⠀⠀⠀⠀⣼⡟⠋⠀⠀⠰⡀⠈⢦⢄⣀⡀⠀⠀⠀⣀⡠⠄⡀⠀⠀⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠙⠩⡀⠀⠀⠀⠀⣫⠖⠀⠀⠀⢠⠕⠀⠀⢗⠢⡈⣁⠈⠙⣽⠐⠀⣙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡈⣆⢐⠀⠈⠒⢀⠔⠊⠁⡀⠄⠐⢀⡾⢂⠅⠀⢸⣮⣊⠂⠂⠀⠋⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢔⠈⠢⡁⠂⠐⠇⡀⣀⢂⠐⢀⣰⠧⡪⢐⡡⡀⠀⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢈⡀⡀⠤⢲⠉⠕⡨⠔⠡⢊⠔⡀⠘⣀⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠤⠄⢀⡀⣀⢣⡈⠔⡡⢊⠤⢊⠄⡀⠈⡓⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡢⢒⠴⡠⢂⠀⡀⡀⠡⡄⠐⡡⠐⡡⢊⠄⠀⠙⢦⡀⠀⠀⠀⠤⠤⠄⠀⠠⠭⠤⠬⠥⠀⠀⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢔⠁⠸⣦⠑⡡⢊⠔⡡⠚⢆⠐⢋⠔⡡⠒⡥⢂⠀⠈⠑⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⢊⠔⡘⢄⡔⡡⢊⠔⡑⡨⠳⣄⠈⠔⢈⠔⡡⢂⠄⡠⠀⡀⠀⠉⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠡⢊⠔⡀⠱⡌⠉⠘⠚⠃⠉⠈⠓⢄⡀⠊⠔⡡⠊⡠⢊⠔⡪⢀⠀⠈⡄⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⠁⠊⠔⢑⡽⠀⠀⢀⠀⠀⠀⠀⠀⠈⠒⢤⣀⠊⠂⠡⣪⢂⢕⠁⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢄⡁⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠠⢀⠀⢔⠀⢄⠂⠤⡀⠄⡀⠠⢀⠠⠄⠠⠀⠠⡀⠠⢀⠀⠄⡀⠀⡀⠀⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠒⠀⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⠤⠆⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠔⠅⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⡄⠀⠂⠂⠀⠉⠀⠀⡀⠀⠀⠀⠉⠑⠠⡀⠀⠀⢀⠦⡄⠠⢀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠔⠒⣤⠀⠀⠀⠓⠤⠔⠁⠉⠿⡀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠐⠀⠶⠒⠄⠀⣠⡯⠿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⢓⠾⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡅⠀⠀⢠⢒⠆⢄⠀⠀⠀⠀⡘⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠸⢿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠰⣧⠃⠀⠈⠢⢄⣀⡔⠀⠀⠀⢠⡁⠀⠀⠀⠀⢀⣴⣤⣤⡄⠙⠢⠄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⣦⣤⣤⣶⣿⣿⣿⠏⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⡐⠀⠀⠀⠈⠛⠛⠛⠻⣛⡓⠒⠂⡜⠁⠀⠄⠲⣿⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠝⢲⠶⠃⠀⠤⡄⠀⠈⢦⡀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠳⡀⠀⠀⠀⠀⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠠⠛⠙⢆⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⣀⠠⠐⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠉⠑⠦⠤⣀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⣦⣤⣶⡄⠀⠀⠳⣄⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⢀⡤⠀⢹⣿⣿⠀⠀⠀⠈⠳⣄⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣷⣆⠀⠀⠀⠈⠑⢄⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠆⠀⠀⠀⠀⠀⠢⡀⠀⢀⢼⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣇⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⢶⣶⣶⠶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡐⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⡤⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠤⠖⣋⣥⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡶⠛⠋⠉⣡⠶⠾⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣇⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⠉⠉⠙⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢠⡖⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣬⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⡠⠔⠒⠀⠀⣀⣤⠴⠒⠲⣦⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡼⠁⠀⢀⣠⠶⠛⠉⠀⠀⣠⣴⠟⢀⣿⣿⠁⠉⠛⠲⢦⣤⣄⣀⣀⣀⣀⣾⣤⣤⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡾⠋⠀⠀⣀⣤⣶⠿⢋⠇⢀⣾⠿⡟⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⣻⣹⣯⣿⣟⣀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⣾⠿⠛⠉⠀⢀⠎⢀⣾⠏⠀⣿⡘⢌⠉⠛⠛⠻⠿⠿⠟⠛⠋⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⣦⣾⡿⠃⠀⠀⠀⣠⠋⣠⡿⠃⠀⠀⠘⣧⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢠⣾⢉⢀⡸⣇⠀⠀⠀⠀⢀⡾⣡⣾⣿⠀⠀⠀⠀⢀⡟⢷⣤⣀⡇
⠀⠀⠀⣀⡀⢀⡾⢿⡿⢾⣟⢻⠀⠀⢀⣴⣯⠾⢻⣿⣿⡶⠦⠤⠤⢾⣅⠀⠀⠈⠁
⠀⠀⣰⡏⠉⠛⠷⢿⣦⣰⣣⠇⠀⠐⠛⠉⠀⠀⣸⡿⢿⣷⣄⠀⠀⠀⠈⢢⡀⠀⠀⠀⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⠀⠀⠀⠀⢰⡟⠀⠀⢉⣿⣷⣄⠀⠀⠀⠹⡄⠀⠀⠈⢢⠀⠰⡄
⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢠⡿⠀⠀⢠⡾⠋⠈⠙⠿⣶⡄⠀⢳⠀⠀⠀⢠⠁⠀⡗
⠻⠿⣦⣀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠴⠋⠀⢀⣴⠏⠀⠀⠀⠀⠀⢹⣧⠀⠘⡇⠀⠀⠘⠀⠐⠁
⠀⠀⠀⠉⠙⠳⠶⣤⣤⣠⣟⣤⣴⡏⠁⢀⣠⣴⠿⠃⡰⠀⠀⠀⠀⠀⠀⢿⣦⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠸⣿⠹⡿⣾⠟⠋⠀⠀⡠⠃⠀⡰⠁⠀⠀⠀⠀⠙⣧⣼⣦⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⠊⠉⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⣿⣯⣀⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢠⣤⡤⢀⣤⣤⣄⣤⣤⣤⠀⢠⣤⡄⣤⣤⢠⣤⢠⣤⢠⡄⣤⣄⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢠⡿⣿⡇⢾⣧⡉⠁⣼⡟⠀⢀⣿⣿⣿⣿⢇⣿⢣⣿⣿⡿⣱⡿⣼⡟⢠⣿⠃⣸⣿⡄⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣯⣠⣿⢿⡿⣴⣆⣿⠇⣸⡿⠀⠀⣼⢿⡿⣿⡏⣾⢏⣾⢻⣿⢣⣿⣳⡿⢁⣾⠏⢰⣿⣅⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠁⠈⠉⠁⠀⠉⠁⠀⠀⠉⠈⠁⠉⠀⠉⠈⠁⠈⠁⠀⠉⠉⠀⠈⠉⠀⠈⠉⣁⣀⣀⣀⡈⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣠⡄⣠⡄⣠⡄⣤⡄⣤⣤⡄⢠⣤⣤⡀⣤⣀⣤⠀⢀⣤⢠⣤⢠⣤⣤⢀⣤⠀⠀⠀⢀⣰⡿⠿⠟⠛⢛⣿⣿⣿⣟⠙⠋⠉⠀⠀⠀⣤⢀⣀⡀
⠀⠀⠀⠀⢠⣿⣷⡿⣱⡿⣽⡟⣼⣿⣿⢃⣿⣯⡿⢃⣿⡿⠃⢀⣾⢯⣿⢣⣿⣿⡿⣼⡟⠀⢀⣠⡾⠋⠀⠀⠀⣴⣿⣿⣿⠋⠻⣷⣄⠀⣀⣀⣼⣿⣿⠿⠋
⠀⠀⠀⢀⣾⢯⣿⢣⣿⣳⡿⣱⡿⣽⡟⣼⣏⣿⠇⣸⡿⠀⠀⣼⣟⣾⢏⣿⠏⠉⣰⡟⠀⣠⣿⣿⡇⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠈⠙⠛⠋⠉⠁
⠀⠀⠀⠈⠉⠈⠁⠈⠉⠉⠀⠉⠁⠉⠀⠉⠈⠉⠀⠉⠁⠀⠀⠉⠉⠁⠈⠉⠀⠀⠉⠁⠀⢿⠟⠙⠃⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡀⣀⣾⣿⠟⠁⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡷⠀⠀⠀⠀⠛⠉⣿⡿⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣦⣟⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⢷⡴⠂⠀⠀⠀⣸⣿⡁
⠀⠀⠀⣀⣤⣸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠘⢳⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⣷⠀⠀⠀⠀⣰⡿⠾⠛
⠀⠀⠘⣿⣿⠿⣦⡀⠀⠀⠀⣠⠶⣤⣾⡷⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⢠⣼⣿⡄⠀⠀⠀⠀⠀⢀⣤⣄⡿⠃⢀⠀⢠⡟⢀⡿⠔⠒⠒⠒⠻⢤⡀
⠀⢀⣼⠏⢻⡄⠀⠀⠀⠀⠀⠀⣰⣿⠟⠶⠚⠁⠀⠈⣿⡿⠆⠀⠀⠀⠀⢠⡏⡀⠀⠀⠀⠀⠀⠀⠘⢀⣿⡟⠛⠋⠀⢘⡗⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠰⠛⠁⠀⠀⣻⣀⣀⠐⠶⣤⡾⠻⣏⠀⠀⠀⠠⡴⠾⠟⣷⠀⠀⠀⣠⠖⠉⠉⠉⠉⠓⢤⠀⠀⠀⠀⣼⠟⠷⣦⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⡠⠒⠉⠀⠀⠀⠉⠓⢤⡀⠀⢹⡆⠀⠀⠀⢀⡀⠀⣿⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣼⢃⣀⡀⠸⠇⢸⠀⠄⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⡇
⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⣉⠴⠊⠉⠉⢉⠉⠙⠢⣄⡇⠀⠀⠀⠀⠂⠀⠀⠀⢈⣠⠔⠋⠉⠉⠉⠉⠒⢬⡆⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⡀⢠⠃
⢸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢣⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠸⡀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⡞⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⢹⠲⠤⣀⣀⠤⠔⢻⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⠑⠦⢄⣀⣉⣀⡠⠴⠊⠁
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢈⡜⡇⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡜
⠀⠀⠈⠒⠤⢄⣀⣀⠤⠖⠉⠀⢱⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡼⠀⠀⠀⠀⠀⠀⠀⠱⡈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⣈⣀⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣈⣀⣠⠤⠒⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠂⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⠂⠽⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠘⣾⣗⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⣀⣒⡀⠀⣳⠈⠁⠸⠂⢀⠠⢀⠀⠀⠀⡀⠀⠀⠒⠀⢠⡀⠀⠀⠀⠃⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠸⠄⡀⡀⠀⠀⠀⣀⡀⣻⢾⡽⣟⡆⠐⠠⢂⠈⢷⠜⠓⠒⠊⠈⠍⠉⠉⠚⡞⣾⠀⢤⠶⠂⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠿⢷⣕⣡⡤⠾⠟⠃⢷⠈⣧⠪⠚⣄⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠾⢤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣈⣑⣨⠓⠒⠟⠷⠀⠈⠱⠄⠁⠈⣀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣀
⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠉⠒⠒⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠄⠄
⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⡀⢠⠠⠙⠋⠑⠁⠉⢈⠂⠂⠐⠡⡠⢁⣀⡴⢀⡈⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⣠⣴⢀⡳⠱⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢊⡡⠔⡀⠀⠘⠁
⠀⠀⠀⠠⡀⠀⠑⠀⠀⠀⠀⠀⠉⠓⠯⣠⡈⠻⠷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠒⡢⠢⠒⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⡪⠅⠒⠉
⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⣶⣾⠑⢄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢄⠂⠀⠿⠞⠋⠓⠘⡋⠁⠀⠠⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣜⡁⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠑⠢⣀⠀⠀⠀⢀⣠⠤⠤⠀⠤⢼⠁⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠴⠉⠈⢳⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⠚⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢶⠁
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠠⠠⠁⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠦⢤⠴⠋⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠊⠀⢘⠤⣀⠀⢀⠏⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡌⢆⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠞⠒⠒⠓⢄⣴⡁⠀⠈⠳⡜⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⠖⣇⠀⠀⠀⠀⣠⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⢄⡀⠀⢸⠀⠀⣠⣤⣄⠀⠀⣿⡟⢢⡀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠛⠉⠈⠉⠒⠄⡀⠈⠢⡀⠀⢠⠴⠖⣶⣄⡇⠀⠀⣀⣀⠀⠀⢹⣦⡟⠀⠀⣿⠿⠃⠀⢠⣿⡇⠀⠉⡆⠀⢀⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢀⡀⠤⣤⣠⠚⠉⢹⣷⠀⠇⠀⢠⣿⣿⠁⠀⢸⣿⡿⠁⠀⣸⣿⠇⠀⠀⠀⢀⣠⣶⣿⠟⠁⠀⢰⠁⠀⣼⣿⠃⠐⡀
⠀⠀⠀⠀⠀⢀⠔⡠⠖⠒⣷⣆⡇⠀⢀⣿⡿⠀⠀⣿⡿⣸⠀⠀⢸⣿⡿⠀⠀⠈⠁⠀⣠⣾⣿⢿⠀⠀⣀⠀⠈⢻⡛⠁⠀⠀⠀⡎⠀⢠⣿⡏⠀⠀⢡
⠀⠀⠀⠀⡴⠁⠀⡇⠀⢠⣿⣿⠃⠀⢸⣿⡇⠀⢠⣿⣷⠃⠀⠀⣾⣿⡇⠀⠀⠀⠀⠻⡿⠛⠁⡘⠀⠀⣿⡧⡀⠀⣙⣦⡀⠀⠘⢷⣿⠿⠿⠀⠀⠀⢸
⠀⠀⠀⡜⠀⠀⢰⠀⠀⢸⡿⠿⠀⠀⣾⣿⠁⠀⢸⡿⠃⠀⠀⠀⣿⣿⠁⠀⢸⣧⡄⠀⠙⢦⡀⣇⣠⣴⣿⡇⠈⠻⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⢸⠁⠀⠀⡘⠀⠀⠀⣀⡀⠀⠀⣿⡿⠀⠀⠙⠁⢠⡄⠀⢸⣿⣟⠀⣀⣾⣿⠈⠲⣾⡿⠿⠟⠛⠋⢉⠖⠊⢉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⡇⠀⢀⣿⣿⠃⠀⢸⣿⣧⠀⠀⢀⣤⣿⣠⣤⣾⣿⠙⠿⠿⠛⣣⠤⠴⠐⠒⠒⠦⣄⠀⢸⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠸⡄⠀⢠⠃⠀⢸⣿⣿⣀⣀⣾⣿⠈⠳⢾⡿⠟⢋⣙⣋⠉⢡⡖⠊⢹⣷⡇⠀⢀⣤⣤⡀⠀⢸⣷⡌⠀⣸⣿⠇⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠱⡀⢨⣤⣴⣾⣿⠙⠿⠟⠛⠋⠀⠀⠀⠀⡎⠁⠀⣿⡇⣸⠀⠀⣸⣿⠁⠀⢸⡿⠟⠀⠀⣼⣿⠇⢠⣿⡟⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠙⢄⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢸⣿⢁⠇⠀⠀⣿⣿⠀⠀⠀⠀⣀⣤⣾⣿⢻⢀⣾⡿⠁⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⣿⠏⠀⠀⢰⣿⡇⠀⠀⣾⡿⠿⠟⠋⠀⡸⢿⠿⠃⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⠋⠀⠀⠀⢸⣿⠃⠀⢸⣿⠇⠀⠀⠀⠈⢧⣾⣷⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡔⠀⠀⣿⣿⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣀⡤⠞⠁⠀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣴⣿⣧⣶⣾⣿⠏⠛⠛⠋⠁⠀⠀⠀⣀⣀⣀⣴⣶⣦⣭⣥⣤⣤⣤⣤⡝⠐⠈⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠉⠀⠉⠀⠀⠀⠀⠒⠀⠘⢉⣉⣉⣉⣤⣤⣼⢤⠤⣤⣤⣤⣤⣴⣮⡀⠀⠀⠀⠀⠈⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠈⠉⢁⣀⣀⣀⣠⣤⠦⠤⠤⠤⠤⠤⣤⣤⣤⠇⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠈⠀⠈⠓⠶⠶⠲⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢢⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⠀⠀⢀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠲⣄⠤⡐⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⢣⢘⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠆⣿⠜⢃⢯⢾⢀⡇⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣁⣄⡄⠉⠒⡌⠁⠘⡌⢧⡐⢸⠿⠎⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⣀⠀⣻⢺⡆⠀⠀⠀⠈⠒⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠑⠥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠆⢀⣠⢀⢢⡜⠉⢦⠈⢆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⠠⣄⠀⠀⠒⠚⢹⣧⣢⠞⠀⠀⠀⠱⡄⠀⠁⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣁⣄⠜⠀⠀⠀⠀⢸⠟⡁⠀⠀⡀⡤⠀⠙⡓⠲⠤⣀⣀⣠⢤⠒⣑⣦⠀⠀⠈⠀⠈⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⡘⠋⠉⠢⡀⠀⠀⠀⣸⠞⠀⢠⠠⢀⡏⡀⠀⢻⢄⠄⠠⡀⠈⣦⣀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠡⡐⠆⠀⠈⢂⠴⠊⠁⠀⠰⠘⢀⡼⢊⠄⠀⠘⡥⣢⡊⠂⡀⠋⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠠⡀⠐⢌⠒⡀⠏⠠⢠⢀⠀⠃⣠⡮⢂⠕⡡⠄⠀⠆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠀⠈⠓⢤⣀⠃⢃⣀⠤⡚⡩⢂⡥⢊⠔⡡⠀⠈⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣁⠀⠀⠀⢣⠀⠡⢖⡵⢊⠔⡡⠀⠈⠢⠈⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⡀⡈⠉⠀⠒⠃⠀⢉⠔⡡⠎⡠⢂⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠇⠀⠔⡠⡪⣊⠔⡡⢊⠂⠄⣱⡀⠈⡠⠊⡠⢁⠔⡀⠈⠢⣄⡀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⠀⠈⢈⠄⠩⠂⠔⡡⢊⠜⡀⡱⣌⠀⢂⠔⡡⠊⡔⢀⠀⠀⠉⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢇⠀⠀⢊⠄⠑⣮⢤⣁⣊⠜⡑⣉⣦⡀⠘⠡⢊⠔⡡⠊⡠⠀⡀⢀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡄⠀⢊⠔⡡⠈⢦⠀⠈⠉⠁⠀⠀⠈⠢⣀⠁⠘⡠⠊⠠⢊⠔⡡⢀⠀⠀⠇⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠊⠐⠑⡤⠃⠀⠰⠀⠀⠀⠀⠀⠈⠑⢤⣀⠊⠐⠡⢊⢔⠵⡃⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⣠⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⡀⠈⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡀⢀⡀⠀⡀⠄⣀⠀⢀⠀⢀⠀⢀⡀⠀⡀⠀⠀⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠁⠈⠁⠀⠉⠀⠈⠀⠉⠀⠈⠀⠈⠁⠈⠁⠊⠁⠂⠉⠐⠉⠤⠒⠩⠒⠨⠔⠢⠔⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣇⣴⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⣎⠀⡀⢸⣯⣿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣾⢿⠿⣿⣏⠀⠻⠓⠒⠉⢹⠏⣁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⣿⣿⣿⣿⣧⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣿⣶⡆⠁⠇
⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠴⠶⣶⣶⣶⡏⠙⣻⡏⢻⣶⣤⣤⣶⣾⣿⣿⣿⣿⣼⣿⣿⣿⣥⣭⣥⣾⣯⡇
⠀⠀⠀⠀⢋⠙⡄⠀⢸⠀⠀⠁⣿⣯⠩⠠⠀⣿⡆⢻⠿⣿⣿⣿⠿⣿⣿⣛⣛⡿⣿⣿⣿⣿⣿⣿⢭⣯⡇
⠀⠀⠀⠀⢈⡀⢃⣀⣈⣀⣀⣀⣿⣿⣶⣿⣿⣶⣿⣿⣽⣟⣵⣿⣶⣮⡋⣉⡍⢡⣿⣿⢿⣿⣿⣿⡝⢿⣧⡀
⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠙⠉⠙⠛⠿⡿⠛⠛⠷⢿⡿⡓⠿⢛⣛⣉⣽⣿⣿⣾⡀⣥⡈⠹⣿⣿⣿⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠉⠀⠉
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣄⣀⡴⠶⠿⠿⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⣼⠴⠋⠀⠀⠀⠀⠀⢸⣇⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣤⣄⡈⠁⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠈⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⢲⢀⡼⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡞⣛⣛⡒⠀⡼⠀⠀⠀⠀⣸⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⡟⠉⠉⠀⢸⠁⡀⠀⠀⠀⠁⢀⡀⠀⠀⢹⠁⠀⠀⠀⠀⠿⠶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡝⡩⣽⡿⡖⠶⣄⡇⠀⠀⠀⢸⠀⠻⢷⣶⣶⣾⠟⠁⠀⠀⠉⠀⠐⡶⠒⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⠳⢞⣯⡷⠀⢸⡇⠀⠀⢀⣼⠀⠀⠀⠈⠀⢷⣄⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠘⠋⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣿⡛⠻⣧⢤⣞⣇⠀⠀⣸⣿⠀⠀⠀⠀⠀⠈⢿⣷⣤⣀⣀⣀⣤⣤⠖⠀⠀⠀⠀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣀⣀⠀⠉⠻⣿⡶⠤⣽⣆⣠⣿⣿⡴⠛⡆⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⢷⣄⣀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⣫⣝⢦⡈⢧⠀⠀⢸⣷⠀⠀⠈⠉⠻⡻⠧⢄⣇⣠⠖⠒⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠰⢤⣤⣤⠖⣁⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⣷⣿⡇⠀⢸⣿⠇⠀⠀⠀⠀⢡⠀⠀⠀⠉⠓⠶⠦⣄⣱⣄⣈⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠳⣝⣋⡴⣳⠟⠀⠀⣼⡟⣸⣿⣶⣶⣦⢨⣄⣀⣀⠀⠀⠨⠀⠈⣧⣷⣮⣿⠯⣕⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠄⠉⠉⠁⠀⠀⢘⡟⣱⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢆⣶⣦⡿⡯⢭⣿⠀⠀⢹⠙⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠴⢶⡶⠶⠾⠷⠤⣤⣤⠤⠶⠿⢶⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⠇⠀⢸⠀⠀⢸⠀⠀⠀⠀⠻⢄⣀
⠀⠀⠀⠀⠀⠀⢸⣄⢈⣿⣇⣷⠅⠀⠀⠀⠀⠀⠀⢸⣄⢀⣿⠗⡷⠀⠀⠀⠈⣩⢭⣭⡉⢉⢻⣿⡟⢲⣾⣦⣤⣼⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣽⠿⠭⠭⠭⠭⠭⠭⢭⣽⣿⡏⣿⡿⢿⠻⡟⠛⠛⢾⢡⡟⣷⡝⠇⣾⣿⣾⢃⣿⢿⣷⣾⣿⣿⣿⣿⣷⣶⣶⠶⠆
⠀⠀⠀⠀⠀⠀⢰⣶⡾⠷⠶⠶⠶⠶⠶⠤⠤⡴⠯⣴⠷⣿⣦⣨⣶⣷⣶⣶⡟⣼⠿⠉⣷⢰⣿⠁⣷⢸⣧⣸⣿⣟⣻⣭⠿⠞⠋⠁
⠀⠀⠀⠀⠀⡽⡛⠷⣶⠶⠶⠶⠶⠶⠖⢒⠒⢛⠛⣿⣾⢟⣿⣿⡟⣽⡿⣿⡇⢿⡷⣀⣿⠈⣟⣷⢻⡎⣿⡯⠋⠙⠁⠁
⠀⠀⠀⠀⣼⣿⠁⣰⠀⣰⠀⣶⠀⢸⡀⢸⡄⠸⡇⢸⡇⣾⠿⡇⢸⡟⠛⢹⣷⡸⣷⣷⢡⠛⠾⠿⠋
⠀⠀⠀⣰⣿⠇⢠⡟⠀⣿⠀⣿⠀⢸⡇⠸⣧⠀⣿⠈⡇⣿⣄⡅⡸⣷⡖⠚⠋⠙⠛⠛⠁
⠀⠐⣿⣧⡋⠀⣼⠇⠀⣿⠀⢻⡇⠸⡇⠀⢻⣀⣹⣤⣷⣿⣿⠜⠉⠛⠋
⠀⠀⠈⢿⣿⣄⠟⢀⣀⣫⣤⣼⣶⣶⣿⡿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠹⣯⡿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠴⠒⡒⠒⢤⡀⠀⠀⠀⠀⡤⠼⠥⣄⠀⠀⠀⠀⠀⡟⣟⠀⠀⠀⠀⢀⡤⣒⣶⣿⠶⢝⣆
⠀⠀⢰⡥⠤⠤⠤⠤⠤⣽⠀⠀⠀⢺⡭⠭⠭⣭⠇⠀⠀⠀⢸⣓⠻⡄⠀⠀⢠⢫⣮⣅⡿⡿⣟⡯⡅
⠀⠀⠸⣏⣙⠾⠭⢞⣉⡿⠀⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⠀⢻⡸⢂⡇⠀⠀⢸⢸⢉⣏⠛⢽⣆⡇⡇
⠀⠀⠀⠓⠚⠢⣠⠞⠓⠃⠀⠀⠀⠀⣇⠀⢀⡇⠀⠀⠀⠀⣸⠀⠸⡇⠀⠀⠀⠣⣙⠭⠾⠶⣊⠜⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢀⡴⡟⣇⡟⡷⣄⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⢀⡠⠤⠦⠤⡀⠀⠀⠀⠀⢀⡴⠋⠻⣷⡄
⠀⠀⠸⡍⠉⠉⠉⠉⣹⠀⠀⠀⠀⢸⠛⠛⠛⢳⢤⡀⠀⠀⢯⠤⡤⠤⡠⢬⠇⠀⠀⠀⡞⠀⠀⢀⡼⠁
⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⢀⣀⣸⣄⣀⣀⣿⣊⡀⠀⠀⠘⡆⢇⢠⠇⡞⠀⠀⣠⣴⡹⠶⠒⠉
⠀⠀⠀⠘⠒⠒⠒⠚⠁⠀⠀⠀⠓⠶⠶⠶⠶⠶⠚⠁⠀⠀⠀⠙⠚⠚⠚⠁⠀⠀⠙⠚⠀⣠⣄⡀
⠀⠀⠀⠀⠀⣀⠴⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄⠀⠀⢠⣞⣓⣞⣳⡄
⠀⠀⠀⡼⠭⠤⠤⠽⡄⠀⠀⢰⠋⠉⠛⠉⠙⠉⠉⢳⠀⠀⠀⠀⠀⣀⡞⠑⠺⡀⠀⠘⡟⢛⡻⢿⠃
⠀⠀⠀⣟⢲⡚⢲⠛⡇⠀⠀⣿⡯⢽⡯⠟⢭⣿⠽⣿⡇⠀⠀⢀⠴⣅⠈⠓⢼⠁⠀⠀⢸⡥⢒⡟
⠀⠀⠀⢸⡀⡇⡟⣸⠀⠀⠀⠙⠛⠿⠭⠭⠭⠽⠟⠛⠀⠀⠾⣙⣆⣈⣧⠴⠋⠀⠀⠀⠀⢟⣹⠁
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⢒⣟⣲⡀⠀⠀⣠⠒⢄⣠⠒⣄⠀⠀⠀⣾⢿⠆⣜⣳⡄⠀⠀⠀⠀⠀⣴⣽⡷⠦⡀
⠀⠀⠀⢀⡴⠋⠀⡯⢽⣻⠃⠀⢸⠁⡸⠈⡇⡹⠈⡇⠀⠀⣿⠸⣤⠏⠘⢦⠀⠀⢀⡤⣪⣾⠞⠀⢀⡗
⠀⠀⢰⠋⠀⣠⠞⣠⠞⠁⠀⠀⠈⢦⠃⡰⢧⠃⡴⠃⠀⢸⠁⠀⢹⠀⠀⢸⠀⠀⢗⡿⠚⠁⠀⡠⠊
⠀⠀⠀⠑⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⢸⣀⣀⣸⣀⣀⣸⠀⠀⠈⠳⠤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣄⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣶⣿⣿⣟⡿⣿⣛⠓⣦⡀⢀⣶⠋⣑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣫⠃⢯⡤⠦⢾⡇⣿⣿⣠⣘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣫⣭⠞⠖⣋⠀⠀⢸⠀⣀⣼⣷⢟⠛⠒⠾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠗⠛⠋⠁⠀⡔⠉⠙⣿⡦⠞⠋⢁⣿⣱⠁⠀⣀⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⢀⡧⠔⠊⠁⠀⠀⠀⢸⡇⣏⠀⠸⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠴⠋⠁⠀⡠⠔⢻⠉⣩⠝⠋⠁⠀⠀⣀⠤⠄⣂⣠⣼⣿⡼⣄⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡏⠀⢹⢸⢰⠁⢠⠤⢒⣊⣭⣴⣾⡿⣽⣶⠟⠉⠻⣾⣥⣴⠞⠙⢆
⠀⠀⠀⠀⠀⢠⠴⢿⣿⣿⡇⠀⠈⢸⠈⣷⣶⡿⢿⣛⣯⣽⢶⡏⢹⡏⣽⡟⠛⠉⠉⠉⠉⠉⠉⠉⣽⠟⠣
⠀⠀⠀⠀⠀⠴⠾⢿⣿⣿⣇⣠⢤⣞⣿⣽⠖⢿⢿⠏⠀⠈⢧⢃⠘⢧⣽⠷⠦⢤⡤⠤⠤⠤⠤⠤⠭⠵⠮⢤⡀
⠀⠀⠀⠀⠀⠒⢛⣛⣻⣿⣿⣷⣿⣿⢿⡇⣀⡠⡿⠖⡿⠂⢸⢸⣧⣼⣤⣤⣤⣼⣤⣤⣄⣤⣤⣤⣤⣤⣤⣴⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣾⣇⠈⢁⣿⡄⠁⠀⣸⡞⠉⠉⣿⡿⢿⡞⡟⢻⣟⣿⣿⣟⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠻⠿⢷⣤⣴⣿⣷⣤⣤⣿⣷⣾⢧⡇⢸⣿⣿⣻⣿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣾⣛⠚⠿⠿⢿⣽⣷⣝⣿⡻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠤⢬⣉⡉⠛⠛⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠫⠙⠉⠉⠀⠀⠀⠈⠀⠀⠀⠈⠙⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⠛⠳⠁⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣶⣃⣀⠀⠀⣀⣠⣎⠀⠀⠀⠀⡱⠄⠀⠤⡀⠀⠠⡀⠀⠉⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠟⠈⢛⠟⠣⡴⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠒⠂⡐⢀⣘⠈⠙⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣻⠀⢀⡎⠀⠀⢸⡇⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⡮⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⣉⣄⠘⣇⡀⠰⣾⣿⣦⣀⣳⣄⢈⣿⣆⡀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠅⠀⢈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⣶⣶⣅⣄⣀⣀⡀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⡻⣿⡿⠻⣯⣽⣟⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⣛⣿⣿⣿⣿⣯⣭⣭⣿⡿⣛⣴⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠁⠹⣿⣿⣿⣮⣹⣿⠿⢿⣿⣿⣿⡖⢤⠴⠒⠢⣼⡟⣻⣿⠿⢿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠀⠀⠀⠀⠋⠙⡿⢿⣿⣿⣆⠀⠹⠉⣿⡇⠀⠀⠀⢠⠉⢠⡿⠁⣠⣾⣿⡿⣋⣵⠟⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⢷⣝⠳⡈⠻⣦⠀⢀⣿⡇⠀⠀⠀⢸⡀⠘⠁⣴⣿⠟⣡⠞⡛⠛⠀⠀⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⠿⣷⣬⡑⠮⡂⠈⠷⢸⣿⡇⠀⠀⠀⠈⡇⢀⡼⠋⠠⣪⠥⠬⣡⣤⣤⣤⣤⣤⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠁⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢹⡄⠀⠀⠈⠁⢀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣾⣭⣭⣁⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⣉⣩⣭⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠀⠀⡀⢰⣿⣿⣿⣿⣄⠋⠁⡤⠄⠊⠃⠄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠠⣀⣀⡀⠀⠻⠟⠉⠉⠙⢿⣷⣿⣤⣄⢀⣀⣄⣡⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢾⣥⣤⣤⣤⣤⣤⡽⠿⠿⠧⣤⣤⣤⡄⠈⠉⠀⠉⡙⢻⣿⣤⣬⣭⣽⣿⣶⣶⣶⣾⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣟⣹⢛⣟⢋⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣶⣶⣶⣄⣤⣿⣿⣿⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠟⠉⠙⠟⠋⠉⠛⠛⠉⠀⠈⠛⠉⠁⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⢦⡀⠀⠀⠀⠛⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠛⢶⣶⠄⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣼⠿⣦⣀⡼⠛⠻⠶⠖⠁⠀⠀⠐⠶⢾⣿⣀⣰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠉⠛⠛⠛⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣷⣶⣶⣦⣀
⠀⠀⠀⠀⠀⣀⡀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡿⣿⣿⣿⣿⣿⣿⣿⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⠾⠛⢉⡖⣿⢫⣾⣿⣿⣿⣿⣿⣿⣷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠤⠘⢋⠁⠀⠀⠀⣾⢱⢁⣿⣿⣿⣿⣿⠛⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠛⠉⠀⠀⠀⣀⣤⡶⠖⠛⢃⢨⠘⣿⣿⣿⡿⣿⣄⣀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠟⠃⠀⠀⢀⣀⣤⠴⠾⣛⣛⣭⣿⣿⣷⢻⣿⣆⠻⣿⣿⣿⣮⣭⣽⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣿⢀⣀⠤⠖⠛⢉⣩⣤⣶⣿⣿⣿⣿⡏⣿⣿⣼⣿⣿⣷⣌⡻⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣠⣤⡤⠀⠀⠀⠀⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣄⣮⣿⣿⠁⠀⠀⠠⠄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠉⠁⢀⣿⣼⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⢀⣠⣶⣄⠶⠚⠋⠉⢻⣿⣟⣋⡄⠁⠀⠀⣇⣤⡤⣿⣾⡇⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⡿⢿⡟⠙⠉⠀⠀⠀⠀⠀⠀⣿⣿⢿⣷⣶⡭⢴⣶⡇⠀⡀⠚⣿⣿⢹⣿⢻⣇⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⠛
⢸⡿⢅⠀⠀⠀⣀⡀⠀⡀⢠⣤⣨⣹⣿⣿⣭⣭⣥⣿⣷⣧⣀⣤⣄⣿⣿⣾⣿⣼⣿⣯⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠸⠾⢿⣿⣶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣻⣿⣻⣽⣿⣿⣹⡝⣿⣿⣿⣿⣿⡿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣏⣻⣏⣻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛⠙⠛⠒⠛⠛⠛⠛⠒⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⣰⣊⡑⢢⠀⠀⠀⠀⠀⣀⢤⡤⠤⣄⣠⠤⡄
⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⣠⣖⣂⣁⣀⣲⣄⠀⠀⠀⠀⣞⣁⢀⣹⣌⢱⡄⠀⠀⠀⣈⠞⠀⡞⠺⣡⡞⢾⣽
⠀⠀⠀⠀⣢⣤⠤⢤⠤⡤⠤⢤⣤⣼⡀⠀⠀⠀⠀⢧⠒⠒⠒⠒⢲⠞⠀⠀⠀⠘⢧⠶⣖⣒⠶⢲⠋⠀⠀⠀⢸⡒⠼⠼⢄⠿⠼⠚⡏
⠀⠀⠀⠀⢱⣊⣉⡲⠮⠭⢷⠭⣙⣤⠃⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⣎⢉⣱⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠣⠤⠍⠮⡇⢙⡴⠵⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣦⠙⡾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⠔⢋⠤⡤⠤⠤⣉⢆⣴⠒⣆⠀⠀⠀⠀⣠⠔⠊⠻⡍⠙⢏⠐⠢⡀⠀⠀⡤⠒⠉⠉⠉⠙⠒⢄⠀⠀⠀⠀⠀⡴⠊⠉⠉⠲⣄
⠀⠀⠀⠀⠎⡞⢙⣚⣁⣡⢞⣕⣋⡀⣇⢸⠀⠀⠀⣜⠁⠀⠀⠀⠘⣄⣸⠦⠤⠜⠀⠘⡤⠤⠤⢤⠤⠤⠤⡞⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡆⡘⠨⠈⠁⠹⢉⠟⢲⢲⠉⠉⠀⠀⢠⠋⠣⡀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠸⡀⢇⠀⡇⢸⢠⠇⠀⠀⠀⠀⠇⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠰⡌⠳⡉⣉⣢⣀⡴⢁⡞⠀⠀⠀⠀⢸⠲⢄⣨⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⣘⡀⢃⣁⡜⠀⠀⠀⠀⣀⠇⣹⠦⠔⠋
⠀⠀⠀⠀⠀⠈⠓⠢⠤⠭⠔⠒⠉⠀⠀⠀⠀⠀⠸⡀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠯⣅⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡆⢠⣆⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢠⣴⡒⢒⣖⠲⠦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣧⣃⣀⣀⠀⠀⠀⠀⠀⠀⢩⠩⣇⡼⠼⡄⠀⠀⠀⠀⢀⠴⢄⡀⣠⠔⢄⡀
⠀⠀⠀⠀⢰⢛⡥⠞⠓⠦⠥⠭⡻⢄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣾⡻⣹⠀⠀⠀⠀⡈⠀⣍⠖⠒⢦⡀⠀⠀⡰⠋⠈⡆⠙⢇⢸⡀⠙⢦
⠀⠀⠀⠰⣏⡜⠀⠀⠀⠀⠀⠀⠘⣾⡄⠀⠀⣀⢀⣱⣄⣀⣀⣤⠞⡛⢩⡁⠀⠀⠀⡞⠁⠨⠁⠀⠀⠀⢹⠀⠀⡇⠀⢠⠁⠀⢸⠀⡧⠀⢸
⠀⠀⠀⢠⣋⣀⣀⣀⣀⣀⣀⣀⣀⡸⠀⠀⠀⠘⠢⢤⣤⣄⣀⣤⠤⠴⠊⠀⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⢸⠀⠀⠱⣄⠸⠀⣀⢮⡀⠇⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⡇⠀⠀⠀⢈⠀⠀⠀⠀⠑⠎⠁⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣿⡒⢢⠀⠀⠀⠀⠀⢸⢾⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⢱⢦⡀
⠀⠀⠀⠀⠀⣀⡠⠤⣐⣵⢿⡿⠊⠉⢣⠀⠀⠀⠀⡜⣈⢘⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⣹⣳⣲⡹⠀⠀⠀⡴⠲⡤⠒⠒⡤⠐⠲⡤⠤⢤
⠀⠀⠀⢰⡯⣒⡲⣩⣓⠵⠊⠀⠀⢀⡜⠀⠀⠀⠸⡩⢍⠉⠈⡆⠀⠀⠀⠀⡰⠗⠒⠉⠁⠀⣠⠇⠀⠀⢸⣄⣈⣁⠠⠄⣁⣀⢀⣁⣀⣠⡇
⠀⠀⠀⠺⣈⠞⠉⠁⠀⠀⠀⠀⡡⠊⠀⠀⠀⠀⠀⢱⢀⠇⠸⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢮⣽⣚⡈⣉⣐⣒⢒⠮⣉⣳⢯⡽
⠀⠀⠀⠀⠘⢆⡀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠏⠉⠀⠸⡄⠀⠀⠑⠤⣄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠢⠤⠒⠒⠠⠤⠁⠂⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⣀⠤⠃⠀⠀⠀⠀⠈⠳⠴⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠓⠉⠁⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢄⡀⠀⠀⠰⡀⠀⠀⠐⡄⠀⠀⠀⠀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣀⣀⣀⣀⣤⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⢹⡟⠛⠒⣯⣽⠏⠀⠀⠀⣀⡄⠀⣀⠀⠀⠀⠀⠘⠐⠄⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠿⠃⣧⠀⣰⣿⡏⠀⡀⠉⠉⠁⣀⣉⠁⠒⠒⠃⠤⠤⠤⡀⠐⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⢠⢖⡩⠁⠈⠙⢧⠉⠉⠛⠛⠀⠾⠿⠠⠞⢋⠉⠉⠛⣿⠓⠲⠦⣄⠀⠈⢉⠀⠉⠀⠉⠶⠂
⠀⠀⠀⠀⠀⢠⣧⣯⠖⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠄⠙⢥⡄⣄⢺⡟⠻⠿⠿⠷⣤⣄⡀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣶⣴⣶⣴⣤⣤⣤⣷⣤⣤⣧⣄⣠⠘⠃⠛⢸⡇⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠘⣿⣟⠦⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⢸⣏⣉⡉⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⣠⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣷⣶⣶⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢀⣠⣼⠛⠉⠉⠉⠉⢹⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⡟⢻⣍⠉⠉⠉⠉⠉⡙⢻⣭⣏⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠁⠉
⠀⠀⠀⢠⣿⣯⣥⣄⣤⣤⣤⣤⣼⣯⣥⣿⣿⣿⠛⠙⣿⣿⣿⣿⠟⠛⠛⠋
⠀⠀⠀⣿⣿⡟⢸⣸⠇⣾⡇⣿⢻⣿⢸⣿⣿⣿⣿⡿⠇⠈⠉⠁
⠀⠀⠀⠈⠻⣇⣿⣿⢰⣿⣼⣿⡾⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉
⠀⣀⡀⠀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⠀⠀⣄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠦⠀⠀⢄⠈⠰⠤⠀⠒⢐⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠸⡁⢀⠄⠀⢀⠀⠀⠀⢀⠐⠀⠀⠀⡐⠊⠀⠈⠸⡀⠀⠀⠀⠀⠐⠀⠈⡀⠄
⠰⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠈⠃⠀⠋⠀⡎⣉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠑
⠀⠀⠐⠒⠒⠚⠁⠀⠀⠀⠀⠀⠊⢲⠂⢑⠤⠘⠁
⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⣀⠀⣀⡀⣀⡀⢀⡀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⢰⣷⠘⣇⠁⢹⠀⣇⡀⡏⢹⢸⢹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⢸⠀⠼⠻⠴⣬⠇⢸⠀⡇⠀⢧⡼⠸⣼⠃⣧
⠀⠀⢠⡀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠌⠸⣧
⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠷⠴⠆⢁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠻⠁⠁⠀⠉⠈⢲⡀⠀⠀⠀⠘⠟⠛⠲⢴⠿⣠⡒⠶⢅⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠦⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⡎⠱⣄⡀⢐⡀⠕⠒⢬⡧⠃⠀⠀⠀⠀⠀⠀⠀⢄⡐⠢⠀⣀
⠀⠀⢛⠀⠀⠀⠠⠈⠀⠈⠀⡀⡉⠀⠀⠀⠀⣤⠀⠐⠃⠐⠓⠒⢬⡀⢂⣤⠈⣠⠀⠀⠐⠀⠀⠀⡀⠄⠉
⠀⠀⠀⠈⠀⢁⠂⠀⠐⡀⠖⠃⠀⠀⠀⠀⠃⠠⠤⠦⣀⠐⢁⠝⢊⠀⠀⠈⠈⣀⣢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⡿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⢻⣿⣿⣿⣸⣿⢿⣿⢣⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣥⣶⣾⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠈⢿⡿⠿⠇⡿⠋⠉⠙⠻⣿⣿⡿⠟⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⣛⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠈⣿⣶⣿⠿⠿⢛⣛⣭⣭⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠶⢦⡿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⠀⠀⠀⠀⢹⣆⣀⣀⣤⣄⣀⣴⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣴⣦⣤⣤⣽⣿⣿⣶⣤⣤⣴⣿⣿⡿⠿⠛⣿⡟⠛⢉⣠⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣽⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣦⣤⣾⣿⢹⠉⢹⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⡁⠀⠀⠀⠀⠀⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⠃⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣟⣉⡉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣭⡿⠀⠀⠀⠀⢸⡇⣿⣿⣯⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡆⢸⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⣀⣤⣄⣀⡀
⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣸⣿⠀⠀⠀⡀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣻⠀⠠⡄⢏⢧⠐⡀⠙⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠠⠀⠀⣶⣿⣿⡇⢀⡀⠀⠀⠀⠣⠀⢸⡄⠈⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⢹⣿⣿⣿⣿⣇⠁⠀⠒⠒⠒⠒⠒⠛⠉⣁⡤⠒⠀⠈⠉⠉⢀⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⢳⠒⠓⠂⠀⡀⠀⡸⢦⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠈⣦⣤⣄⠀⠀⢀⡏⣠⠈⢙⡳⢦⡤⣄⣀⣀⣀⣤⡤⠤⠆⠒⠃⡀
⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣶⣤⣾⣧⡇⢸⠸⣡⣼⢇⡐⠂⠐⠀⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡼⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠙⠿⠿⠿⣿⠻⠿⠿⣿⣿⣼⣿⣇⣀⡀⣠⢼⣋⣴⡡⠇
⠀⠀⠀⠀⠘⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡀⠀⠀⠀⠠⡀⠀⠈⠛⠪⠿⠭⠬⠭⠭⠿⠖⠋⠁⠀⡇
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠾⠿⠿⠿⠿⠿⠿⠟⠛⠁⠀⠉⠐⠒⠒⠂⠘⠑⠒⠀⠤⠤⠤⠤⠤⠤⠀⠤⠠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣥⡶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠁⠀⠀⠸⠇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⢦⣄⠀⠀⣼⠀⠀⠀⠈⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢤⣠⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣿⣵⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢂⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣀⠀⠀⠀⢀⠐⠢⣄⠀⠠⠈⠠⣄⠀⠀⠀⠊⠁⣾⡏⠀⠀⠀⠀⢠⡄⢀⣀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣈⡀⠀⠈⠙⠀⠀⠀⠙⠃⡀⠀⠀⣸⡿⠂⠀⠴⠃⠀⠹⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠂⠂⠉⠉⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠠⠶⣎⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣼⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢀⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠉⠉⠁⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠶⢶⣯⡴⠇⠀⠀⠤⠤⣿⣟⣠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠒⢄⡈⠳⣌⢀⠠⣼⠓⠀⢀⣿⠃⠀⠀⠀⠘⣧⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⢳⡄⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠈⠓⠀⠀⢹⣿⡟⠛⠛⠛⠓⠒⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣿⡀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣷⣿⠿⠆⠀⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣿⡟⠁⠀⠈⡄⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⣾⣿⠇⠀⠀⠀⠹⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⣿⠿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣟⣻⣟⣿⣿⣿⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⠀⠀⢀⡰⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡎
⠀⠀⠸⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠸⠀⠀⣨⠀⠀⢵⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡟⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠳⣄⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⠀⠀⠀⢓⣲⣖⡚⠂⠀⠀⡏⠀⠀⠈⡆⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣆⢠⡏⠀⠀⠀⠈⣧⠀⢐⠀⢀⡜⠉⠀⠀⠉⢢⡀⠀⡇⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠐⢸⡇⠀⠀⠀⠀⣿⠀⢸⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⢹⣿⡏⠲⣄
⠀⠀⠀⠀⠀⢠⠃⢸⡇⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠳⡀
⠀⠀⠀⠀⠖⠁⠀⠘⠷⠶⠶⠶⠶⠟⠀⢸⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣾⣿⣤⣤⣤⣤⣤⣼⣿⡇⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡗⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣶⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣀⣀⣀⡇⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈
⢠⣶⡶⠶⠿⠿⠿⠟⢿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⢿⠻⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠷⣿⣦⠀⠀⠀⠈
⠘⠿⡇⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠿⠟
⠀⠀⠛⠛⠛⠛⠛⠀⠰⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡀⠀⢸⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣤⣤⡦⣰⡄⠀⠀⢰⡦⢦⣰⣤⣤⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⠀⣶⠓⣦⠀⠀⠀⠀⠀⣤⡀⢀⣠⡀⢠⣄⡀⣀⡀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⠀⠙⠒⣿⡄⠀⠀⣿⠀⠑⠾⠟⠛⠃⠚⠻⠟⠘⠛⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⢀⡿⠁⢈⠀⣯⠀⢰⠀⣤⢀⠀⡾⢀⣄⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠟⠀⡇⠀⠋⠀⢿⢹⢠⡇⢸⡇⠀⡁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠑⠈⠁⠁⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢓⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⠂
⠀⠀⠀⠀⠀⠀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀
⠀⢀⠤⠠⣤⣠⣇⡔⠇⠀⣀⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠤⠤⠤⣄⡀⠀⠀⢀⡠⠤⠀⠒⠂⠀⠀⠉⠀⣠⡴⢿⡀
⣤⣯⣤⡚⠀⠀⠈⡟⠉⠲⡀⠀⠀⢱⠀⠀⠀⣀⠤⢄⠀⠀⠀⢠⠖⠊⠉⠁⠀⠀⠀⠉⠘⠒⠢⣄⡙⣦⠀⡸⢤⣂⡀⠀⠀⠀⠀⣤⡼⢟⣴⣾⠇
⡇⠠⠀⠙⠶⢤⠴⠖⠒⠲⠿⣤⣤⣞⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠒⠄⠀⠀⢀⡐⠀⡂⡀⠂⠘⠏⢹⡆⢰⠆⢤⣿⣋⠐⠒⢚⣩⡴⠟⠋
⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⢻⠶⠇⠀⠀⠀⠀⠀⡀⠀⠀⣸⣦⣤⣄⣄⣠⣄⣠⣦⣠⣦⣶⣶⣞⣿⠀⠀⠒⢄⠉⣁⠴⠟⠋⠁
⢸⠀⡆⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣧⠀⠀⠨⣀⠀⠀⡇⠀⢾⢀⡙⠓⠛⠳⠶⠛⠷⠞⢛⣋⡭⠖⣻⠏⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠛⢆⡀
⠘⡄⠁⠀⠀⠀⠀⠀⡔⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢥⣭⡭⣭⣭⣭⣭⣭⠭⠴⠖⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠸⠀⢀⠨⡸⡄
⠀⠉⠛⠛⠛⠓⠒⠺⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣈⠀⠀⠈⠇⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡘⠲⠂⠠⢀⠉⠛⢦⣄⠀⠀⠀⠀⢷⠀⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣀⣠⣴⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠰⠞⠃⠀⠘⠀⠀⠀⠀⠀⠀⢀⡞⠱⠀⠀⠀⠀⠐⠢⡀⠈⠳⣄⠀⠀⠘⠇⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⢋⠉⢊⠈⢉⡏
⠀⠀⠀⠀⠀⢀⣘⠃⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡀⠀⠀⠀⠀⠈⠢⡀⠈⣆⠀⠀⠀⠃⠀⢀⡀⠸⠀⠀⠀⠀⠀⠠⡐⠠⠑⢨⠅
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠁⠀⠀⢀⣠⣶⠶⠛⠚⠋⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡏⠰⠀⠀⠀⢠⣀⣴⠾⠿⠋⠁⠀⠀⠀⠀⠀⢰⠀⠀⡈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠰⢀⠢⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠂⠀⠀⠀⢀⡿⠀⡀⢈⣤⡶⠛⠋⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⢰⢬⠁
⠀⠀⠀⠀⠀⠀⠀⡆⢉⣻⣦⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⢸⣃⣴⠾⠛⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠶⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⡠⠦⠴⢤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡤⠶⠛⠿⢫⡥⠅⠀⠦⢤⡀⠀⠀⠀⠀⢀⣤⢠⣤⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⢀
⠀⠘⠀⢤⠀⠈⡇⠀⠀⠀⠀⠀⣀⠠⣤⡄⢠⠶⠤⠀⠀⠀⠀⠀⠀⣴⠋⠁⠉⠚⠀⠀⠀⠀⣀⠀⢀⣿⠀⠀⣠⣤⢴⣤⣤⣤⢴⡄⢠⠀⠀⠀⠈⢳⣿⣄⠼⠶⣤
⠀⡆⠘⡆⠀⠀⣿⠀⠀⠀⣠⣾⠟⢁⡽⠓⠉⠉⠛⠛⢴⣄⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣫⣽⠀⠀⠈⣽⡇⠉⢉⢻⡸⡇⣸⣤⠀⠀⠀⠀⠋⠀⠈
⠀⠃⣴⠃⠀⠀⣿⠀⠀⢰⠻⠏⡠⠊⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⣿⡀⠀⠁⣀⡠⢤⣶⠿⡿⣋⠁⣴⠼⠃⣤⠀⢸⣏⣤⣸⣄⣧⣷⣿⠃⠀⠀⠀⠀⠘
⠀⢸⠋⠆⠀⠀⡟⠀⠀⠘⢾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠻⠿⡏⠉⢀⣬⠥⠌⣻⣯⣭⠶⡞⢻⠃⠀⠘⡆⠀⠉⠉⠉⠀⣼⠁⠀⠀⠀⠀⠀⢢⠤⠬⠉
⠀⢸⣠⡇⠀⢰⡇⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠀⠒⠒⠒⠁⠀⠀⠀⣳⣟⠦⠴⣤⣾⡿⠛⠋⠀⢀⡷⠋⠀⠀⠀⢷⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⡂⣀⠰⠊
⠀⠈⣇⠀⠀⣼⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⣄⣀⣀⣉⣠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠸⣆⣰⠇⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠐⠒⠐⠒⠋⠀⠀⠀⠀⡀⠔⠄
⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢠⡄⠲⡀
⠀⠀⠀⢈⢧⠀⠀⠀⠠⡤⠤⠤⠤⢤⡄⣀⣀⣀⣀⣈⣐⣄⠀⠀⠀⠀⡤⢀⣤⣤⣴⠾⠿⠛⠉⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣣⠀⠈⣢⡀
⠀⠀⠀⠘⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢉⡀⠀⠙⡀⠀⠀⠔⠉⠝⠉⠁⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⢀⣀⣀⠤⠼⢧⡽⢤⣾⠿⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠐⢦⠀⠀⠀⠀⣀⡴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡃⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⠐⠃⡀
⠀⢀⣀⠀⠐⣬⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠐⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⣠⠏⠀⠀⠀⢀⠴⠀⠀⣁⠈⠀⠀⠀⢀⠀⠀⡴⠋
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⢀⣀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⢀⡈⢉⠀⠀⠉⡠⠆⠀⠃
⠀⠀⠀⣀⠀⠀⠀⠋⠀⠈⠛⠂⠴⠓⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠀⠀⡄
⠀⠀⠂⠌⠀⠀⣀⢀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠛⡒⠤⠀⠀⢸⠀⠀⠀⠀⠂⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⡀⢀⡠⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠄⠄⠀⠀⠀⠀⡀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⠀⢀⠌⠀⠠⠒⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠱⠄⠀⠣⡀⠐⠁⠿⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⠀⣀⠀⡀⠀⠀⠀⠀⠋⠒⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⡴⠒⠀⠀⠀⠀⠀⠐⡌⠓⠀⠃⠀⠀⠀⠀⠀⠁⠂⠀⠀⠐⢢⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⡄⠐⠀⣠⠞
⠀⠀⠤⠀⠀⠓⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣴⢟⣉⡁⢀⠀⡀⠀⠀⠀⠀⣉⡡⠤⠔⠋
⠀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠷⠀⠀⠀⢀⡤⠀⡆⠀⠔⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠒⠋⠁⠐⢀⣡⣌⠢⣀⡤⠟
⠀⠉⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠋⠉⠉⠈⠉⠈⡧⣈⠂
⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⣠⡄⠀⠹⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⡰⠃⠀⠀⠀⠄⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⡀⠀⠈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠢⢌⠙⢤⠀⠀⠀⠀⠀⠁⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⢇⠀⠀⠀⠀⢤⣀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠒⠒⠀⠀⠀⠀⠀⠐⢄⠀⠈⠀⠀⠀⠀⠀⢀⠀⡸⠁⠀⠀⠀⠀⠈⠗⢠⡎⠀⠀⠀⡀⠀⠀⠀⠀⠈⡦⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡤⠒⢀⠀⠄⢀⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢀⠤⠀⠀⠀⠀⠃⠀⠀⠠⠀⠸
⠀⠀⠀⠀⠁⠊⠀⠀⠀⠈⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠐⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠙⠲⣄⢀⡤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠏⠀⠀⠀⢀⡀⠈⠁⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⡷⠒⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠿⠿⠯⠭⣗⢦⠀⣿⠀⢀⠜⠀⠀⠀⢠⣸⠀⠀⠀⠀⠇⢸⠥⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣄⡀⠀⢸⣿⠂⠉⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣤⣄⣀⡼⠙⢤⣄⠤⠚⢇⠀⠀⠀⠀⠀⢸⠃⠀⣦⠆⠀⠘⡄⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣸⡇⠀⢹⣿⠁⠀⠀⠀⠀⠀⠈⠳⠤⣤⠤⠶⢻⡀⠀⠃⠀⡀⠀⠁⢀⠀⠀⠸⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣷⣼⣿⣷⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠳⢤⠤⠊⠳⣤⣠⣤⡀⠹⣦⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠾⢥⡀⠉⢻⡛⠻⠿⣿⣇⠀⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢵⣤⠬⢷
⠀⠀⠀⠀⠀⢀⠏⣠⡀⠀⢷⠀⠀⢧⠀⠀⠀⠀⠉⠙⠛⠣⠴⣿⣿⣿⣿⣿⣭⣀⠒⠢⢤
⠀⠀⠀⠀⠀⠸⡀⠻⠃⠀⣾⣄⡀⡼⠀⠀⠒⠠⠤⢤⣀⡀⠀⠀⠀⠙⢿⠛⢿⣿⠀⠰⠍⣀
⠀⠀⠀⠀⠀⠀⠳⣤⣤⣾⣿⣿⣿⢃⣾⣿⣿⣶⣶⣤⣤⣌⣉⡁⠂⠀⢘⠆⠘⣿⠀⠀⠀⠀⡿⢿⢿⣿⣿⣿⣿⣿⡷⠤⢀⡀
⠀⠀⠀⡤⢤⡀⠀⠼⠿⠿⢿⣯⡵⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⣴⡇⠀⢉⡐⠘⠷⢾⣀⡀⠉⣹⣿⣿⡏⠐⠂⠀⠉⠒⠠⠄⣀
⠀⠀⠈⢦⡼⠛⣀⠀⠀⠀⢸⣀⣿⠆⣀⡀⠀⣈⢉⣉⡉⠙⠛⠛⣿⣃⣿⣼⢧⣼⣿⡉⠏⣷⣧⢸⠀⠀⠉⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡟⣿⢿⠟⣿⣿⠿⣾⣿⡿⣿⣿⣿⠛⠙⢿⣿⠛⠙⢳⣾⣽⣠⣿⡙⢿⣿⣿⢱⡆⢹⣿⣾⣀⣀⠐⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠟⣸⡟⠈⣸⣿⡟⠀⣿⡿⠀⣾⣿⣏⢰⡆⢹⣿⢰⡇⢘⣿⢹⣿⠿⠀⢺⣿⣿⣾⣇⢸⣿⡿⢻⣿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣼
⠓⢯⣠⡿⠀⢠⣿⡟⠀⢸⣿⡇⣠⣿⠛⣿⡌⢡⡼⢿⡄⢁⣼⣿⢿⣧⡳⢈⣿⡿⢿⣽⢿⡿⢿⣟⣣⣿⣃⡿⣿⣺⣗⡿⠿⠿⠿⢿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⡠⠔⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⡀⠔⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠶⠦⣤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⢤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⣿⡇⠀⠀⠈⠁⠠⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠉⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⣿⡇⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠐⠀⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⢶⣾⣧⣤⢬⣿⣧⣏⣀⣿⡇⠀⠀⣴⡻⣯⡍⠏⢭⡭⠭⣙⢻⣶⣿⢯⣭⣭⣙⣛⠲⡦⢤⣀⡀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠶⣶⡌⢿⣧⠀⠀⠀⠙⣏⠉⠉⠉⠉⠙⣿⠛⠛⠿⠿⢾⣧⣀⣸⣿⣏⠉⣿⣿⣿⣿⣿⣷⠗⠀⠈⠉⠛⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢹⣷⢸⣿⣦⣤⣤⣀⢹⣄⣀⣀⣀⣀⢸⣆⣀⡀⠀⠀⢹⣿⣿⣿⣿⠀⠟⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⡀⠀⣼⡿⣸⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣽⣯⣭⣭⣿⣿⣾⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⡿⣿⠾⠟⢱⡇⢹⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣶⣶⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠿⠿⠷⠶⠿⠿⠿⡿⠿⠟⠛⠛⠛⠋⠉⠉⣹⡟⠉⠉⢧⣿⠁⠀⢹⣿⢀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣤⣤⣤⣤⣤⡤⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡇⢴⡆⢸⣿⣀⣿⣨⣯⣸⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣯⢀⢠⢀⠎⡄⡀⢰⢠⡁⣿⣿⢁⡈⣿⡇⣦⢹⣿⣿⣧⣨⡵⣾⣿⣯⣀⣾⣿⣿⡽⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣼⣿⢣⢏⡞⣼⢰⡇⣿⢸⠜⡇⢻⣿⡜⢃⣿⣷⣤⣾⣿⣿⡿⠷⠾⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠈⠻⣅⣫⣬⣥⡥⠦⠷⠶⠶⠛⠚⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢩⠓
⠀⠀⠀⠀⢀⡤⠊⠁⠀⠠⢄⠘⢶⠂⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣫⣴⠾⠃⣤⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠀⢠⣾⡄
⠀⠀⠀⠀⢸⡀⡀⠀⠓⠒⡢⠤⠤⠾⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠾⡋⢻⡴⠏⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢿⡾⠇⠿⣤⣤⣦⠉
⠀⠀⠀⠀⢸⣿⠩⣀⡴⠊⠀⠀⠀⠀⠀⢮⣀⡀⠀⠀⠀⠀⣤⠂⣰⣟⢻⣅⡦⠟⠉⠀⢀⣰⡿⠃⠀⠀⠀⠀⠀⣆⠚⢧⣼⡇⠨⣶⡄⠒⠉⠉⠛
⠀⠀⠀⠀⠀⠙⠢⠿⠇⠀⠀⠘⠷⠜⠀⠈⣬⡃⠀⠀⠀⠀⠙⢀⣷⡜⠋⠁⢀⢀⣶⣿⡶⠛⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠹⣿⣯⡀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⣀⠀⡀⠀⠤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠻⣀⣴⣷⣉⣴⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⡉⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠶⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠂⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⢾⣁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠛⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠦⠀⠀⠃⡀⠂⣨⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡆⠀⠀⢾⠆⡠
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⠀⢀⣀⣐⢃⣠⣴⠾⢃⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⢿⡀⢻⣇⠀⠀⠰⢺⠃⣾⣷
⠀⠀⠀⠀⠀⣾⠁⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢶⣮⣽⣿⣿⣧⣬⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⣿⡖⠏⠉⠓⠀⠀⢼⣯⣥⠂
⠀⠀⠀⠀⠀⢉⠀⠀⠠⣿⠇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣿⣏⣉⣙⣛⣭⣼⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠠⠟⠋
⠀⠀⠀⠀⠀⠈⠳⢀⣰⡙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀
⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡤⣤⡿⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣠⣴⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠠⡄⠀⡀
⠀⠀⠀⠀⠀⢠⣧⣤⣴⠶⢠⣾⣷⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠲⠦⠟⢿⣻⡆⠀⠀⠀⠀⠀⠀⠀⢠⡶⣾⣷⣶⡿⣿⣿⣿⣗⠂⡄⠐⡀⠁
⠀⠀⠀⠀⠀⠘⢩⠟⠳⠶⠷⣬⣭⣵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁⠒⠂⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢘⠿⣿⣹⣯⣷⣿⣛⣻⣿⣷⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⣴⣶⡖⢢⣾⡏⠀⠀⠀⠀⠀⠀⠀⠛⢶⣌⠙⢳⣤⣿⣿⠿⣋⣽⠃⣸⢳
⠀⠀⠀⠀⠀⠀⠀⣧⡐⢿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⠬⠁⠼⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⣿⠸⣦⣾⣿⡇⠀⡿⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢷⠀⠉⠀⣉⠹⠟⠃⠘⠃⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠛⠶⠾⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⣶⣬⠓⣯⣾⡻⠛⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣹⡧⠀⠀⢀⣼⣅⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢹⢻⡄
⠀⠀⠀⠀⠀⣠⠊⣿⣶⣶⡉⣭⢳⣾⣿⣖⣠⡇⠀⠀⠀⠀⠀⠀⠀⣿⡗⢩⣭⡧⠀⢠⣿⠧⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⣮⣤⡿
⠀⠀⠀⠀⠀⠛⢶⣿⣛⠻⣿⣶⣿⣤⢒⣽⡿⢋⣆⠀⠀⠀⠀⠀⠀⣶⠀⠀⢸⡇⠀⠈⡇⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⢃⠲⣼⠷⠆
⠀⠀⠀⠀⠀⠤⢂⠈⠙⠻⢿⣍⣙⠿⠼⢿⣤⡾⠛⠀⠀⠀⠀⠀⠀⣿⠀⣤⣼⡇⠀⠀⡟⢰⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⡘⣟⣓⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢠⣀⡠⠈⠙⠿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠉⢹⣷⠀⠀⣷⠈⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢫⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⣸⣯⠀⠀⢹⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣦⡜⣷⣷⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠲⠤
⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⣿⢡⣷⢸⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠂⡀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣇⣸⡟⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⣡⠔⠃⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠚⠛⠻⠿⣿⣿⣴⣶⡀
⠀⠀⠀⠀⠀⠐⣷⠿⠿⠿⠿⠿⢧⡾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⠐⠊⠁⢀⣴⣿⣿⣿⡟⣻⠀⠀⠀⠀⠀⠀⠰⢖⣀⣀⠐⠠⠔⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⢀⡐⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⡁⠤⣳⡿⢻⣿⣽⡿⠽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢷⣦⣄⡀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣷⠾⣿⡿⠶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡻⢶⣬⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠈⠀⠠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡔⣍⣁⣀⣀⣈⣹⡵⣄⣤⣤⣤⣤⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠓⢸⣿⣿⣿⡟⣳⣾⣤⣠⡈⢀⠀⠀⣀⣱⣧⣼⢻⣿⣿⣿⡆⠈⠘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⢠⡟⠀⣹⢟⣣⣹⣏⣘⣿⣯⡉⢹⡄⣿⣿⣿⣧⠀⠀⠀⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡀⢤⣿⣿⣿⣿⡶⣟⣽⣿⡿⠟⢛⡛⠿⢿⣿⣿⣿⣇⣿⣿⣿⣿⡄⠠⢀⣯⣉⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢸⣿⣿⣿⡇⢠⣿⡟⠁⠐⠀⢸⠃⠀⠂⠉⢿⣷⡌⢸⣿⣿⣿⡇⠀⠀⠀⠸⡗⢻⣿⣷⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢸⣿⣿⣿⡇⣿⡟⠀⠛⠀⠀⢸⡀⠀⠀⠚⠈⢿⣷⢸⣿⣿⣿⡇⠀⠀⠀⢀⠟⣫⡿⠿⢿⡃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠱⢤⠤⢼⣿⣿⣿⡿⣿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣾⣿⣿⣿⡷⢤⡤⣤⣼⡼⡿⠁⠰⣟⣙⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇⢻⣿⡄⠿⠀⡀⠀⠀⢀⡀⠚⣰⣿⠇⣿⣿⣿⣿⠀⠀⠀⢸⣩⠼⠃⠠⣖⠻⣏⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⣿⣿⣿⡄⠻⣿⣶⣄⣁⠐⠂⣀⣥⣾⣿⠋⣸⣿⣿⣿⠇⠀⠀⠀⡘⠁⠀⣴⠲⣎⠛⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠹⠅⠛⠻⢿⡿⠿⠿⣛⡫⣹⠙⠛⠛⠛⠛⠉⠉⢉⡉⠁⣴⠶⡜⠓⢾⡗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣾⣽⢷⡞⣷⢠⡶⣦⢠⢶⡄⣿⢹⡆⠹⢦⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠼⣿⡁⢸⣧⠟⠸⣠⡇⢙⣿⣇⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠋⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⢀⠀⠀⣀⠀⣠⠀⢠⠀⠀⠀⠀⠀⠀⠠⡄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠓⠀⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠼⠤⢀⠀⢀⠀⠀⠤⠀⠀⠈⠀⠁⣀⡀⠄⣀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣢⠈⠀⠀⠀⠀⠊⠀⠀⣡⡀⠀⢄⣀⡀⠀⠀⠀⠂⠁⠀⠀⢀⡀⡠⠀⠒⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡇⠀⡇⠀⠀⣤⡤⢄⠀⠈⠉⠀⠀⠀⠀⠙⠛⠀⠙⠐⠚⠓⠂⠀⠉⡭⠈⠀⠀⠀⠀⡁⠀⠀⠠⠀⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣾⣇⣘⣀⠀⢀⡟⠁⢠⠛⠓⠶⠶⠦⣾⡯⢷⣀⣤⣤⡤⢤⣤⣤⠀⠈⢀⠀⠐⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡀⠀⠙⢿⠉⠁⠙⢿⡿⠋⠑⡶⠂⢐⢂⠙⠓⠲⠿⡿⢾⡷⢶⢀⣭⡵⣶⣤⣬⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣖⢳⠴⠀⢰⢀⠉⠁⢠⠁⢀⡀⣱⠀⠈⠀⠉⠉⠐⠀⠹⠀⠙⠂⢹⣿⣽⢻⣯⡸⡄⠀⠀⣀⣀⣠⡤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣤⣶⣹⣿⣴⣦⣶⣷⣉⠉⣉⢭⣭⣿⡛⣂⢀⠶⠶⠶⠶⠺⠸⠗⠀⠈⢉⣉⠉⢰⣾⠿⢿⣿⣿⡷⣷⠿⣾⣦
⠀⠀⠀⠀⠀⠀⡀⣠⠂⠂⠻⣿⣿⣿⡿⠁⢃⠀⠀⢻⣿⣿⣿⣿⢀⡀⢀⣿⣉⡿⣷⣷⣶⣼⣿⣾⠀⠀⠀⡀⢀⡁⢸⣿⠀⠀⡄⢸⠀⠄⠀⡿
⠀⠀⠀⠀⠀⣖⠠⠀⣈⣿⠾⠶⠯⠔⣳⣧⣩⣭⣤⣤⣥⡤⠤⠤⣖⣀⣤⣤⣭⣤⣤⣤⣤⣤⣤⠤⠤⢤⣧⣥⣤⣄⣸⣿⢀⡤⠀⢸⠀⠡⠄⣿⠄
⠀⠀⠀⠀⡴⠀⢢⣤⣄⡞⠂⡐⠀⡨⢽⣁⣾⣿⠻⢵⣧⢹⠀⠀⠈⣟⢿⡿⣿⣟⢿⡿⣫⣭⣻⡟⣯⣽⣿⣿⣿⡿⠿⢿⣠⣤⣤⣤⣤⣴⣤⠤⣤
⠀⠀⠀⠀⠀⠈⡚⠉⢩⣷⢰⣐⣿⠶⢾⣡⣗⢶⡶⢈⡋⡼⠀⠀⡼⣿⣿⣹⣟⣻⣟⣻⣿⢻⣿⣼⣿⣻⣿⣿⡟⠀⠀⠈⠃⠡⡉⠋⠩⠨⢀⣀⢈
⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣶⣭⣍⣀⢨⣿⣉⣿⣟⣭⡗⢳⢤⡼⣿⢟⣿⣿⣿⣟⣽⣯⣿⣿⣿⣮⡿⣿⣥⠤⠀⠰⠒⠒⠀⠀⠊⠉⠁⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣛⣻⡿⠿⠿⠴⠒⠓⠚⠃⠉⠙⠋⠉⠉⠉⠉⠉⠉
⠀⠄
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠉⠙⠳⡤⠶⠠⠀⡀⠀⠀⢀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⣼⣿⣓⠦⣄⡀⠀⢀⣀⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠳⣄⠉⠉⠀⠀⠉⠻⠋⠉⠩⠋⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠴⣚⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⠷⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣥⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⡀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠳⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠁⠀⠀⠀⠀⠁⢐⡟⠀⠀⢀⣀⣠⡴⠖⠋⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠈⠛⠻⢯⣍⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⣻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⢾⡛⠉⠋⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠃⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⢰⣴⣮⡀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡼⠃⢿⠹⣿⡏⠇⠙⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣠⢤⡖⠒⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⠁⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣆⠀⡤⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠲⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡏⢸⡄⠀⠀⠀⠀⢀⣄⠀⠀⠀⢘⡆⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠀⠀⠙⠶⣤⣤⠶⠋⠹⣄⣀⣠⡾⠁⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢨⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠙⠙⠂⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠋⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠀⠐⣂⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡖⠀⠀⠀⠀⠀⣼⡆⠀⠀⠰⡀⠁⠋⠀⢹⡵⠋⠀⠰⢀⠀⢀⡁⢀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡭⠁⠀⠃⠀⠈⠓⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠊⠰⠄⠀⠀⠀⠀⠊⣭⢤⡼⢃⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠸⣦⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠒⠒⢿⡣⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢴⡾⠛⠓⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡄⢸⣷⠀⣿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⣀⡏⠉⠁⠐⠘⠀⠀⠀⣤⠠⠞⠃⠰⠆⢠⣤⣌⡶⡚⠀⡆⠀⢩⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣼⠃⠁⠀⢰⠆⡴⠃⠰⠦⠐⠤⠄⠀⠃⠀⣀⣀⣤⢅⡆⠇⢴⡀⢈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣾⠗⠀⢠⡖⠐⠺⢦⡀⡦⠤⢿⣷⣶⣶⣦⣭⣥⣴⣾⣿⣷⣆⣀⠘⣿⣯⡴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠻⣦⣒⠲⣽⣮⣻⣯⣙⣭⢙⠉⢻⣭⣿⣤⣯⣛⣛⡛⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠛⠉⠀⣯⣽⠙⣈⣁⢉⡞⠂⠨⣻⣿⡃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢊⠉⠹⠻⡇⠳⢷⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠉⡛⣻⡆⢀⠤⡆⢄⢟⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⢸⠀⣘⡇⠸⡀⣴⣿⣨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⣼⣿⡏⠗⢀⣀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠃⠿⠿⠁⠶⠌⠁⠀⠙⠋⢹⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠰⠀⣀⠀⠀⠉⠙⠃⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⣲⣿⣠⣄⢲⣴⣤⣤⣦⣬⣿⣟⡾⣠⣤⣀⣰⣽⣿⣵⣆⣀⠀⠠⠤⠶⡤⣦⣤⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠠⠤⠤⠬⠿⠿⠶⠌⠐⠂⠒⠚⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⡀⢀⡁⠀⠀⠀⠀⠀⢀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠲⢤⣀⡐⠒⠂⠀⡀⠀⠄⠒
⠀⠀⠀⠑⣂⣾⢛⣻⠗⠶⣽⢳⣖⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠎⣰⣌⣩⢥⡓⢒⡦⣟⣩⠇⢀
⠀⠀⢰⣿⢻⣿⠿⠿⢿⣿⣿⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⢳⣶⣩⠵⠲⢿⣿⣶⣾⣷⣆⣻⠇
⠀⠀⠀⣁⠩⢵⣶⡆⠈⠁⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣄⣀⣀⣂⣤⠀⠀⠀⣠⣠⣤⡤
⠀⠀⠀⠉⠉⠉⠛⠛⠛⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⢤⣖⠚⢿⣤⠿⣿⣶⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣞⠃⢿⠿⡇⢡⣜⠉⢀⣼⣿⠜⠥⣆⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⣉⡀⠴⠰⠀⠀⣐⣚⣙⣀⣐⣔⣀⣀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣛⣭⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄⣿⡇⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠟⣰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣷⣠⣤⣶⣿⣷⢻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣵⣤⠹⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣃⣿⠿⠃⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣋⣩⣭⣭⣍⠉⢴⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⠀⠈⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢄⣐⣒⣲⣖⣚⣛⣓⣒⠒⣤⡀⠀⠀⠀⠀⢰⢁⣀⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠔⠒⢦⢸⠀⠴⠒⠆⠀⠢⠀⡇⠀⠀⠀⠀⠸⡀⢀⡼⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢹⡆⠀⠀⢸⠀⠀⢠⡇⠀⠀⠀⠀⠀⠁⠉⡇⠀⠀⢠⠚⡟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣘⡤⠀⠨⠇⣀⣀⠀⠀⠀⣶⣶⡇⠀⠀⢸⠀⡏⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠠⣼⡗⡺⠋⠀⠈⠁⠈⢉⣴⣟⡋⠫⠉⠁⠬⠏⢃⡼⢷⣴⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠅⠐⡒⣖⢺⣷⠓⠒⠦⠤⠤⢤⣼⠁⠀⠀⠀⠀⠀⠉⢠⣿⠀⠤⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢸⡟⢨⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⢠⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⡀⠀⠉⠀⠀⠀⣼⠀⡠⠄⠀⢀⡀⠀⢸⣇⠰⡀⢈⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⡀⠀⡧⠰⠧⠂⠉⢈⡀⠀⠐⠻⢼⣀⡠⠀⡌⡅⠀⠈⠫⡂⣀⠩⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠐⣗⣓⢆⣉⣀⡀⠀⠄⠀⠀⠀⠀⠍⢙⠛⠐⠲⠷⠶⠯⠤⢴⢒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠰⣏⠿⢰⡧⢄⠼⣆⡴⠓⠲⠋⢓⡶⡄⢸⡏⠋⠋⠙⠋⠉⠙⠉⣺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⢷⡉⢠⡟⡦⡿⢲⠀⠀⠁⡇⢸⠅⠀⡈⡀⠀⠀⠀⠁⢫⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⠀⠬⢀⡀⡀⡟⢹⠀⠀⠘⡨⠰⡄⠀⠀⠪⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⢟⣲⠤⣼⣤⣽⣧⡤⠬⢞⡿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣒⣒⣒⣒⣚⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⢀⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢗⠴⠀⢛⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⡏⣽⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠠⠔⠂⠈⠉⢡⠼⠉⠈⠙⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⡄⣀⢀⡀⢈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⣶⣿⣿⣿⣷⣮⣿⣦⣶⣭⣶⣶⣶⣖
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⣠⠄⠴⡉⠉⢣⠀⡝⠛⢲⡀
⠀⠀⠀⢀⡤⢧⡀⣠⣿⣶⣿⣿⣿⣿⣿⣷⣤⡤⠤⣄
⠀⠀⢰⡋⠀⢀⣾⣿⣿⠿⠿⣿⠛⠛⢯⠀⠙⡆⣀⣠⠃
⠀⠀⢠⠟⠒⣿⣿⣿⡇⠀⠀⠈⡆⠀⣼⡤⠞⠫⡀⠀⢱
⠀⠀⠱⡄⠀⣿⣿⣿⠗⠤⣀⣠⠞⠉⠀⣇⠀⣠⠗⢴⠋
⠀⠀⠀⠙⠂⢿⣿⡿⠀⡀⠀⠑⠤⠤⠜⠁⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠉⢆
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠙⠂⠀⠀⢄⢤⣀⠴⢂⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⠈⢁⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠤⠤⣀⣠⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠰⠀⣠⠀⡄⢸⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠝⠉⠙⠶⠤⣤⣤⠤⠚⣦⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠁⠀⠀⠀⠀⠈⠲⠤⣠⣀⣀⣀⣀⠴⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⢰⠓⠦⡤⠶⠦⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⢩⠀⢸⡉⠑⠦⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠈⠙⠋⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠇
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠒⠒⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠋⠁
⠀⠀⠀⠀⡠⠊⠡⠀⠀⠀⠄⠀⠀⠒⠀⠠⡈⢳⡀
⠀⠀⠀⠀⣇⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⣧⠉⠒⠲⠦⡤⠤⠄⠔⢶⠒⢋⣽⡞⣽⡄
⠀⠀⠀⠀⣿⣙⣓⣚⣺⣦⣤⠤⢶⡧⢾⠛⠒⢏⡹⡀
⠀⠀⠀⠀⢼⠀⣉⢹⠀⢸⠉⠉⡉⠚⠐⢅⠠⢃⡵⢇
⠀⠀⠀⠠⡛⢦⣄⣙⣤⣼⣉⣉⣥⡤⡴⠖⠚⣹⣤⡏
⠀⠀⠀⠀⠸⡖⠢⠤⢤⣌⣀⣀⣠⣤⣏⡴⢾⠉⢠⠃
⠀⠀⠀⠀⠀⠱⢄⣁⠀⠀⠉⠁⠀⠠⠂⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠈⢀⣈⡻⡍⢢⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣟⠵⡜⣞⣧⠂⡇⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣂⣉⣉⠐⠲⢄⠐⠀⢣⠻⣆⠰⢹⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⢁⡀⢹⡖⣴⠀⠃⠀⠀⠑⠊⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠺⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠕⢀⣤⠄⡔⣰⠃⠑⢆⠘⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⢦⠀⠀⠘⠈⠁⣿⡮⠞⠁⠀⢠⠀⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡠⠶⡊⠀⠀⠀⠀⢰⢟⡠⠀⠀⡠⢐⡂⠀⠘⣌⢕⠒⠤⠤⠴⠲⡈⠍⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠙⠦⡀⠀⢀⠴⠋⠀⠀⠇⠃⣼⡱⠁⠀⢹⡅⡢⡚⣀⠀⡿⠇⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⢄⠡⣀⠀⣤⠋⠀⠀⢀⡠⠈⢀⠜⡡⣂⠕⠀⠘⡋⠚⠰⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠑⢄⡂⠈⡴⡐⠖⠂⣠⠴⢋⠅⣊⠔⡨⢂⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠐⠊⠁⠱⡐⠡⢊⠔⡩⠐⡡⠂⠀⠲⣄⠑⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⢀⠉⡉⠉⠐⠒⠀⠀⠷⠄⠁⢊⠄⢊⠔⡡⠀⠀⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠡⢊⢔⡕⡪⢒⠔⡢⢂⠔⣆⠀⠔⡡⠊⡠⢊⠄⡀⠙⠦⣀⠀⠀⠒⠀⠐⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢈⠕⠁⠹⡢⠡⢊⠔⡡⢊⠜⡧⡈⠰⢊⠔⡡⢊⡡⢂⠀⠈⠉⠓⠂⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢊⠜⡡⠈⢶⡥⢎⡔⣡⣊⣔⣝⠦⡀⠊⠔⢋⠔⡡⢚⡅⢁⡠⢀⡀⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢊⠔⡡⢂⠑⡄⠀⠀⠀⠀⠀⠀⠈⠲⢄⡁⠊⠔⢁⠔⡡⠔⡡⡢⢀⠀⠸⡀⠠⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠁⠊⠐⠁⠡⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣁⡈⠐⠡⠊⢔⠕⠀⠀⡅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠄⡁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠤⢒⠤⢐⠠⠄⡂⠄⠒⠤⢒⠤⠐⠠⠔⠢⠔⠢⠔⡂⠄⡂⠤⢐⡀⠄⡀⠤⣀⠠⣀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⣳⣤⠄⢀⣠⣴⡾⠛⠚⠛⢶⣶⣤⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢕⢶⣿⡿⠟⢻⠿⠒⠣⠀⠀⠀⢉⠙⢿⣤⡄⠲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⠋⠀⠃⠁⠀⠀⣀⣄⡀⠀⠀⠽⣿⠿⣾⣷⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡿⠖⠀⠀⠀⠔⠉⠀⠀⠈⠁⠀⠀⠈⠀⠈⢻⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⡿⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣇⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⡢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣫⣷⡁⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡿⠉⠛⠦⣌⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢫⡻⢿⣿⣷⡷⣄⠙⠚⠳⢤⣤⠒⠅⠀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠛⠚⠛⠛⠋⠙⠿⠿⠿⠿⠛⠓⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⠒⠒⠊⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠛⠋⠉⠉⠉⠉⠉⠛⠓⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠘⣆
⠀⣰⠇⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⣆
⢠⡏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣤⠀⠀⣤⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣼⠁⠀⠀⠀⠀⣠⠤⠤⢤⡤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⠀⠿⠀⠀⠿⠀⠀⠀⣠⠤⠤⢤⣤⠤⠤⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠈
⡟⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸
⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⣷⠀⠀⠀⠀⠀⠀⢀⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⠤⠤⣤⣄⣀
⢹⡀⠀⠀⠀⠀⢀⡟⠀⠀⡷⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⣧⠀⠀⠀⠀⣼⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠸⣆⠀⠀⣰⠇⠀⠀⣼⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠒⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠹⣆⣰⠏⠀⠀⠀⠛⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡖⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⣀⣀⣀⣀⣀⣈⣓⣦⣤⣤⣤⣤⣶⣖⣒⣛⣋⣓⣲⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣖⣚⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠶⠤⠾⠶⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣦⣼⡇⣾⣿⣿⣿⣶⣶⣶⡍⣭⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⢻⣿⢸⡧⡀⠂⠀⠉⠑⢶⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠬⠭⠭⠭⠤⠭⠭⠭⠭⠭⠭⠬⠭⠤⠤⢤⠀⣉⣀⠀⢸⠀⠀⠀⠉⠓⠐⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡤⡤⠄⠀⠀⠀⠀⠀⣈⣙⠉⠁⠒⠒⠲⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣸⣯⣷⢶⠀⣼⠟⣿⣳⣿⣿⣿⣿⣯⡼⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠀⠈⣦⠃⠀⢁⠀⠀⠈⠉⠉⠀⠀⠀⣀⣀⣤⡤⠀⠒⢀⣈⣩⣥⠤⠤⠒⣒⠀⠠⠼⣶⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠐⢀⠚⠉⠀⣀⣤⠤⠾⠟⣛⣩⡤⠀⠚⣋⡥⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⠀⣀⣀⠀⢀⣠⡀⢀⠀⠀⠀⢀⣤⡄⠀⠁⠀⣠⠔⢛⣩⠠⠶⠛⠉⢀⣠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⣤⡄⣤⣤⣤⣤⣄⣠⣤⣤⡄⠀⠀⢠⡶⢴⣫⣴⠶⠛⠉⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠹⠧⠽⠿⠿⠿⠷⠾⠿⠏⠀⠀⣴⣿⠶⠛⠉⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⠿⠏⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⢿⡿⣿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣿⣻⣿⠒⡗⡷⢺⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣧⡀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣯⣹⣿⣩⣏⣯⣹⣿⣛⡛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⢸⢿⣿⡿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡯⠼⣿⠶⡧⡷⢾⣿⠄⠀⣾⡦⠀⠀⠀⠀⠀⠀⠀⢀⣬⡟⣯⡀⢀⣻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠉⠉⠉⣿⠍⢷⣟⣻⣿⠀⢠⣼⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢻⠻⠏⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠛⣾⣤⣤⣤⣦⣿⣴⣬⣞⡏⠽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣍⣉⣏⣉⣭⣉⣭⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⠿⠉⠉⠉⠉⠙⠿⠇⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡆⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⠿⠟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⡻⢛⠀⠀⠀⣿⣿⠙⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⣴⣿⣿⠇⣿⣿⣦⣄⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠿⢿⣿⠿⢿⣿⡇⢹⣿⡷⠂⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢠⣭⣥⣈⣹⣿⣿⣶⣾⣿⣿⣅⣠⣭⣥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢈⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠁⠀⠀⠀⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣋⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢈⡏⠁⣠⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⠁⠃⣨⠙⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠶⠀⠸⠇⢀⡾⢡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣱⠄⠀⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⡱⣦⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠧⠀⠀⠋⠠⠋⠔⠁⠀⠀⠀⠀⠀⠀⢀⡀⡠⠀⠃⠀⠀⠀⢠⣄⣂⣀⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⡄⠇⠀⠀⠁⠀⠀⠀⠉⠙⠛⠻⠷⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠒⠶⠲⢀⣤⠄⣠⠴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠟⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠰⠀⠐⠂⠘⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠙⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠆⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠞⠢⠄⠀⠤⠊⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⡀⣀⡀⠠⢀⠐⠃
⠀⠀⠀⠀⠀⠀⡬⢀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣷⡾⠷⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣈⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠠⢛⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⡄⠐⠃⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⢤⡀⢤⠈⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟
⠀⣠⠀⠀⠀⠀⠈⠀⣀⠒⣀⠀⠂⡐⢂⣤⡄⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡀⣀⠀⡀⣀⡠⠆
⠘⢋⡙⠉⠉⠁⡀⠀⠻⠿⣃⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠚⠃⠰⠂⠉⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠼⢇⡨⠍⠀⠀⢀⠄⠀⠛⠀⠀⠠⠀⠐⢢⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡃⠐⢀⠀⠀⡁⢠⡤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠛⠂⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡼⠃⠀⠚⠃⠀⠀⠀⠁⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤
⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠁⠀⠀⢠⡀⢃⡰⠐⠶⠀⠑⠲⢄⣠⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡰⠚⠎⠀⣠⣀⠀⠀⠀⠀⣀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀
⠀⠀⠐⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠉⠀⠀⡰⠀⠀⠀⠀⠠⠤⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀
⣀⣀⣀⣀⣈⣉⣉⣁⣀⣘⣢⣄⣀⣀⣐⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡶⣻⣽⣏⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶
⠀⢠⣶⣶⣶⣶⣶⣒⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⢿⣿⡿⠿⣿⠿⠿⠿⠿⣿⣿⣿⠛⠛⣿⡋⠙⣿⡟⠋⣽⣿
⠀⢸⣿⠛⢻⣿⠋⠹⣿⡏⢩⡟⠉⣨⣀⠉⢿⡇⠐⣤⡀⠉⣿⠀⢸⡿⢀⣼⣿⠀⢰⣶⠀⢸⣿⡏⠀⡄⢸⣷⡀⢹⠃⢰⣿⣿
⠀⠸⣿⡇⠈⣿⠀⠀⢿⠀⢸⡇⠀⣿⣿⠀⢸⡇⠀⡟⠃⢀⣿⠀⠘⠀⠹⣿⣿⠀⢸⣿⡇⠀⣿⠃⢰⡇⠀⢿⣷⡎⠀⣿⣿⣿⠇
⠀⢸⣿⣿⡀⢫⢰⡇⠸⡀⣿⡇⠀⢿⣿⠀⢸⡇⠀⣷⣆⠀⢻⠀⠰⣦⠀⠹⣿⠀⢸⣿⠇⠀⣿⠀⣸⣤⡀⠸⣿⡇⠀⣿⣿⣿⡇
⠀⠈⣿⣿⣇⠘⣾⣿⠀⢳⣿⣿⡀⠘⠟⠀⣸⣇⠀⣿⣿⣀⣸⣇⣀⣿⣧⣠⣽⣤⣬⣤⣤⣾⣯⣤⣿⣿⣷⣶⣿⣷⣶⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠙⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢤⠀⠀⡀
⣿⣿⣿⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢉⠩⠁
⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠀⢛⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠈⠁
⣿⡿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⢹⡀⢰⠀⠀⠰⠀⠓⢄⡁⠀⡇⠀⢸⠀⠀⢹⠀⣮⠀⠀⠇⢸⡇⠀⣿⠠⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠟⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠓⠄⠀⠀⠃⠀⠙⠀⠓⠀⠘⠂⠀⠘⠂⠘⠢⠀⠀⠈⠃⠀⠛⠀⠑⠠⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠀⠰⡆⠀⢰⡄⠀⢰⡄⢠⠀⠀⢢⠀⣶⠀⡆⠀⣆⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⢰⡇⠀⢠⡇⠀⢸⡇⠸⡄⠀⠸⠀⣿⠀⣇⠠⡄⠙⠆⠀⠀⠀⣤⣶⡄⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣧⡀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣌⡻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠈⠿⢿⠮⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣾⣿⣿
⠀⠘⢷⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⢭⣇⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠟⢻⡟⠛⣿⠿⣿⡇⢹⠿⡿⢿⢿⣿⣿⣿⢻⣿⣿⣿⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡀⢸⣇⠀⣿⣀⣿⡇⢸⣀⣧⣸⣸⣧⣄⣤⢠⣤⣼⣧⣦⣼⣴⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡻⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠄⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠒⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⠿⢛⠿⢿⣿⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡯⠀⠀⠀⠀⠀⠈⢿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⢛⣛⣁⣀⣀⠀⠀⠀⠉⠉⠘⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠤⠀⢰⠂⠀⠀⣀⢀⡀⠀⢀⠀⠀⠀⢸⡏⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠁⣀⠀⠀⣿⡀⠏⢢⡿⣿⡟⢠⡎⠀⠀⠀⠘⣷⢹⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠈⣿⡆⢇⢹⠀⠀⣿⣿⠀⠀⠀⢸⡇⠨⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣷⣄⢹⣇⣾⡄⡅⡀⢹⡏⠀⢸⣷⣿⠁⢠⡀⠀⠀⠀⠀⢻⡗⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢿⡸⣿⣿⣻⣧⡀⣷⢸⠇⠀⣼⣿⠇⠀⣼⣧⣤⠄⢰⡄⠚⠓⠼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠷⠛⠛⠉⢻⣿⣿⣾⡰⢠⣿⣿⣶⣦⣿⣿⣿⣴⣀⣤⣐⣴⣦⡀⠘⠿⡃⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠻⠿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠛⠉⠉⠁⠀⠀⠀⠉⠉⠙⠟⣿⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠉⠁⣀⡤⠴⠶⠶⣶⠶⡶⠖⠲⠦⠤⠤⠴⠃⠈⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢦⡨⢛⣩⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠐⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡈⠉⠘⡿⠿⣛⣋⣻⣍⣉⡋⢉⡉⠙⣛⣻⣛⡛⠛⠃⠲⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⢁⣶⣾⣿⣿⣿⣿⣿⠿⠿⠷⢶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⣈⠻⢿⣍⣍⡀⠀⡀⠆⠁⠈⠀⠀⠀⠈⠈⠉⠑⣢⣦⣠⡴⠏
⠀⠀⠀⠀⠤⠤⠶⣶⣾⣿⣿⣤⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⣴⠿⠶⠞⢛⣟⣓⣛⣛⣻⣟⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣻⣟⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣾⣿⠿⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠛⠿⠿⠿⠿⠟⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡤⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⣀⡀⣠⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⢀⡀⠄⠀⠀⠀⠁⠀⠀⠐⢦⡤⠾⠋⠀⠘⣁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡄⠀⠂⠀⠀⣼⠫⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⣠⠌⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠶⠤⠀⢄⣴⠋⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠈⢡⡄⠀⠀⠀⠀⠛⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⠀⠀⠄⣼⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠿⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠐⠀⠈⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠲⣌⠁⡰⠛⠋⠉⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣦⣀⠀⠈⠀⠀⣼⠀⢄⡀⠀⠀⣀⠀⠐⢦⣶⡾⠋⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣾⣧⡧⢾⣦⣼⣶⠿⠷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡆⢾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⢺⣿⠓⢶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠂⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸⣿⠏⠁⣤⠆⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⣛⣿⡿⠀⠀⣾⠠⣤⠀⠀⠀⠀⠀⡄
⠀⠀⢀⣤⣀⠀⠒⠀⠀⠔⠀⠀⠀⠳⠒⠶⠟⠷⢄⡀⣹⠀⠉⠀⠰⠄⠀⢀⣀⠀⠀⠀⠀⠀⠃
⠀⠀⣽⣽⣿⣷⣿⣤⣽⣤⣴⣀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠇⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠁⠙⠛⠖⠺⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠒⡀⠐⠒⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣌⡙⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠉⠉⠉⠉⠁
⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣶⣶⣶⣦⣾⣦⣾⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠸⠄⢠⣿⣿⠄⠀⠀⢠⣶⣦⠀⠉⡏⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣿⣿⡟⠀⠀⢀⣾⣿⡟⠀⠀⢀⡈⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠿⢿⠁⠀⣰⣿⣿⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⣿⣿⡿⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⢻⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠈⠓⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠹⣿⣿⣶⣴⣶⣿⣿⡿⠟⠁⠀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠈⠛⠿⠿⠟⠋⠁⠀⠀⢀⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⠛⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⣿⣿⣿⣿⢿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠠⠴⠶⢒⣒⣛⣉⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⠖⠒⣛⣉⣭⡭⠤⠶⠖⠒⢀⣈⠉⣩⣥⣄⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠴⠆⢀⣚⣛⣉⡉⠡⠴⠖⠒⠒⠋⢉⣁⣀⡀⠰⢶⣤⣾⣇⠈⡿⠁⠀⠹⣿⡏⠀⢸⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠐⠖⢒⢛⣩⣭⠥⠤⠶⠖⠚⢛⠉⣉⣅⠠⣤⣤⣀⠀⠘⣿⣿⣷⠀⣙⣻⠿⠀⠈⠻⣿⣿⣧⠁⠀⠀⠀⢙⣃⡀⠘⡇
⠀⢰⠛⢋⣭⡥⠤⠄⠐⠒⠂⣈⠁⠀⣤⣤⣤⠆⠀⠲⡞⠀⠈⢻⣿⣧⠀⣹⣿⠟⠀⠀⢹⣿⣿⡄⢻⣿⣶⡄⡀⠀⢸⣿⣿⣧⠀⠀⠀⠛⠛⠁⡀⣷
⠀⠘⠇⠀⢤⣤⣴⡆⠘⣻⢿⣯⠀⠀⢸⣿⣿⡆⠀⠀⢿⠀⠀⢸⣿⣿⡇⠹⣿⣿⣇⡄⢸⣿⠿⠧⠈⠛⠛⠋⣁⣀⣉⡤⠤⠤⢖⣒⣚⣻⡭⠭⠄⠚
⠀⠀⢧⠀⠘⣿⣿⣇⠠⢿⣿⣿⠀⠀⠸⣿⣟⡇⠀⢀⡼⠀⠀⠨⠿⠿⠛⠂⣙⣛⣉⣠⠤⠤⠶⣒⣒⣛⡩⠭⠽⠶⠒⠚⠛⠉⠉⠉
⠀⠀⢸⠀⠀⣿⣿⣿⡀⢸⣿⣿⠧⠀⠀⠉⢛⣛⣁⣠⡤⠤⠴⢖⣒⣚⣫⡭⠭⠶⠖⠒⠛⠋⠉⠉
⠀⠀⠀⡆⠀⣈⣉⣉⣥⠄⠤⠶⣒⣒⣛⣭⠭⠭⠶⠒⠚⠛⠉⠉⠁
⠀⠀⠀⢦⠭⠭⠵⠖⠒⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⡠⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠊⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠰⡎⠀⠈⣓⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣢⣠⣼⣷⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢚⠀⠀⢈⣙⡂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠶⠙⠓⠶⠃⠨⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠒⠂⠠⢀
⡄⠀⠒⢄⡘⡀⠐⠐⠒⡄⢀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⣤⣄⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠠⡄⠰⠋
⠉⠀⠀⠂⠀⡀⠆⢷⣾⠐⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡒⠠⢔⠈⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢈⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠁⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠈⠭⠇⠈⠑⢄
⠀⠀⠀⠂⠀⠀⠀⠘⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠉⠀⠐⠑⠀⠂⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠲⠀⠆⠠⠠⠇⠰⠀⠀⠀⠀⠀⠀⠀⠢⠂⠅⠨⠘⠆⠇⠰⠈⠒⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠦⠤⣤⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠋⢀⠀⠀⣀⠀⠀⡂⡁
⠀⠀⠀⠀⡛⠚⠃⢛⣣⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢒⡆⠤⠠⢄⡀⣀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⠉⠉⢢⠀⠐
⠀⠀⠀⠀⠛⠃⠀⠘⠓⠁⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⢁⡃⡒⠰⠠⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⢰⠀⢸
⠀⠀⠀⠈⢁⡀⣀⢀⡀⠀⠲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⢁⠂⠒⠠⢁⠁⡂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⡈⠠⠤⠘⢀⠆
⠀⠀⠀⠀⠨⠀⠀⢀⢮⠇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣀⠂⠂⠬⢈⢁⠂⠔⢠⠀⠀⠀⢹⠀⠀⠀⠀⠀⠃⠀⠀⠀⢧⡠⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠑⠂⠁⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠉⠒⠤⢂⠬⣈⠁⢂⢉⡹⠒⠾⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢠⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠃⠐⠂⠀⠀⠂
⠀⠀⠀⠀⠚⠂⠄⠘⠀⠄⠰⠃⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠟⠠⠄⠵⠘⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠤⠄⠠⢀⡠⠤⠤⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⡀
⠀⠠⠀⠀⠀⢘⡀⠀⠀⠀⢈⡀⢀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⡤⢄⢀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠰⢆⠁⠀⠀⡇
⠀⠠⣀⠀⢤⢾⠉⠀⠀⠀⠋⠀⠈⠑⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⡠⠐⠐⢀⠀⠃⠀⠀⠀⠀⠱⠀⡐
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⢠⠀⠀⠄⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⣀⡌⣀⠂⠀⠀⠀⠀⠢⢀⡀⠄⠁⠐⢄⡤⢃⣠⡜⠪⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡜⠁⠸⢳⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⢀⡁⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠳⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠠⠨⠀⠀⠀⠀⠀⠠⢀⠀⠁⠀⢈⡄⠂⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢨⢨
⠀⠀⠀⢰⢠⡄⠂⡀⢠⡄⡢⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠋⠿⢢⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡀⠀⣀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠔⠒⠒⠊⠁⠀⠉⠀⠈⠋⡍⡵⠂⠤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠲⠗⠀⠐⠂⠀⠐⠶⠆⠀⢀⢠⣤⣀⣀⣀⣤⠄⠀⠡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⢠⡀⠀⠀⢠⣤⣤⡶⣄⣠⣔⣷⣿⣿⣿⣿⡁⠀⠀⠀⠀⢀⣙⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢀⠀⢄⠀⣙⣶⠞⣟⠁⣾⡅⠈⣹⣿⣿⣿⣿⣿⣿⣣⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠴⠾⠗⠴⠿⠿⠷⠰⠟⠛⢛⡿⠿⠻⠿⠿⠿⠿⠿⠟⢫⠆⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠜⢳⣄⠀⠀⢀⣄⠀⠀⣀⠀⢇⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡈⣤⣾⣿⣿⡟⠉⠉⣿⡆⢰⠯⠸⣦⢼⠛⣷⠈⡄⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣽⡆⢸⣿⣿⣿⡗⠀⢀⣿⣇⣸⢀⡸⠿⢿⠾⢿⠄⠃⢀⣽⣷⣦⣄
⠀⠀⠀⢀⠀⠀⠤⠤⠀⠐⠒⣶⡆⠟⠛⣸⣿⣿⠉⣀⣱⠃⣠⢄⢤⠟⠤⣤⠀⢤⠤⠤⢤⣿⡿⢿⣿⣿⣧
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⠹⠟⣓⣒⣛⠓⠒⣓⣚⣸⣷⣴⣦⣶⣶⣴⣦⣼⣿⣧⡏⢿⣿⡇
⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣤⡂⢽⡿⢫⣦⡐⠈⣻⣿⣿⣿⣿⠩⠝⣿⣿⣿⣿⣷⣽⣾⣿⣦
⠀⠀⠀⢳⣴⡴⣆⣆⣰⣐⣸⣿⣿⣿⠸⠉⡇⢾⡇⢻⡙⠧⠠⠿⠿⠿⠟⡛⠐⢸⢫⢹⣿⣿⣿⣿⣿⣿⣡⣷⣄
⠀⠀⠀⣢⣾⣠⣿⣁⣟⢀⣾⣿⣿⣿⢰⣀⡆⣶⡆⣴⣀⡖⢸⣿⣿⣟⢧⢷⣷⣿⣿⡿⡾⣛⠛⣿⣿⣿⣿⣿⡿⠟⢗
⠀⠀⣽⣿⣯⣽⣟⣿⣟⣋⣟⣿⡿⠿⢧⢉⣴⣿⣿⣜⠟⣡⣿⣿⢿⡿⣸⢹⣿⣿⣿⣿⣯⢸⡇⣾⣿⣿⣿⣿⡟⣎⢎⢳⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣖⣖⣾⣯⠭⠭⣽⣟⣑⣛⣛⣛⠿⠿⠿⠭⣼⣿⣿⣿⣿⣿⣿⣼⣧⣳⣻⠦⡀
⠀⠀⢿⣾⣟⣻⣭⣿⠟⢿⣿⣿⠿⣿⣿⣿⡿⣿⡿⢿⣿⢿⠿⣿⣿⣷⡶⡶⡾⢭⣭⢭⣟⢛⡒⠒⠶⠶⠤⠬⣭⣭⣍⣉⠛⠛⠁

⠑⠀⠈⢠⡀⣧⠛⠾⡓⠀⠀⠀⠀⠀⠀⢀⠸⡃⠀⢀⠀⡀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠐⣠⠄⠀⣠⠊
⢀⣶⣕⠌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠁⠀⠐⠁⠘⢆
⡉⠀⠁⢠⠶⠈⠀⠀⠀⡀⠆⠘⠖⠒⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠈
⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠓⠀⠀⠀⢀⠐⠑⠆⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠐⠂⠁⢀⠀⣀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠁⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠋
⠀⢀⡄⠀⠂⢘⠀⠀⠀⠀⠏⠈⠀⠀⠢⠀⠀⠀⠁⠐⠀⠀⠀⠸⠂⢈⠄⠋⠈⠁⡆⠓⡀⠀⢄⠀⠀⠀⠐
⡈⠀⠀⠀⠀⠠⠛⠈⠁⢐⠀⠊⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠥⠀⠀⠰
⠉⠁⠀⠀⢀⠤⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠂⠠⡄⠀⠀⢨⠥
⠓⠠⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰


⣉⣉⣀⠤
⣉⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⣉⣤⡴⠖⡊
⠉⣥⠶⢃⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⢿⣶
⣈⣴⣮⣅⣤⣴⣎⣠⣠⣄⣤⣄⣠⣇⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣀⣤⣤⣈⣤⣌⣵⣦⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠊⠇⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣉⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣇⠀⡠⠼⠔⢣⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⣠⠔⠚⢆⢫⠀⠀⠘⡆⢰⠀⠀⠸⠀⡎⠉⠑⢢⢀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⣈⡮⣆⠀⠀⠱⠘⠀⠀⠀⡿⠀⠀⢀⣃⠏⠀⠀⢹⠂
⠀⠀⠀⠀⢀⣀⠤⣤⣴⠦⠤⠶⢾⠀⠷⠶⠦⢴⣦⣤⠧⣀⣧⠀⠸⡀⠀⠀⢻⡂⠀⢀⠇⠀⠀⡘⠉⢓⠄⢠⠃
⠀⠀⠀⢰⣅⠰⢍⣀⠀⠀⠀⠀⠘⠖⠁⠀⠀⠀⠀⣀⡩⠆⣨⡄⠀⠇⠀⠀⢸⡇⠀⠸⠀⠀⠀⡇⠀⡞⠀⡏
⠀⠀⠀⠘⡓⠮⠭⠭⢛⣛⣛⣓⣒⣓⣚⣛⣛⣛⡛⠭⠭⠵⢺⠹⡀⢸⠀⠀⢸⠇⠀⡇⠀⠀⢰⠀⢠⢁⣼
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠳⢇⡀⡆⠀⢸⠀⠀⡇⠀⠀⢸⢀⡼⠋⡌
⠀⠀⠀⠀⢰⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣶⠀⠀⠈⠑⠒⠚⠤⠴⠇⠐⠒⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠘⡀⠀⠀⠚⠁⠘⢃⣤⣤⣤⠘⠃⠈⠃⠀⠀⢀⠿⠀⠀⡴⠛⢶⠄⠀⠀⠀⢠⠞⠳⡦⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⡿⢿⠇⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠻⠦⠞⠀⠀⠀⠀⠀⠀⡌⠀⢡⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣅⡢⡖⢈⡉⠭⠶⣞⡢⢤⣤⣤⣤⣈⡉⣀⡀⠀⠀⠠⠼⡤⢤⣐⡲⠶⠍⣉⣑⠦⠄⣤⣄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠱⣹⣉⣐⣲⣖⣂⡉⠉⣉⣒⠢⣍⡙⠛⠛⢛⣛⡻⠟⣋⣒⡢⢤⣴⣶⣊⡕⠊⠉⠁⠈⠆
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠈⢇⡀⣠⠞⠉⠀⠶⠀⠬⠍⣁⠙⣃⡐⢛⣒⠛⠓⠒⠚⣛⠚⠋⢻⠉⢉⣍⢀⣄⠀⠈⠙⢦⡀⢀⠆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠋⠀⠀⠀⠙⠂⠈⠶⠀⠁⠗⠈⠃⠠⡏⠰⠃⠘⠃⠴⠂⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠤⠤⢀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⠠⠤⠤⠤⠄⠒⠒⠊⠁



⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠀⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠒⠠⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣥⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⡀⠀⠀⠀⠐⡂⡀⠀⡀⠀⠐⠀⠀⠀⠠⣠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⡠⠾⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⠐⠄⠀⢀⢊⡒⠀⠒⣤⢄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⡠⠀⠐⠋⠀⠀⠀⠉⠉⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠈⠉⢀⢀⣔⣛⡌⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢱⣵⣊⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠂⠀⣠⢠⠄⠈⢆⠀⠀⠀⠌⠀⠀⠀⠔⠀⠀⠀⠀⠀⣀⡀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠉⠁⠚⠀⠀⠀⠈⢦⣀⣀⣀⣠⣾⣿⣿⡟⠀⠀⠈⠑⠢⢄⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⡿⠿⠋⠀⠀⡰⠀⢀⠠⣤⣴⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⠔⠂⠀⠀⠀⠀⠀⠀⠀⡀⠑⠢⣄⣤⠄⠀⣀⠀⠙⢧⡀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⡈⠀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠰⣄⠀⠀⠀⠀⠠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠈⠖⢢⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⠉⠒⠤⢀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢄⡀⠀⠀⠀⠈⢡⣤⣤⣤⠀⠀⠐⢄⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⣀⡄⠀⣿⣿⡇⠀⠀⠀⠑⢦⡀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⡀⠀⠀⠀⠙⢆⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⠀⠀⠀⠀⠀⠱⡀⠀⢀⢼⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣧⣼⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠬⠒⠃⠀⠀⠀⠈⠀⠄⠀⠀⠂⠀⠀⢀⠀⠘⠦⠀⠀⡀⠀⠅⠀⠁⢧⡀⢹⠋⢻⣬⢺⣣⣼⣼⡿⠉⡽⠁⡨⢋⠁⠃⠼⢁⠞⠹⠃⢈⡼⠋
⣅⡀⠀⠀⠀⠀⠀⠈⠀⠈⢢⣠⣤⣄⣤⣀⡀⠀⠠⠀⠀⠀⠀⣠⠖⠾⣇⡀⢱⢋⡷⠻⠋⠀⠈⣷⡼⢁⣀⠀⡈⠀⠀⢀⡀⠀⣀⠐⠁⠀⠈⠀⠀⢀⡴
⢤⢉⠁⠤⣀⠀⠀⠀⠀⠀⣾⠉⠀⡀⢀⣉⣻⡖⡦⠥⡀⣀⣴⠧⠁⠀⠙⠉⢨⠮⣤⡀⠀⠀⠰⠟⠗⠛⠉⠙⠉⣹⠋⠁⠹⠏⢉⠷⡄⠀⡀⠔⠊⠉⠉
⣓⠀⠀⡀⠀⠐⠀⠀⠀⠀⢻⡍⠀⠈⠯⡉⠁⠀⠁⠀⠀⠉⠉⠗⠲⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠉⠀⠀⠸⠀⠀⣈⡗⠂⠁⠀⠀⠠⠐
⠦⣠⠀⠁⠉⠒⠀⠀⠀⠀⠻⣆⡄⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⣲⢤⠤⢤⠀⠀⠀⠀⢲⡋⠀⠀⠀⠀⠠⣄⠼
⠂⠀⠅⠀⠂⠀⠀⡀⠀⠀⠀⠈⣟⠁⠀⠀⠀⠀⢀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⡀⠀⠠⠆⠀⠈⠹⠀⢀⣸⠃⠀⠀⣀⣠⠇⠀⠀⠀⠀⠀⠀⢀
⠙⠃⠀⠀⠀⠀⢀⢀⣠⣔⡓⢺⡋⣷⠒⠀⠀⠀⠀⠀⠀⠈⠁⠉⠠⠄⠀⠀⠱⠀⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡰⠞⠁⣴⣃⣠⡀⠀⠀⠀⠀⠄
⠚⠛⠓⠲⠆⠀⢰⣏⡀⠉⠀⠀⠃⠈⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠹⠻⡟⢲⡄⣀
⣛⠖⠃⠀⠀⢀⣿⠉⠀⣀⠴⠚⠁⠀⠙⠂⠀⠀⠀⠒⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠀⠀⠀⠁⠀⠀⢀⡼⢋⣑
⠻⠍⣠⣶⠋⠙⠇⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶
⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⣀⠀⠀⠀⢠⣤⣄
⠤⠼⢿⣓⣤⣰⠯⠀⠸⣧⣀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠂⢠⠀⢀⡀⠀⠀⠀⠀⠁⠀⠉⠉
⠃⠉⠀⠀⠀⠉⢳⣀⠀⠀⠈⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠘⠆⠀⠀⠁⠢⠄⠀⠀⠀⠀⠀⠀⠀⠈⣠⣸⠇⠀⣠⡼⠟⠂⠒⠠⠤
⣴⡖⠊⠀⠀⠀⠀⠈⠛⠷⠖⢡⡀⠀⠀⠀⠀⠺⢤⠴⠦⠄⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠠⠀⠀⠠⠨⠆⠀⢀⠀⠀⠀⣹⡝⠀⢙⠀⠀⢄⣀⠀⠘⠑
⡩⠀⠀⠀⠀⠀⣀⠄⠈⠁⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⢆⣀⡔⠀⠀⠰⣤⠤⡀⠙⠆⠀⠀⢀⣄⠀⠀⡀⠘⠒⠋⢹⣷⣛⠁⢠⣴⡏⠀⠀⠀⠀⠉⠀⠈
⠂⠀⢀⡀⠄⠊⠀⠀⣀⡤⡾⠊⠳⠴⠤⠴⠻⣄⣀⣰⣯⠉⣅⡀⡐⢀⣽⡆⠁⠘⠲⢤⢶⡞⠉⠓⠚⠻⣤⣤⡽⠛⠀⠉⠙⠋⠁⠀⠀⠀⠀⠑⠢⢈⡐
⣪⠕⠉⠀⠀⣀⠔⠛⡉⠈⠁⠀⠀⠀⠀⢀⠀⠀⠁⡰⠃⢠⠻⣤⠶⣞⠈⡻⣆⠀⡀⣀⡾⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠁⠀⢂⡠⠋⣡⡴⡋⢀⣄⣠⠊⡰⢂⠔⣉⡴⠀⣰⠃⣰⣦⣢⠘⣶⡔⣾⣧⣨⣃⢹⡉⡀⠀⡀⠀⠪⠀⠰⣄⠀⠐⠀⢀⠀⡀⠀⠀⢀⠀⠀⠀⠐⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⣄⠀⣀
⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⡰⠟⡗⠚⠎⡛⡹⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢀⣄⢠
⠀⠀⠒⠚⠋⠉⠉⠀⠀⢠⡌⠈⠀⠀⠀⠐⠀⠈⠃⠀⠀⣠⣴⡶⠂⠀⠀⣀⡠⠂⣑⣀⠔⠡⣬⠀⢇⠎
⢠⣀⢄⠈⢉⣆⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠠⢾⡿⠗⠁⠀⠀⡘⠲⡇⠀⣝⡏⠀⡰⡾
⠈⠲⠃⠀⠈⢀⣀⡀⠀⠠⠀⠀⠀⠀⠃⣀⢀⡀⠀⠀⠀⠀⠀⠰⠀⢠⣅⣙⡃⣰⢾⠁⢠⣿⠁⠠⠂
⠀⠀⢀⢄⠀⡆⠄⠔⠁⠀⢠⣍⡆⠀⢘⢖⠉⠃⣠⠠⠻⣀⠠⠀⠀⢸⠃⠀⠉⠈⠉⠋⠒⡇⢀⢄⣠⡄
⠀⠒⢁⢈⠀⠃⡡⠴⠀⢀⢃⠭⡸⠀⠈⣲⠍⡆⠀⡙⣎⡁⢠⠶⣦⢸⠘⠂⠉⠐⠥⠀⣾⠀⠀⠀⠕⡁
⠀⠀⠀⢻⠈⠂⠃⠀⠀⠘⠊⠀⠓⠃⠀⠑⠒⠁⠀⠑⠐⠃⠈⠋⠁⠈⠓⠒⠒⠂⠲⠀⠃⠀⠀⢠⢰⠟
⠀⠀⠠⠒⢣⡀⠃⡑⠀⠀⠠⠫⡷⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⠞⠁
⠀⠀⠀⠀⠁⠈⢙⢤⡄⠀⠀⠁⣂⡀⡀⠀⠀⠹⠒⠇⠀⠀⠠⠀⠀⢠⡔⠀⠀⣀⡀⠠⠀⠀⠰⣿⠴⠂
⠀⠀⠀⠀⠀⠀⠣⠜⠁⠀⠀⢸⠔⠒⠊⢀⢎⢭⢳⠀⡔⡒⠄⠀⠀⠠⡀⢀⠞⠉⠙⢦⠀⢠⠶⢦⡀
⠀⠀⣼⣷⠀⠀⠠⠀⠀⠀⠀⠘⢨⠴⠂⠸⡘⠐⡸⠰⠐⠝⡘⢰⠸⠵⡘⠘⡀⠀⠀⢸⠀⠃⠀⢸⠃⠁
⠀⠀⢳⣿⡇⠀⠀⢀⣀⠠⢀⠘⠚⠀⠀⠀⠉⠉⣠⠤⢵⡮⣀⠘⠒⠈⠠⠀⠘⠢⡤⡎⠀⣀⠔⠁⠀⠸
⠀⠀⠀⠉⣴⣖⠈⠙⢷⣄⠈⣆⢤⠀⠐⠈⢀⠼⠢⡖⠚⠳⡤⣇⠠⢰⡅⠀⠀⠀⢧⠥⠀⠿⠀⠠⡂⠢
⠀⠀⠀⠀⡍⢮⣦⣠⠾⣿⠊⠡⠀⢠⣤⠀⢸⠑⠾⠛⠓⠛⠓⠺⠀⠈⠀⠀⠀⠠⡀⡄⠀⠀⡄⠀⠜⠤
⠀⠀⠀⠘⡄⠀⠈⠀⠀⣿⠀⠀⡇⠀⠉⠀⠀⡀⡆⠀⠉⠊⠀⠸⠀⠀⠀⠀⠀⣀⣥⣤⣠⡀⠁⠀⢱⡎
⠀⢀⣀⡀⠙⠂⠂⠒⠘⠛⠂⠉⠀⠀⠀⠀⠀⢟⠿⠚⡟⠛⠛⡇⠦⠀⠀⠀⠀⢠⣉⣉⣉⡁⠀⠀⢅⡸
⠀⢠⡸⣈⡵⡆⢠⣶⡐⡎⢱⠀⢔⣉⡱⠀⠀⡘⠲⠐⠓⠒⠒⠃⠀⢰⣉⡕⠀⠸⠶⠴⠴⠇⠀⠀⡔⢢
⠀⠠⠳⣦⣄⣈⣋⣀⣉⡥⠋⠀⠀⠀⠀⠀⢼⣽⠰⣿⠠⠴⠦⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠁⠀⠀⠘⠇
⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷
⠀⠀⠀⢰⣦⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⢿⠟⠀⢠⣶
⠀⠀⠀⢸⣿⡀⢠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢉⣴⣿⣧⠀⣸⣿
⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣧⣀⣀⣀⡀⠀⠀⠀⢸⡇⣶⣶⣶⣶⡆⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣀⣀⣠⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⢸⣿⠇⣿⣿⣿⡏⢛⣿⣿⣿⣿⣦⣤⣤⣼⣇⣿⣿⣿⣿⣇⣸⣿⣀⣀⣀⣿⣿⣿⣿⣿⣄⣶⣶⣿⣿⣿⣛⠛⠉⣿⣿⣿⡇⣿⣿
⠀⠀⠀⢸⣿⠀⣿⣿⣿⡇⠙⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠀⠀⣿⣿⣿⡇⢸⣿
⠀⠀⠀⢿⠀⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇⠀⢸
⠀⠀⠀⢸⣶⣶⣾⣿⣿⣿⣏⣿⣿⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡇⠀⠀⠀⠀⢸⣿⣯⣿⣿⣿⣿⣶⣶⣿
⠀⠀⠀⠈⠉⠉⣿⡋⠉⠉⠁⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠉⠉⠉⣿⡏⠉⠉
⠀⠀⠀⣠⠞⠛⠉⠛⠛⢦⡀⣿⣿⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⣠⠞⠛⠉⠙⠛⢦⡀
⠀⠀⠘⠿⠀⠀⠀⠀⠀⠸⠿⠻⠿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠘⠿⠻⠿⠀⠀⠀⠀⠀⠸⠿








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡆⠀⠀⠙⠀⠀⢆⣰⢰⡍⠀⠀⢰⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⣶⣿⣿⡹⣏⣯⣾⣿⣿⡟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠈⠈⠒⠀⠀⡌⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⣿⠿⣿⣟⣭⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢠⠀⠀⢀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠎⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄⠀⠀⠀⠀⠀⠀⡀⠈⢈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠙⠢⠄⠀⠄⠀⡀⡀⠀⠀⠠⠁⠀⠁⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠀⢀⠠⠀⠀⢀⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠁⠀⠀⠀⢀⠖⠈⠉⠉⠙⢢
⠀⠀⠀⠀⠓⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠠⠀⠀⠀⠀⠀⡨⢤⣀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢠⡀⠀⡀⣀⠆⠀⠀⠂⢀⠀⠤⠤⠠⢤⡄⠀⠀⠀⠀⠐⡄⠈⢂⡀⠀⠀⡀⢀⡠⠚⣠⠋⠀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠣⠌⢀⠅⠨⠀⠀⠖⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠐⠀⠀⠀⠀⠠⠈⠂⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠈⠀⢀⠊⠀⠀⠄⣀⡤⡄⢠⠃⢀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡁⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠴⠁⠀⠀⢰⠃⠀⡈⠀⠀⡠⠂
⠀⠀⠀⠁⡀⠁⠂⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠈⠱⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡀⠀⠀⢠⠀⠀⢡⠀⠀⠑⡄
⠀⠀⠀⠀⠀⢀⠀⠈⠣⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠘⠃⠁⠀⠘⢣⠀⠀⢣⡀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⢼⠂⠀⠀⠱⡀⠠⠓⢄⠠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⢠⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠐⣅⣀⡠⠂⠐⠀⠀⠀⠰⠄⠈⢆⠠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠐⠢⠄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡄⣀⢔⠲⣀⡦⡀⠀⠀⠑⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢵⣔⠶⠙⠣⡀⣻⠖⠁⡈⠁⠈⠡⠼⠦⡀⠀⠱⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡢⠟⠚⠉⠀⠀⡤⠀⠹⡎⢤⠀⠀⣀⠀⠘⠀⠀⣌⠀⡸⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢀⡤⣄⢳⢾⣛⡀⠀⠹⡀⠀⣏⠀⢈⠇⣆⢀⣂⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢷⣛⣆⢻⣯⡽⣗⠂⠹⡖⡆⢈⣥⡤⣔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⣏⢘⣯⠸⠒⠛⡄⠀⠹⣉⢧⡎⢀⠆⠉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠛⠠⠤⣀⠰⣞⣡⡖⠀⠙⡇⢹⠀⠐⠋⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠰⢺⢵⡀⠹⡄⠻⣖⠀⠘⣃⠄⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢽⣛⡷⠃⠀⠈⠀⠀⣘⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠁⠀⣠⡶⣦⣦⡝⠋⢁⠜⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣲⠝⠏⣀⠠⢧⣧⢊⣁⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⠃⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡤⠐⡛⠀⠂⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢭⠃⠐⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠼⠠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣥⣐⣂⣈⡵⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠀⠀⠀⠰⠠⠐⠀⠀⠐⠀⢺⠄⠐⠀⠠⡂⠐⠀⠉⠉⠀⡀⠀⠰⡍⠕⡀⢤⡀⠀⠀⠀⢳⠂⠀⠀⠀⠣⠘⠀⠶⠀⠀⠀⠀⢀⠀⠠⢀⡀⠘
⠀⠐⡀⠀⠀⡀⠅⠀⠀⢠⠠⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡠⣌⠉⠃⠊⢀
⠀⠀⠀⠀⠐⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠐⠏⠝⢀⡄⢲⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠎⠙⠃⠀⠀⠀⠺⠆⠁
⠀⠀⠀⠀⠄⠈⠁⠀⡠⠚⢁⠤⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠎⠕⠀⠀⠀⠉⠁⠀⠀⠠⠀⠀⠀⠂⡀⠐⢠⣀⠀⠀⠀⢀⠀⠀⢀⡠⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠈⠣⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠁⠘⠀⠀⠀⣀⠀⠀⠂⠈⠙⠃⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠇⠀⠐⡔⢣⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠂⠰⠂⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠑⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠠⠀⠚⠀⣄⠀⠂⠀⢀⠀⠀⠀⠉⠀⠀⠀⡋⡜⠃⠀⠀⠂⠀⠐⠀⣤⣄⣁⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠁⠈⠀⠀⠢
⠀⠗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠃⠀⠄⠀⢀⠧⡀⡮⠸⠃⠀⠀⠀⠀⠤⡁⠉⠛⠃⠀⠒⠶⠃⠀⠀⠀⠀⠢⠲⠁⠲
⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠆⢀⠀⠐⠃⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⢼⠁⢀⠎⡁⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⡀⠀⠠⠈
⠀⣀⠀⠠⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢀⠘⠄⠄⠀⣤⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⠀⠀⠀⠂
⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠆⠀⠀⠀⠘⠀⠀⠄⠀⠀⠀⠀⠀⠚⠠⠉⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⡂⠠⠄⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⡠⠒⠀⠐⢦⡀⠀⠀⢀⠔⠂⠀⠒⢄⠀⠀⠀⢠⠔⠀⠀⠢⡄⠀⠀⠀⡠⠒⠀⠐⠢⡀⠀⠀⢀⠔⠂⠀⠒⢄
⠀⠀⠘⠀⠂⠀⠐⠂⠁⠀⠀⡎⠐⠂⠀⠒⠀⡆⠀⠀⠃⠒⠀⠀⠂⢸⠀⠀⢸⠀⠒⠀⠐⠂⢱⠀⠀⡌⠐⠋⠀⠓⠀⡃
⠀⠀⠘⢄⠢⠤⠔⣠⠂⠀⠀⠡⡀⠒⠀⠢⡠⠁⠀⠀⠣⡠⠤⠔⢁⠜⠀⠀⠘⢄⠫⠈⠩⢃⠆⠀⠀⠰⣄⠊⠉⠐⡠⠃
⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⢀⠠⠤⠤⡀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⢀⡠⠤⠤⡀⠀⠀⠀⠀⢀⠤⠤⠄⡀
⠀⠀⠰⠁⡄⠀⢠⠌⠆⠀⠀⡘⠐⡄⠀⡔⡘⡄⠀⠀⠎⢠⠀⠀⠄⢱⠀⠀⢠⠃⣄⠀⢀⠄⢂⠀⠀⡐⢡⡤⠀⢤⠌⡆
⠀⠀⠰⡀⠀⠀⠀⠀⡄⠀⠀⢃⠀⠤⠤⠄⢋⠇⠀⠀⡆⠀⠀⢀⡄⢰⠀⠀⠸⡀⢠⠐⣠⠀⡘⠀⠀⢡⠠⡤⠤⢠⢀⠇
⠀⠀⠀⠑⠢⠄⠔⠊⠀⠀⠀⠀⠑⠠⠤⠔⠁⠀⠀⠀⠈⠒⠬⠥⠒⠁⠀⠀⠀⠈⠢⠤⠄⠊⠀⠀⠀⠀⠑⠪⠩⠔⠈
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢀⠎⡁⠀⢈⠑⡄⠀⠀⠠⢊⠀⠀⢈⠢⡀⠀⠀⡔⢉⡀⢀⡉⢂⠀⠀⢀⠔⠁⠀⠀⠑⠄⠀⠀⢠⠪⡁⠀⡈⠳⡀
⠀⠀⢨⠀⠁⣀⠈⠁⠐⠀⠀⠇⠈⠁⠀⠉⠀⡇⠀⠠⣳⢀⣀⣀⡀⣞⠄⠀⢸⠀⠋⠀⠈⠀⠰⠀⠀⠆⠀⡩⠤⡉⠀⡅
⠀⠀⠈⠢⢀⣉⣀⠔⠁⠀⠀⠘⠮⣉⣉⡩⠟⠀⠀⠀⠑⢌⣂⣐⡡⠊⠀⠀⠀⠣⢉⣉⣉⠵⠁⠀⠀⠈⠢⣢⣤⡊⠔⠁

⠀⠀⠀⡠⠒⠀⠒⢤⠀⠀⠀⢀⠔⠒⠀⠒⢄⠀⠀⠀⢀⠔⠂⠐⠢⡀⠀⠀⠀⡠⠒⠀⠒⠢⡀⠀⠀⢀⡤⠒⠀⠒⢄
⠀⠀⠘⠐⠖⠀⠐⠂⠁⠀⠀⡎⣄⠃⠀⢃⣄⡆⠀⠀⠃⠘⢀⢀⣁⢸⠀⠀⢸⠀⠒⠀⠐⠂⢡⠀⠀⡌⠐⠊⠀⠓⠀⡇
⠀⠀⠘⣄⠀⠀⠄⣠⠆⠀⠀⠸⡈⠐⠒⠈⡸⠁⠀⠀⢣⡀⠘⠑⢊⡜⠀⠀⠘⢄⠑⢶⠖⢁⠆⠀⠀⠰⡈⠫⠩⠝⡠⠃
⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠉⠙⡲⠀⠀⠀⠈⢻⠋⠀⠀⠀⠰⡞⠉⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⡠⠊⠀⢀⣀⣤⠤⠼⠤⢤⣄⣀⠀⠈⠢⡀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡠⠊⣠⠴⠚⣉⡤⠤⠶⠶⠶⠦⠤⣌⡉⠳⢤⡈⠢⡀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⡏⠀⠀⠀⡠⠊⡹⠊⣡⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡉⠺⡉⠢⡀⠀⠀⠈⡇
⠀⠀⠀⠀⢳⠀⡠⠊⢀⡞⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⣆⠈⠢⡀⢰⠇
⠀⠀⠀⠀⠈⠋⠀⠀⡞⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⣆⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠁⡞⠀⠀⠀⢀⡴⠚⠲⡄⠀⠀⠀⢀⡔⠚⠲⡄⠀⠀⠀⠘⡆⢹
⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⠀⠘⠁⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢻⡀⠀⠀⠀⠀⠀⠀⣇⣠⠤⢤⣸⠃⠀⠀⠀⠀⠀⠀⣸⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢳⡀⠀⠀⠀⠀⠀⠈⠳⠤⠖⠁⠀⠀⠀⠀⠀⠀⣰⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠳⢄⡙⠲⢤⣀⡀⠀⠀⠀⠀⣀⣠⠴⠚⣁⡴⠛⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠉⠓⠦⢤⣉⣉⣉⣉⣉⣡⠤⠖⠊⠁⠀⠀⠀⠑⢄


⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢰⡂⡖⠲⣰⠐⡖⢰⡄⢰⡢⠀⠀⣖⡀⠠⡂⠐⡖⢰⡢⡴⠒⡄⣤⠂⣖
⣤⣤⣤⣤⣤⣤⣤⣤⣷⣼⣼⣤⣧⣯⣽⣴⣼⣴⣤⣧⣤⣤⣼⣤⣥⣬⣵⣵⣴⣥⣭⣦⣧⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣀⠀⠀⠀⢀⣀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠎⡀⠀⠈⢋⢲⠞⠋⠈⠉⠋⠉⠛⠁⠈⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡞⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣢⠖⢢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡉⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⢀⠆⠀⠀⠀⠀⠀⠀⠘⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣁⠀⠀⣨⠀⠀⠀⠀⠀⠠⠀⢤⡠⠞⡀⠀⡀⢀⠖⠓⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣗⠀⠐⠠⠀⠀⠀⠀⢠⣾⡶⣿⣆⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⣦⣤⡄⠀⠀⠀⠀⠀⠩⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠃⠀⠠⠀⣀⡀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠠⠘⠋⠻⠟⠁⡀⣀⠀⣄⣀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢇⠆⢀⣤⠂⠀⠀⢀⡇⠂⠀⠀⠀⠀⠀⡄⠀⢀⣀⡵⣅⣩⠴⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠓⠋⠛⠉⢷⠀⠀⠀⠀⠀⢸⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄⡴⠊⣿⡁⠀⠀⠀⠀⣿⠦⢤⡤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠐⡂⢹⡤⢄⡀⠤⣀⣿⢐⠤⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠆⢀⠀⣀⣄⠁⠐⠀⠀⣀⣀⣀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⡏⠈⠛⠦⢾⡶⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⢧⡀⠀⢀⣠⠊⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠐⠒⢴⡉⠉⠋⡇⠀⣀⢀⣿⡁⠈⠉⠡⠀⠀⠀⠳⢦⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⢀⠐⠋⠁⢀⠀⠊⠙⠞⢄⠁⠀⠁⠀⠁⠀⠀⠀⠈⠁⢀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡃⠆⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠰⢎
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠛⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠉⠑⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠛⠃⠉⠀⠀⠀⠀⠁⠀⠐⠐⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠁⠈⠉⠙⠓⠊⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⢍⠹⠿⢖⢚⠇⠠⠦⠤⠤⠤⣄⣀⣀⣖⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⡁⣠⡴⣊⣰⣄⣀⣄⣠⣤⣄⠠⠤⠴⢇⣄⠭⠭⣍⢿⣠⣅⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⡤⠤⢤⣠⣍⠒⠒⠒⠀⠉⠉⠈⠁⠀⠀⠉⠉⠲⠉⠳⡀⠀⠀⠀⢙⣇⣀⣹⡀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣈⡥⠄⠈⠀⠐⠒⠤⠼⠋⢉⡀⣀⣤⢄⣤⠀⠄⠒⠒⡀⠰⡶⣿⢺⣿⣷⠄⠿⠻⣿⠉⣽⠀⠟⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡀⡒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢸⣯⡖⢺⣿⠀⠀⣀⣣⡁⠄⠗⠛⢉⢻⢫⠀⠀⠠⡿⠀⣏⣠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⣀⡀⠚⠂⠀⠀⠀⢀⣀⢠⣘⣯⡃⠘⠛⠀⡉⠉⠀⠀⢀⠈⠅⠀⣬⢸⠀⠀⣾⣧⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠳⡄⠀⠀⠀⠈⠉⠉⠴⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⣤⠀⣏⣉⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠶⠾⠇⠀⠀⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡾⣫⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢠⢒⡒⣆⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⡀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠤⣾⣿⣿⡯⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠟⠀⠀⠀⠀⠐⠀⠀⠀⣇⠤⣼⡂⠀⠄⡤⢀⣂⣵⣾⣵⣛⡽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠈⢭⡁⠐⣒⣂⡀⠀⠠⠤⠤⠬⠭⠕⠂⢀⣡⣶⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠵⣼⣤⠴⣟⠟⣯⣿⣷⡀⠀⢀⠘⡂⣀⣸⣯⢿⡿⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣫⠵⠞⠛⠛⠋⠭⠭⠭⠬⢶⣾⣿⢟⣫⠖⠋
⠀⠀⠀⠀⠀⢀⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠞⠀⡜⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡐⠄⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⡴⠦⠴⠒⢦⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠊⠄⠀⠀⢀⣀⣀⣀⣀⣀⣤⣽⣶⡄⠀⣠⠼⠃⠀⠀⢀⡼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠏⣀⣤⠴⠒⢛⣉⣉⣩⣤⡴⠶⠶⠶⣄⣠⠇⠀⠘⡾⠁⡠⠀⣹⢀⡤⠦⡖⠋⠉⠉⠳⡄
⠀⠀⠀⠀⠀⢀⡿⠛⢩⠶⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡞⢀⠜⠃⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠊⠙⡆
⠀⠀⠀⠀⠀⠈⠛⠓⠺⣆⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠞⠀⠀⠀⠀⠀⣮⠤⠀⠀⣀⡤⠄⠀⠀⠀⠀⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⠀⠀⠀⣀⠤⠒⣉⠠⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢻⡀⠀⠀⠀⠀⠀⣠⢞⣭⡌⣇⣠⠤⠒⠉⠀⠂⠁⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠄⠀⠀⡾⣱⡿⠟⠋⠉⢀⣂⣈⣭⠥⠤⠴⠒⠒⠒⢻⡁⢀⠀⠀⠀⣄⣠⠟
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠘⣇⠐⠀⢸⢧⣶⣶⣺⣋⠉⠉⠀⠀⠀⠀⠊⠄⣤⣴⠉⠙⠉⠻⡦⠤⠖⠁
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⡄⠂⠸⣞⣛⣻⣿⠬⣷⠀⠀⠀⠀⠒⠲⠲⢦⡤⢤⡄⠀⢴⠃⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠸⣄⡠⠤⣀⡼⠁⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠄⡀⠸⡆⠀⠀⠀⠀⠀⠀⢿⣀⠤⠔⠒⠲⢄⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⢤⡈⠂
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢷⡀⢄⡀⠀⠀⣰⠋⠁⠀⢀⣀⠀⠀⠱⡄⠀⢀⣴⠋⠀⠀⢀⣤⡀⠀⠘⢆
⠀⠀⠀⡃⡇⠀⠀⠛⠛⠿⠭⣍⠁⠀⢞⢄⣀⠼⠶⢪⠃⠀⢠⠞⠛⢌⢱⡀⠀⢳⠀⣾⠁⠀⢠⠞⠉⠰⡜⡆⠀⠘⡄
⠀⠀⠀⣀⣇⣀⣀⣀⡀⠀⠀⠀⠱⡀⠀⠉⠁⠀⡀⡾⠀⠀⡞⠀⠀⠈⡆⡇⠀⢸⡇⡇⠀⠀⡎⠀⠀⠀⢡⣰⠀⠀⣇
⠀⠀⠀⠘⠂⠒⠒⠒⠩⡳⡄⠀⠀⢡⠀⡠⠤⣀⡇⣇⠀⠀⣇⠀⠀⠀⢅⡇⠀⢰⡇⡇⠀⠀⢇⠀⠀⠀⢘⡞⠀⠀⡇
⠀⠀⠀⠀⣀⣀⣀⣀⡠⠗⠁⠀⠀⡜⢸⣧⣀⡸⢃⢹⠀⠀⠘⠦⣀⣠⠞⠁⠀⡸⠇⢳⠀⠀⠈⠦⢀⣠⠜⠁⠀⣰⠃
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠉⠉⠀⠈⡀⠳⣀⠀⠀⠀⠀⠀⣀⡔⠁⠰⡈⠣⣀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⢸⠃⠒⠖⠄⠶⢒⡪⠏⠀⠀⠀⠀⠀⠀⠀⠈⠓⠨⠽⠓⠲⠞⠛⠁⠀⠀⠀⠈⠢⠌⣙⣓⣒⠲⠚⠁
⠀⠀⠀⠀⠈⠉⠉⠉⠉