Environmentally friendly Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⢱⠀⠀⠀⠄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠁⠀⠀⠐⠢⣀⠊⠀⠀⠈⠀⠘⡤⠀⠐⠠⠬⢀⠀⠈⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⠐⠂⠈⠀⢂⠀⠈⠂⠦⠀⣂⠀⠔⠀⠀⠘⠑⠰⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠈⡀⠀⠀⠀⠃⡀⠀⠴⣦⣸⠀⠀⢀⡜⢀⠀⠂⢀⠀⡠⠔⠂
⠀⠀⠀⠀⠀⢀⠘⠦⣤⣄⠀⠀⠀⠀⡀⠀⠄⠘⡺⠠⠜⠖⠈⠉⠀⠐⢂⡐⠀⢣⠌⣁⠈⠂
⠀⠀⠔⠢⢀⡠⢄⠀⠄⠊⠱⣔⠀⠁⠠⠐⠀⠁⡔⠒⠀⠁⠀⡆⠤⠀⠀⠧⡔⠁⠀⠀⢀⡡⠠⠄⠀⠄
⠀⠀⠀⠀⠑⠀⢂⠰⠒⠒⡠⡏⠀⢅⠀⡠⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠦⡚⠋⡡⠀⠈⢀⡀⠀⠀⡄
⠀⠀⠀⢀⠀⠀⠇⢀⣀⡠⠓⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⠤⠀⠔⢉⠈⠙⢂
⠀⠀⢨⠀⡰⠲⠴⠶⠘⠀⠀⠀⠔⠀⠀⠀⠒⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⠘⠀⠄⢁⣉⡉⠲⡀⠀⠀⠀⠔⠈⣈⣉⠳⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠈⠀⣿⣿⣿⡆⢰⠀⠀⠘⠀⣿⣿⣿⡇⢐⠀⠁⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠄⠀⡀⠁⠀⠙⢄⠙⠛⠛⠁⠂⠀⠐⠈⢄⠙⠛⠛⢁⠈⠈⠐⠤⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠇⢠⠀⠲⠈⡀⠀⠀⠀⠀⡈⠉⠀⠈⠀⡀⠸⠐⠀⠐⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢄⠀⡨⣅⠂⠀⠀⠀⠑⠄⠀⠀⠄⠀⠀⠀⠀⢪⡥⡀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠢⢀⡀⠀⠀⠀⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠡⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠄⠁⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢨⡀⠀⠀⠀⡠⠎⠀⠂⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠊⠀⠀⠈⠑⠄⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⢠⠀⠜⠢⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡸⢂⠂⠀⠀⠀⠀⠀⡈⠒⠐⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢾⣿⡆⠀⠀⠄⢸⣿⡆⠀⠀⠙⢉⠦⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠉⠁⠀⠀⠀⠀⠉⠁⠁⠀⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⠈⠈⠂⠤⠤⠒⠂⠈⠀⠉⠁⠚⠉⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠔⠃⠂⠄⠠⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⡀⡠⡅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡑⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⠉⠀⠈⠉⠀⠀⢨⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠡⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣱⠄⢀⠠⠄⡠⠀⢀⠤⠈⣙⢠⠴
⠀⠈⢤⠀⠠⢦⠀⠀⠨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠋⡉⡖⠁⠦⣨⠃⠉⠑⠀⠀⡰⢀⠌
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⠀⢰⠰⣰⠀⠄⡠⣀⣄⠄⠂⢠⠀⠀⡀⠀⠈⠉⠉⠁⠀⠀⠈⠀⠀⠀⠡⡉⠀⠈⠈⠁⠐⠒⠊⠁⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠘⠠⠙⠀⠄⠓⠙⠇⠄⠂⠈⠀⠀⡇⠀⠀⠀⠲⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠤⡀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡈⠉⠁⠀⠃⠀⠀⠁⠀⠀⠠⠀⠰⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⢠⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢄⠀⠀⠂⠀⠀⠀⠆⠀⠀⠐⠀⠐⠀⠀⢀⠂⠀⣤⣚⣃⣀⣰⠀⠀⢠⣒⣃⣀⠴⠂⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢄⣤⡤⣤⣤⣤⣌⣀⠀⠀⡾⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣡⣿⢏⣴⣎⢿⣿⣿⣿⣿⣶⣄⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⣼⣿⣏⢾⣿⣿⢎⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⡻⠿⣿⡟⣼⣿⢿⣿⣮⡛⣫⣾⣿⢿⣿⣿⣿⡿⣿⣿⣷⡀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡖⣤⣭⣍⢰⣮⣙⠇⢟⣩⣶⣞⣿⣶⣦⣾⣿⣿⣿⣿⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢣⣿⣿⣿⡸⣿⣿⡇⣾⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣶⣭⡆⣮⣵⣾⣿⣿⣿⣿⣟⡛⢛⣽⣿⣿⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⢰⣶⣶⣶⣶⣶⣶⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⢛⣡⣌⡛⢟⣫⣬⣛⠿⣛⣥⣝⡛
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⢿⣿⠿⠿⠿⠿⠇⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣛⣭⣥⡔⣶⣾⣿⣿⣿⡇⣩⣴⣭⣛⣩⣶⣝⣛⣭⣦⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣜⢿⣿⣿⣿⡇⣿⣿⢿⣿⣿⡿⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡻⣿⣿⡇⣭⣵⣶⣭⣭⣴⡦⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠊⠻⠇⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢂⠀⠀⠐⠁⢠⠀⠲⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣠⠀⠀⠀⠀⠀⢀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⡀⠀⠀⠀⠗⠀⠀⠀⡈⠀⠀⢀⠀⠀⣀⠀⠀⠄⠀⣀⣀⠉⠆⠓⠀⢈⠀⡀⠀⠰⠄⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢁⠀⠀⠀⠈⠀⠄⢠⣄⡀⠠⠊⠀⢀⠤⠂⠁⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠂⠄⡀⠈⢣⠊⠀⡠⠁⢃⠀⠀⠀⠔⠁⠀⠀⠆⢀
⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠈⠆⠊⠐⢄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠂⠀⠀⠀⠀⠈⡦⠆⠀⠰⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠠⡀⠀⠀⣠⠀⠔⠁⠀⠀⠀⠑⠄⢁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⣀⠀⢀⠔⠀⠈⠢⠀⠀⠀⠀⠀⡀⠔⠓⢄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠠⡀⠀⠇⠀⠀⠀⠀⢢⠃⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠔⠃⠀⠈⠀⠁⠀⠀⠀⠀⢀⠀⠀⠱⡀⠀⡴⠈⠤⠀⠀⢀
⠀⠀⠀⠀⡀⡀⠀⣀⠀⠤⠀⠆⠐⠀⢄⠀⠀⠂⠀⠀⣀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠠⠋
⠀⠀⠀⠀⠄⠸⠄⠡⡄⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠈⡀⣀⣀⠀⠀⠐⠁⠀⠐⠂
⠀⠀⠀⢀⠤⢤⠐⠀⠈⠀⢄⠀⠀⠀⠀⠀⣨⠐⢄⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠈⢂⠀⡗⠀⠄⢀⠊⠀⠈⢂⡀⡀
⠀⠀⠀⠘⠤⠔⠀⠀⠠⠀⢀⡈⠅⡀⢈⠠⠸⠀⠀⠁⠀⠀⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠄⠘⠀⠀⡐⠊⠉⠀⡠⠀⠀⠀⠀⠃
⠀⠀⠀⡰⢢⠀⠀⠂⠀⠀⠀⠀⠀⠈⠅⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠨⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠘⠁⠈⠀⠂⠀⠐⠉⢑⠀⠘⠄⢀⢀⠐⡀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣤⡀⠹⡃⠀⢈⡁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠲⣄⠀⠈⠄⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠉⠓⠊⡓⠀⠀⠀⣐⠗⠉⠘⠃⠀⠉⠛⠋⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠐⠀⠊⠀⠀⠄⠀⠀⠈⢶⠒⠨⡄⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢠⡋⠐⢱⠞⠁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠑⢄⠀⠁⠂⠄⠀⠀⠀⠀⠀⠀⢀⠔⠚⠁⢀⠠⠊⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠂⠐⠒⡒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡆⠀⠘⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠒⠂⠉⠉⠉⠉⠉⠈⡱⠒⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⣤⡠⢱⠀⠄⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⠉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⡀⠀⠀⡠⠊⠀⠀⠀⠘⡄⣇⠄⠜⠀⠀⠀⢚⠂⣌⠑⡄⠀⠀⢀⡔⠉⠢⠻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡎⣀⠤⢄⠀⠀⠀⠈⠒⠄⡠⢪⠇⠀⠀⠉⠁⠀⠈⠆⠀⢸⠀⡠⠐⠑⠳⣜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠘⢌⠈⢚⡀⣠⣴⣆⡀⠈⡕⠛⠂⠀⠀⠀⠀⠀⠀⠒⠒⠁⠈⠆⢸⢈⣐⠳⠹⣦
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⢫⣛⠉⠸⣇⡀⢰⠚⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠢⠘⠫⠀⢢⠘⠨⣄⢥
⠙⡉⠒⠠⢀⡀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠡⡃⠁⠀⠈⠑⢷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⢄⡀⠀⠀⢀⢀⠇⠀⠈⠉
⠀⠰⡀⠀⠀⠈⠑⠠⣀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠱⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⡀⠀⠐⠁
⠀⠀⢃⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⡆⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠘⠀⠀⠀⠢⡀⠀⠀⠀⠈⠢⣠⠇⠀⠀⠀⠀⠀⡄⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠰⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣀
⠀⠀⠀⠆⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢄⠀⠇⠀⣠⣀⢤
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡑⠒⠂⠁⠀⠀⠀⠀⠀⢀⠤⠤⠠⠔⠉⠉⠀⠀⠱⡤⣔⠭⠤⠎⣀⠜⠘⢁⠂
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠈⢣⡀⠀⠀⢀⠴⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⢀⡹⢶⡈⠉⠢⡙⢦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠉⠓⢦⣌⡂⢝⢦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢷⣤⡀⠀⠀⠈⠆⠀⢀⠃⠀⠀⢀⡀⠤⠒⠁
⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣶⣶⣾⣶⣾⣶⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠉⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠒⠲⠄⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠚⠓⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡋⠛⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠛⣋⠾⠃⠀⣿⡟⠛⠉⠀⠀⠀⢀⣰⡾⢿⣿⣷⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⢶⣠⣬⣥⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠛⠈⠁⠀⠀⠀⠀⠀⠀⢠⣼⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣤⣤⡁⠉⠉⢙⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣯⣝⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠻⢧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⠛⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠁⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠈⠛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠊⠉



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⠀⠀⠀⠐⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣀⣀⣀⣸⡁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠛⠻⣯⡁⠀⠀⠀⠈⠀⠉⠓⢦⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠈⢟⢆⠀⠀⠀⢀⡀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣀⠀⠀⠀⠀⡸⠈⡆⠀⠀⡎⠛⡂⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠈⠀⠀⠀⠀⢀⡜⠀⠀⠘⣆⢀⠃⠀⠡⠀⠀⠀⠈⠗⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⣁⣼⡅⠀⠙⠀⠀⠀⠘⢾⠀⠀⠄⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⡄⠀⠉⠟⠒⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠲⢖⠚⠛⠉⠉⠉⠉⣇⠸⠂⠴⠐⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢆
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠀⢰⠁⠀⠀⢀⠂⠀⠀⠀⢠⠎⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠄⠆⠈⠀⠄⠈⠀⠀⠀⠀⠘⢆⠀⠀⠀⠈⢀⣼⠆
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⢀⢿⠀⡀⠠⡀⠀⠈⢦⡀⠀⠀⠘⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⢎⠔⠒⠒⠂⠒⠒⠀⣦⠡⠀⠄⠀⠀⡴⠃⠘⠤⠤⠤⠴⠤⠤⠤⠥⠝⠛⠓⢀⠆⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣎⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠂⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢽⢆⠀⠀⠠⠀⡀⠀⠀⡄⠀⠀⠀⠈⢧⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⡴⢯⡖⠀⠀⠀⠀⠀⢀⢍⡶⠰⠢⣀
⠀⠀⠀⠀⡀⠀⠀⠀⠚⠁⠂⠀⠙⠂⠀⠂⠁⠀⠀⠀⢰⡄⠀⠀⠀⠙⢄⢠⡧⠤⠤⠤⢴⠖⠚⣉⣴⡡⠽⣿⡀⠀⠀⠔⡰⣡⣧⣰⣆⠨⢳
⣈⠁⠀⢤⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣦⣦⠀⠈⠢⣀⠀⠀⠀⢻⠇⠀⠀⠀⢳⠀⣺⢿⠿⡿⣾⣳⢠⡘⠀⠘⢏⠛⣯⣿⣷⠒⣸
⠉⠒⠂⠈⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠑⠦⢬⠤⠔⠊⠀⠀⠓⠀⠀⠈⠣⢤⣉⣤⠴⠃
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠂⠈⠉⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠊⠁⠉⠀⠤⠀⠄⡀
⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡜⠀⢀⡀⠀⠐⠀⠀⣀⠀⠀⠎⠀⠀⠤⠠⠓⠄⠀⢄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⣄⠂⠙⠉⣴⣷⠀⠄⢠⣁⠐⠈⡒⣖⣆⠀⢨⠴⣒⡁⠠⠀⠀⢀⣄⠙⠊⠀⣀⡀⠀⢈
⠀⠀⠀⠀⡄⠀⠀⢏⡀⠀⠀⢸⣿⠂⠀⠁⠈⡹⠀⡇⠡⠈⡆⣀⣠⠂⢹⠀⠀⠙⠿⡿⠀⠀⠀⠘⢿⡇⠀⠀⢀⠄⠓⠁
⠀⠀⢀⡀⣀⠀⠀⠀⠁⣀⠀⠉⠁⠀⠀⢀⠔⠁⠐⠁⠈⠈⠀⠀⠀⠈⠈⠡⠀⠀⠡⡄⠀⠀⠀⠂⠀⠀⠀⢀⠄⠀⠀⢀⢀⡀
⠀⠀⡏⠈⡙⠑⠒⠒⠋⠉⠀⠀⠒⠐⠘⢅⠀⠀⡇⠀⠀⠀⠂⠀⠠⠀⠀⠠⠀⠀⠀⠈⢰⠤⡤⢠⠤⠄⠖⠅⠀⣀⠠⠈⣁⣹⠂
⠀⠀⠀⠀⠀⠂⠠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠁⠢⢥⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠔⠈⠐⠀⠀⠀⠀⠀⢠⠀⠀⢨⠔
⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠁⠂⠄⠠⡓⢄⡀⠀⠀⣀⡀⠴⡥⠂⠀⠚⣀⡄⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠑⢠⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢑⠀⡀⠄⡀⢠⠀⠀⡅⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢀⠀⠒⠲⠃⠘⠄⠠⢀⡄⠀⠀⡖⠊⠈⢎⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⢸⠀⠀⠀⠀⡔⠒⠢⠀⠀⠀⣄⢅⣀⠀⡔⠐⠈⣦⢀⡀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠠⠀⠀⢀⠃⢸⠀⠀⠀⠀⠀⠠⠊⠘⠃⡀⠀⠡⡠⠄⠀⢊⠠⠍⠠⠂⠘⠀⠀⠀⠀⠈⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠆⠄⣠⠂⠀⢸⠀⠀⣄⠀⡠⠄⠴⠆⠀⡷⡀⠀⠇⢀⠴⠁⣃⠀⢀⠀⢀⠀⠀⠈⠀⠀⠈⡄⠀⢄
⠀⠀⠀⠀⠈⠓⠦⠤⠴⠀⠘⠦⠤⠤⠴⠈⠐⠀⠐⠓⠁⠈⠀⠁⠀⠀⠒⠃⠐⠀⠲⠭⠤⠬⠇⠀⠐⠦⠤⠔⠚

⠀⠀⠀⠀⣀⣀⢀⣴⡆⠀⠀⠀⠀⠀⢤⣾⠿⢿⣤⠀⠀⠀⠀⠀⠰⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡖⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⢀⣾⡯⠁⠨⣛⡁⠀⠀⠀⠀⠀⠸⣷⣤⣼⠷⠀⠀⠀⠀⠀⠀⢻⣿⣿⣲⣾⠟⠀⠀⠀⠀⢀⣤⣬⣃⢿⣿⣇⡀⠀⠀⠀⠀⢹⣿⣿⣿⣤⡄
⠀⠀⠸⡔⢦⡄⠘⣻⠃⠀⠀⠀⠀⠀⠀⣈⣹⣉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣃⣉⡀⠀⠀⠀⠀⠘⠻⢿⣿⡏⠙⠛⠁⠀⠀⠀⠀⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠈⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢀⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠐⣿⠢⠟⠁⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣦⠀⠠⡄⠀⠀⠀⠀⠀⢠⡙⡴⠒⡲⣔⢡⠀⠀⠀⠀⢸⠷⠶⠾⠆⠶⢿⡄
⠀⠀⢰⣤⠐⣿⡃⠀⠀⠀⠀⠀⠀⢤⠸⣆⣿⣤⡞⢀⠀⠀⠀⡞⠁⠘⣀⣄⠀⠛⠄⠙⡄⠀⠀⢒⡸⡅⠀⠘⣸⢐⠂⠀⠀⠀⢸⣛⣛⣛⣓⣛⣛⡇
⠀⠀⠀⠙⢃⣿⡇⠀⠀⠀⠀⠀⠀⠸⡷⢿⡿⠿⠧⡟⠀⠀⠀⠙⠦⠔⠁⠁⠀⠑⠤⠞⠁⠀⠀⠀⠔⣩⢓⠛⡑⠆⠀⠀⠀⠀⠀⠉⢩⣽⣯⡍⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⣆⡼⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⣼⡋⠛⠛⣴⠂⠀⠀⠀⠀⠀⠀⡿⠿⣿⡃⠀⠀⠀⠀⠀⢈⢱⡃⣴⡀⣳⣉⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢠⣦⣦
⠀⠀⠘⠀⡧⠶⠴⣏⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⠀⠀⠀⠀⠀⠀⠀⠔⢳⡙⣱⠓⠄⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⢸⡉⠁⠈⣻⠃
⠀⠀⠀⢸⡇⠀⢸⡟⠆⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠴⠋⠀⠀⠀⠀⠀⠀⠀⠓⠶⠖⠃

⠀⠀⢀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢸⠥⠶⠌⣇⠙⣷⠀⠀⠀⠀⠀⢮⡹⣄⡜⣡⠂⠀⠀⠀⠀⠀⡤⢼⠤⢼⠤⡄⠀⠀⠀⠀⠀⢐⣾⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣷⠂
⠀⠀⢸⣷⣶⢶⣿⠀⢸⠀⠀⠀⠀⠀⢰⠙⣦⡊⢱⠀⠀⠀⠀⠀⠀⡇⠈⢀⣬⠀⡇⠀⠀⠀⠀⠀⢸⡟⢤⠜⢿⠀⠀⠀⠀⠀⢸⣿⣧⠀⢀⣀⠑⡀
⠀⠀⣸⣿⣤⣾⣟⠢⠜⠀⠀⠀⠀⠀⡨⢎⣀⣙⢮⡀⠀⠀⠀⠀⠀⣇⠀⠛⠋⢀⡇⠀⠀⠀⠀⠀⠸⣷⣶⣶⡿⠀⠀⠀⠀⠀⠘⠟⠀⠀⢿⣿⠟⠁
⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢦⣄⣉⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣌⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢺⣿⣿⣿⣿⠉⣹⣿⣿⣿⣿⣿⣍⠲⢄⠀⠀⠀⠀⠀⠹⣷⣄⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣴⣾⣿⣿⣡⣶⣿⣿⣿⡏⣬⠋⠀⠀⠀⠑⣄⠀⠀⠀⠀⠈⢿⣦⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠸⠋⠈⣿⣿⣿⣿⣿⣿⣿⣷⠾⠇⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢻⣧⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣄⠀⣶⡤⠀⠀⠈⢇⠀⠀⠀⠀⠀⢿⡆⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢹⡇⣠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠾⠿⣿⣿⣷⡆⠀⣀⠀⡾⠙⣆⠀⠀⠀⠘⣿⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠁⠀⠸⣆⠉⣿⡇⠀⡟⡆⠀⠀⠀⣿⡀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡿⠀⢠⣧⠇⠀⠀⠀⢸⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠘⣿⡿⠈⠉⠻⣿⣿⣿⣿⣿⣿⣄⡀⣀⣀⠀⠀⠀⠀⢀⣾⠇⠀⢸⡟⠀⠀⠀⠀⢸⠀⣿⣿⡇
⠀⠀⠈⠣⡀⠉⠉⠉⠒⠢⢤⡀⠀⠀⠀⠸⣿⠀⠀⢹⣿⡄⠀⠀⠘⠻⢿⠏⠘⣿⡏⠹⣿⣿⣇⠀⠀⠀⣾⡏⠀⠀⣼⠃⠀⠀⠀⠀⡞⢸⣿⣿
⠀⠀⠀⠀⢱⠀⠀⠀⠀⢄⠀⠈⠢⡀⠀⠀⠙⡆⠀⠀⢿⣿⣦⠀⠀⠀⣸⠀⢠⣿⡇⠀⢿⣿⡏⠀⢀⣼⡿⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⣄⠀⠱⡀⠀⠀⢻⡀⠀⠀⠉⠛⠣⣄⡼⠋⠀⢸⣿⡇⠀⠘⢿⣧⠴⠛⠉⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠘⢧⡀⡧⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠘⢷⡇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢰⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣠⠤⠚⢿⣦⡀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⣠⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇⠀⢠⡇⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⡇⠀⠀⠀⠀⠀⡇⠀⢸⠃⠀⠀⠀⠀⣸⣧⣴⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣶⣤⣷⣤⣾⣶⣶⣶⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠈⠑⢦⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⡆⠀⢀⡠⠼⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠤⠊⠈⠁⠉⠦⣀⣠⠰⢅⡴⠁⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢠⣤⣤⢊⠀⠀⠀⠀⠀⡠⠂⣱⣦⡸⣙⠻⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⣄⣀⠞⠔⠁⣰⣿⣆⠀⣀⠀⡀⠀⢿⣿⢿⠇⠈⠀⠀⠲⣀⡰⢂⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣰⡉⠑⠀⠀⢆⠀⠻⣿⠏⠀⠠⠇⠈⠒⠒⠉⢸⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣇⠀⠀⡈⠭⡀⠀⠐⠂⠊⠀⠁⠀⡼⠃⠀⠀⠀⠀⣰⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠂⠀⠀⠀⠀⢀⣀⣴⣊⣀⣀⣀⣀⠤⠒⠁⢻⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠒⠲⢈⡩⠝⠀⠀⠀⠀⠀⠈⡇⢀⡠⠖⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣹⠁⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⠉⠊⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠁⢀⣣⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⡼⠉⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡰⡇⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡰⠁⠰⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠁⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠤⠤⣴⠁⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣍⣉⡦⠀⠀⠀⣏⣭⣭⣭⣍⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⣀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⠀⠀⡒⠁⠀⠀⠀⠢⠼⢆⠀⢠⠎⠀⠀⠀⠀⠣⣀⣬⠇⣀⠀⠀⣴⢉⣀⣉⠀⠈⠉⠈⠉⠉⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣀⡠⠜⢢⠀⠀⠀⢠⡀⢀⠀⠑⢮⡀⠀⠀⠀⡄⠀⠀⠀⣰⢇⡉⣲⠀⠀⠀⠀⠉⠑⢄⡀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢑⡆⠀⢺⠉⠀⠀⠀⢀⢣⡀⠀⠀⠙⠒⠷⠤⢄⣡⣀⡰⠟⠀⠀⠀⡰⠁⠁⢀⡇⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠀⠀⠸⠄⠀⠀⠈⠀⠀⠳⡀⠀⠀⢀⣠⣤⣀⣹⡤⠤⠄⠀⠀⡰⠁⠀⠀⠸⠀⢠⠃⠀⡇⣀⣴⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢆⡠⡞⠉⠧⣺⢸⢀⣠⣉⠦⠚⡅⢠⠆⢀⠃⠀⡷⠀⣠⠏⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠽⠶⢤⣬⣀⡄⠀⠀⡇⠀⠀⣀⡠⠤⠒⠊⠉⣙⠟⠢⠔⢹⠛⠁⠀⠀⠀⠀⠈⠛⣄⡌⠀⠈⢱⠾⢥⣀⡀⠘⠀⠉
⠀⠀⠀⣠⠤⣄⠀⠀⢀⠀⠀⠀⢀⡤⠜⠻⣄⢰⠓⠂⠉⣀⣠⠤⠒⠊⠉⣠⠤⠤⠤⠚⠓⠒⠢⣄⣀⣀⠀⠀⢸⣁⠀⡔⠁⠀⠀⠃⠈⠉⠉⣀⡀⢀⣠⣀
⠀⠀⠘⠢⠴⠚⡰⠒⠁⠉⣧⠀⣁⡀⠀⢀⣸⡞⠒⣈⠥⠤⠉⠢⠀⠀⠀⠑⠤⣄⠀⠀⠀⠀⡰⠀⠀⠀⠈⠉⠉⠀⠙⣄⡠⣤⠀⠀⠀⣖⠉⠀⠈⠁⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠈⠛⠒⠉⣡⠚⡁⠈⠋⡥⠦⡧⠀⠑⡄⠀⢀⠔⠀⠀⠀⠀⠀⠀⠳⠀⠀⡜⠁⠀⠀⠀⠀⠀⠘⠻⢍⠋⠁⣨⠶⠀⠀⠸⣀⣀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⡱⠈⠀⢀⡷⠶⠃⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡇⠀⠀⠀⣀⡀⠀⠀⣠⠞⢉⡭⠧⠷⡄⠀⠀⠀⠀⠉⠊⠁⠈⠁
⠀⠀⠀⠀⡤⠴⠋⠉⢂⢱⡁⡴⠲⡶⠋⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠙⠢⠔⠊⠀⠀⠉⠉⠀⠀⡌⠀⠀⠀⠘⣄
⠀⠀⠀⠀⡧⠀⢀⠍⠾⠄⠟⡷⠚⠁⠀⠀⠀⠀⡔⠋⠀⠀⠀⡈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⡄
⠀⠀⠀⠈⠣⡼⠁⠀⠀⠀⢠⠃⠀⠀⢀⣠⠄⡼⠀⢠⣠⠞⠒⠋⠒⠣⣴⠀⠀⠀⠀⠀⠀⢠⡤⠚⠒⠛⠒⠦⣤⠀⢀⠔⠃⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢠⠋⠀⠀⠀⠀⡜⠁⣠⣴⣶⣶⣄⠀⠳⠀⠀⠀⠀⢠⠊⠀⣠⣶⣶⣦⡄⠈⢆⠘⢦⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣄⠀⠸⡀⠀⠀⠀⠰⠀⠀⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣿⠀⢸⠀⠀⠈⠙⠢⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠈⠢⣀⠈⠒⠂⠒⠚⢇⠀⠹⢿⣿⣿⠟⠁⣠⢁⡤⠒⢄⠘⡄⠈⠻⣿⣿⡿⠏⠀⡜⠉⠒⢤⡀⢀⡅⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠢⡀⠈⡆⠀⠀⢀⣀⠈⠳⢄⣀⠀⣀⡠⠞⠁⠈⠀⠀⠀⠀⠘⣦⢄⡀⠀⣀⠤⠊⠀⢀⣀⡀⠈⠉⠀⣠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠒⠧⠤⠔⠉⠮⠤⢠⡄⠀⠛⢄⣀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢠⡤⠤⠗⠉⠓⠒⠋⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠤⣄⢀⡀⠀⠀⢀⣛⢃⡄⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣍⣛⡀⠀⠀⡠⠔⠒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⢦⡀⣆⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠰⠯⢐⣇⠜⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠢⢄⣀⣀⠠⢄⠀⠀⠀⠁⠀⠀⡰⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣘⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣀⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠒⠂⠠⠄⠀⠐⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⣴⣿⣿⠟⣩⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⣿⣷⡄⠀⠀⣾⣿⠟⣡⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⢿⣿⣿⣿⡄⢸⠟⢡⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣎⠻⣿⣿⣧⠈⣰⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡘⢿⡏⣸⠁⠀⠀⠀⠀⣠⠤⠄⢀⡤⠶⠶⢀⣤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠃⠀⠀⠀⠀⠀⣿⠦⠆⢸⠁⠀⠀⢸⡇⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠿⠤⠤⠘⠷⢤⠴⠈⠳⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣠⣄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⣀⠀⣠⠐⢰⠀⡠⠒⢦⢰⡄⠒⡄⢠⠖⠲⡇⢸⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⠀⢸⠀⢯⣉⡁⠸⠇⠀⡇⠸⣀⡠⠄⢠⠀⠹⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⣋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣠⣶⣿⣷⣾⣿⣷⣾⣿⣿⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⠀⠉⠈⠉⢿⠁⣾⣿⣿⣿⣿⣿⠟⢿⣿⡿⣿⣿⣿⣿⣿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣿⣿⣿⡿⠋⠀⠀⠀⠈⠁⠈⠋⠈⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢨⢭⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡀⡀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡼⠲⡌⠃⠀⠀⠀⣠⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣲⡏⠁⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢄⢴⣔⡀
⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠣⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠐⠨⢀⠀⢀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⠁⠈⠘⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠐⠄⠀⢁⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⢁⠀⠁⠀⠀⠢⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠐⠢⢀⠅⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⢁⠘⠑⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⢁⡰⠓⢄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠈⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠐⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢤⡀⠀⢀⣠⡤⠤⠤⠶⠦⠤⠤⣤⣀⠀⠀⣠⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⢹⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠞⠁⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡞⠀⠀⡇⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⡰⠉⢳⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠰⡆⠀⠀⠀⠀⠉⣻⠋⠁⠀⠀⠀⠀⣶⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠱⢤⣀⣀⣠⠴⠋⠳⢄⣀⣀⣀⣠⠏⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣤⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⠤⣤⣤⢬⡓⠦⢤⣀⣀⠀⠀⠀⠀⣀⣀⡤⠔⠋⠑⠀⣾⡄⠛⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⣤⣄⠸⣿⠁⠉⠉⠐⠃⣶⣶⠈⠋⢩⣽⡍⢁⡌⠀⣾⣻⡆⠀⣾⡇⣴⢲⣄⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⡏⠙⢿⡀⣿⠀⠀⠀⠀⠀⣿⣿⠀⣰⡿⠛⠁⢸⣧⠀⣿⣿⣧⠀⣿⡇⡿⡟⣻⣇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⡁⢀⣼⠁⣯⣤⣤⡤⠀⠀⢿⣿⣴⣿⠃⢤⠄⢸⣿⠀⣿⠀⢿⡀⣿⡇⣿⡇⠀⢹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣏⣿⣿⣷⡀⣿⡇⠈⠁⠠⠄⣹⣏⣿⡇⢀⠀⠀⢸⣼⠀⣿⡄⢸⡇⣿⡇⢙⡃⠁⢨⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠐⣿⡋⠉⢻⣇⣿⡅⠀⢰⠄⠀⢨⣿⠙⣧⠀⠀⠀⠸⣿⠀⡿⡇⢸⡇⢸⡇⣿⠇⠀⢠⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⡇⠀⣸⡏⣿⣇⠀⠀⠀⠤⢸⣿⠀⢩⣧⡀⣀⠘⣿⠂⣿⡇⠀⣿⣿⠃⣿⡇⠠⢸⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠂⠘⠿⠾⠋⢠⠘⠛⠟⠛⠛⢀⠸⠟⠀⠀⠙⠿⠃⠀⠹⠃⠻⠁⠁⠘⠟⠀⠳⠶⠶⠟⠁⠖⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢋⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢸⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣷⠤⠖⠳⠤⢤⡴⢦⣄⠀⠀⢠⠏⠘⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠖⡻⠃⠀⠀⠀⠀⠀⠈⠀⠈⠙⢶⠋⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢠⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⣜⣀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠔⠋⠁⠑⠂⠀⠀⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡰⠛⢦⠀⠈⡍⢀⡤⠒⠢⠖⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠲⣶⢾⠃⠰⠃⠀⠸⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠇⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢤⣀⠀⠀⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠠⠤⣀⣀⣀⣀⣠⡀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠤⠔⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⢟⠶⣄⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠐⣺⠏⢠⡞⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠚⢷⡦⠽⠷⠶⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠴⠒⠒⠋⠁⠀⢸⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣤⣇⣀⣀⣀⡀⠀⠀⠉⠉⠙⠛⠓⠒⠒⠂⠈⠉⠳⣄⠀⠀⠀⠀⠀⢸⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠃⠀⢀⡟⠀⠀⢀⡞⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣀⣠⡴⠋⠀⠀⣠⣟⠀⠀⠀⢰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⣠⠞⠁⠈⢧⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠞⠁⠀⢀⣀⣤⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢰⡶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⣠⡶⠶⣶⡾⠿⣶⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⡀
⠀⣿⠠⠷⢾⡀⠟⣻⡘⢃⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠐⢇⠶⠇⠄⠄⠒⠔⠄⠶⡀⠀⢠⠂⠀⠀⡀⠀⡀⠀⠀⣀
⠀⠈⠛⠚⠋⠛⠛⠛⠛⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠄⠀⠤⠤⠀⠀⠀⡠⠄⠊⠀⢀⠎⠠⠀⡇⣰⠀⠈⢂
⠀⠀⢀⡀⠀⠀⠀⠀⡀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⢹⣐⣠⠉⠑⠢
⠀⢀⢺⠇⡀⠀⠀⡄⠈⠖⠒⠂⢁⠀⠀⠀⠀⠀⠠⣀⡤⣤⢀⡤⡀⢀⠤⣤⠀⠔⡀⡜⠀⠀⠀⣤⡄⠀⠈⠀⢄⠀⠀⡈⠀⠀⢀⠀⠈
⠀⡇⢸⠁⢰⠀⢂⠠⠑⠀⠀⠀⠂⠃⠁⠤⠀⠀⠀⠸⣏⣡⢾⣀⣠⢿⣀⡸⠂⠛⠚⠁⠠⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⠁⠀⠐⠁
⠀⠁⢼⠀⠈⠀⡀⠀⠂⠀⠀⠤⢀⠄⠑⠀⠀⠀⠀⠀⢀⠀⠀⢈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠘⢒⠨⡤⢄⡐⠂⠀⠁⠀⣾⠀⠒⠚⢀⠀⣠⣙⡆⡠⠀⡈⠢⡀⠀⡀⠀⠐⠤⢀⡤⠤⠊⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠤⡀⣿⠀⠂⠀⠀⠘⠀⠀⠀⡇⠀⠈⠆⡇⠀⠉⠀⠀⠀⢀⠀⢀⠀⠀⠈⠉⠉⠉⠁
⡔⢘⡠⠰⠀⠀⢰⡁⠈⠀⠑⠄⠀⠰⠁⠀⠈⠻⠤⠤⠄⠘⠦⣀⡠⠀⢣⣄⣈⡠⠃⠀⠀⢀⠤⠂⠀⠀⠀⢱⠀⠀⠀⠀⠀⢘⠀⠀⣀
⠈⠁⠐⠈⣀⣀⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠈⠈⡆⠀⠀⠀⠻⠃
⠀⠀⢴⣿⡀⢀⠀⡤⢽⣷⣄⠀⠀⠀⠀⠀⢪⢀⡤⠀⢰⣝⢆⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⢀⠠⠁⠄⠀⠀⠁
⢀⢿⣦⠙⠁⠉⣰⣾⣿⣿⣿⣧⠀⠀⠀⡄⠀⠠⠑⣀⠻⡌⠈⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠢⡀⡄⢰⡁⠄
⢸⣤⣾⡗⠀⠀⢈⣴⣶⣄⠿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠘⡟⠙⢁⠀⠀⠸⠿⢿⣿⡟⡼⠀⠀⠈⢱⠀⢀⠀⠀⢠⠊⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣾⠿⣿⠇
⠀⠹⢿⣿⣷⠄⠀⠀⠀⢿⠑⠁⠀⠀⠀⠀⠁⠀⠆⠀⠈⠀⠀⠈⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣃⣀⣀⣀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠴⠦⠤⠄⢀⠀⠀⠀⠀⢀⡀⠀⠀⢠⡀⠀⠀⠀⣠⣤⣀⣥⣤⣄⠀⠀⠀⠀⢅⠋⠂⠁
⠀⠰⢁⠀⢄⠀⢀⢀⡀⠀⠀⠃⠀⢃⠈⠉⠀⠀⠀⠀⠈⠀⠀⡠⠖⠉⠁⠀⠀⠈⡇⠀⠀⢸⡏⠶⢸⡇⠈⣿⠂⠀⠀⠀⠀⠈
⠀⠘⠀⠊⢀⠐⠃⠂⠀⠈⠀⠀⠀⠀⠀⠰⠀⠀⠳⠀⠀⠀⠘⠃⠀⠁⢀⠄⠀⣤⠁⠀⠀⠈⠛⢿⡿⢫⢽⡟⢻⣷⡀⠀⠀⠹⠆⠀⠄
⠀⠀⠀⠀⢀⠔⠒⠆⠤⣀⠀⠀⠀⠀⠀⠀⠐⠂⠁⢀⠀⠀⠢⠀⢀⡔⠉⢉⣴⠋⠨⠀⠀⠀⣤⢾⠿⡦⣴⠶⣦⡿
⠀⠀⠀⢀⡦⠴⠒⠚⡩⠉⠀⠀⠀⣠⢈⢀⠀⡀⡀⠉⢠⠀⠀⠀⡌⣀⠴⠋⠁⠀⠂⠀⠀⠐⣿⣠⣀⣇⣿⣚⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠶⠓⠒⠒⠊⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠃⡀⡄⠀⠀⠀⠀⠀⠈⠓⠒⢦⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠀⠈⠀⢄⠃⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠁⢠⠡⠙⢆⠀⠀⠘⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠗⠀⠀⠀⠀⠹⡖⠼⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠀⠓⠒⡤⠂⠈⠀⠀⠹⢶⠼⡦⡴⠀⠀⠠⢂⠆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⢰⡀⣠⢀⠀⢤⠀⣠⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡰⣂⣽⢦⡀⠀⣡⣶⡄⡀⢀⣠⣌⠀⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⣃⣠⡈⠉⠁⠀⡐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡁⠀⠂⠂⣀⠙⠋⠙⣀⠈⠛⠋⠀⠠⠃⢦⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⡁⠀⢀⢀⡄⠈⢀⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢠⠂⠀⠈⢻⣷⣠⠀⠀⢀⡀⠀⠀⡄⠐⡌⢢⡃
⠀⠀⠀⠀⠀⠀⠘⠀⢀⢤⣳⠥⠬⠦⠥⠴⣫⢖⡄⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⢄⡣⡧⠬⠴⠌⣴⡥⣶⡀⠀⡸⠁⠀⠈
⠀⠀⠀⡀⠀⠀⠀⢀⠮⣗⠯⠭⠭⠭⠭⠽⠉⡷⢖⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠫⡳⢻⠭⠭⢽⣿⣿⡟⢔⡻⠄⠈
⠀⠀⠀⠀⠆⠀⠀⠶⡽⠃⣏⣉⣉⣋⣉⣙⠛⢭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠳⠝⠀⣬⣭⣭⣭⣭⣭⣇⠈⢪⠽
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⠉⢉⣩⢉⣤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⠀⠓⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡄⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠰⠟⠀⠨⠅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠰⠠⠳⠜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠅⠽⠈⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡰⣰⠃⠀⠳⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢀⠠⣔⠤⠂⠐
⠀⠀⠀⠀⠀⠚⠁⠖⠀⠀⠀⠀⠙⠄⠈⢨⠆⡤⠶⠄⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠈⠉⠀⠀⠠⠄⠀⢠⠀⡀
⠀⠀⠠⣀⠀⠀⠀⢀⣿⡆⠀⠀⣰⡆⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⢉⠀⠀⠀⠀⣴⡐⠀⠀⠳⡽⣦
⠀⠀⠀⠈⡁⠀⠀⠀⠋⠀⠀⠂⠛⠁⠀⠛⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠁⠁⠀⠁⢹⣧⠀⠀⠀⠻⠇⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠻⠇⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠉⠀⠃⠠⠄⠀⠀⠀⠀⢀⣈⠀⣠
⠀⠀⠀⠀⠀⠀⠉⠲⠠⠤⡴⠀⢀⠀⠈⠐⠻⠂⠀⠀⠀⠀⠀⠀⠰⠛⠉⠈⠉⠻⣦⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠐⠤⠦
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⢦⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠂⠀⠀⠄⢠⠀⢁⡠⣄⡀⠀⠈⠾
⠀⠀⠀⠘⠚⠁⠀⠸⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡈⠅⡆⠅⢆⢱⠀⠀⠺⠤⠖
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠁⢀⠨⠐⡀⡵
⠀⠀⠀⠀⠀⠀⠄⠣⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠘⠰⠖⠘⠒⠉
⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⢠⠀⢀⣠⡄
⠀⠀⠀⠀⠉⠉⡄⡀⠈⢀⠀⠱⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠈⡄⠀⡀⠐⢀
⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠈⠉⠒⠋⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠈⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⡀⠀⠀⣀⠦⢄⣀⡤⠚⢦⣀⣀⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢠⣄⢀⡰⡩⠝⠫⢅⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣅⢨⠀⠁⢐⠀⢀⣤⣶⣧⠀⠀⠀⡔⠈⠉⠀⢂⢹⢢⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣄⠀⠈⠢⣸⣿⡿⠃⠀⢙⠆⢃⢠⣾⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠤⠬⠷⢄⣀⣰⠖⠶⠭⣶⡚⠍⡆⠉⠛⠋⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢨⠟⠒⠲⣦⠠⠭⢝⡲⠦⡷⠒⠚⠀⠀⣠⣾⡥⠤⠄⠶⠒⠒⡖⠊⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡘⠉⠉⢩⠃⠈⠐⢶⠊⠅⣥⠤⢤⠖⠊⠁⠈⣅⡀⠤⠐⠲⠾⣄⣦⣽⡪⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣃⠀⣠⠃⠀⠀⠀⠀⠉⠉⠀⠀⢸⠀⠀⢀⣠⠯⠀⢀⡠⠤⠤⠤⠿⠦⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠔⠊⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠅⠀⠀⣔⠀⠉⠉⠁⠒⢤⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠘⠒⢒⠒⠊⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⢤⣀⣀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠉⠉⠙⠒⠒⢲⠞⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡰⢹⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡰⠁⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡰⠁⠀⠸⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠤⠀⣴⠁⠀⠀⠀⣄⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⣙⠲⡄⠀⢠⣅⣀⣀⣈⣓⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉

⡿⠿⠿⠿⠿⢻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠲⡄
⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⢪⠐⠇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠛⣠⠞
⠀⠀⠀⠀⠀⠀⡞⠓⢤⡜⠀⠀⠀⠸⡆⠀⠈⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢸⠃⠀⠘⠦⣄⡀⠀⠀⢳⠀⠀⢻⠀⡏⠀⠈⠉⠉⠙⠛⠲⣤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠙⡆⠀⠈⣇⠀⠸⡆⢹⠀⣰⢲⠶⠤⣤⠟⠁⣀⡴⠋
⠀⠀⠀⠀⠀⡇⠀⠀⡠⠐⠢⠄⢸⣀⡠⠞⠉⠙⢧⡏⢠⡏⢛⡶⠞⢁⡴⠮⡉⠳⡀
⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠈⠄⢫⠀⢠⠖⠉⠁⠀⠈⠳⣏⡠⠴⠿⠓⠒⠛⠉⠉⠱⡄
⠀⠀⠀⠀⠀⠈⢧⠀⢇⠀⠀⠀⢸⠈⢆⡜⡔⠉⠉⠒⠢⠀⢸⠀⣀⠤⠴⠒⠒⠒⢄⠀⣧⡤⠖⠲⢤⣀
⠀⠀⠀⠀⠀⢀⣸⡄⠈⢦⠀⠀⣸⠀⠘⣤⠁⠀⠀⠀⢠⠀⢸⠀⠇⠀⠀⠀⠀⠀⠈⡄⢏⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠰⣅⠀⡱⠀⠀⠉⠉⠁⠀⠀⠈⡀⠀⠀⠀⠸⢀⡏⡀⢀⠀⠀⠀⠀⠀⠀⠇⢸⠀⡠⠖⢆⠐⡆⢳
⠀⠀⠀⠀⠀⢹⠂⠉⡑⠒⠒⠒⠒⠒⠠⠤⠼⠤⠤⠤⠧⠼⠽⠧⠼⠤⠤⠤⠤⠤⠤⠼⠤⠯⠔⢀⡸⠀⠇⠈⣇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⢸⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣧⠀⢸⢦⣠⠇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⢻⡀⡸⠀⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠉⠭⠉⣉⠙⠛⠻⢿⣿⣿⣿⡿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⣻⠟⠉⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠈⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣠⣤⣤⠄⠀⠹⣇⠂⠄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠑⠠⢀⠀⠀⠛⢷⣦⣄⠀⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠘⢧⡀⠀⠉⠐⠠⢄⡀⠀⠀⠀⠀⠀⠁⠒⠤⢀⡀⠉⠒⠠⢀⣉⢻⡆⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡿⠁⠀⠀⡀⠀⠀⠀⠝⠶⡀⢀⠀⠀⠀⠉⠐⠂⠠⠀⢀⡀⠀⠀⠀⢉⣁⡠⠴⠞⢉⡅⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡿⠁⠀⠀⠔⠀⠀⣠⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠰⠟⠉⢠⡴⢖⣡⡍⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⡠⠊⠀⡀⠔⠁⢀⠠⠊⠀⠀⠀⠀⠀⠀⠠⠀⠉⠒⠆⠀⠠⠤⠤⠤⠤⠀⠶⢂⡈⠉⠁⢀⣉⡱⠂⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠉⢻⣷⡖⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠻⣿⣿⣿
⡿⠿⠛⠉⠀⠀⢀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣄⠀⠀⠈⠙⠛
⣷⣤⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠠⡀⠀⠀⠀⠀⢀⠀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⡡⠋⢁⠄⠒⣀⠀⢀⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⠀⠀⠐⠀⣴⠃⠠⠊⠀⠀⠀⠀⢳⣦⠈⠻⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⠀⠀⠀⠀⠀⢰⡇⠀⠇⠀⠀⠀⠀⠀⠀⠃⠐⡄⠘⢿⣿⣿⡿⠁⠀⠀⣠⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠎⠀⠀⡠⠶⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣸⣆⠈⢛⠉⠉⢤⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠇⠀⣌⠀⠀⠀⠀⠀⠀⣠⠄⠠⠒⠀⠐⠑⠊⣰⡏⠙⡄⠈⠅⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠀⠰⠀⠉⠂⠄⣀⡄⠀⡏⠀⠀⠀⠀⠀⠀⣴⣉⢈⠀⠴⠐⠚⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘⠀⠆⠀⣀⠀⢀⠋⠁⠀⡑⠋⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⡀⠀⠀⡀⢰⠀⠀⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠰⢀⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⠀⠃⡄⠀⢆⡡⠄⠀⠀⠀⠀⠀⡀⠤⠰⠎⡡⠊⠱⠤⢅⢤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠃⠀⠋⡴⢂⡀⠀⢀⡴⠊⠀⢀⡈⠖⠁⠀⠀⠀⠈⡄⠡⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⠀⠈⠧⠐⠉⠀⠀⠀⠈⠁⡜⠀⠀⠀⠀⢀⡰⠄⠃⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠏⣉⣁⢐⠀⢄⡄⠒⠈⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠑⠢⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠓⠰⠦⠤⠤⠀⠀⠐⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠐⠂⠤⢄⡀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠔⠈⠒⠀⠀⠀⠤⠤⠤⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣀⣀⣀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠾⣿⣿⡿⢿⣿⡿⣛⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⢸⣿⣿⣿⣇⠺⣺⡏⠀⠀⠘⣧⣏⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⣀⣀⣀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⡇⠀⠻⣿⠟⠁⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣦⡀⠤⢀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠻⣿⠟⣉⣿⣿⡏⢸⡿⢹⣏⢩⣽⠋⢻⣿⣿⢻⠛⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⢸⡇⣿⠀⣿⣿⣿⡇⣸⢃⣿⣿⢸⣿⠀⡌⣿⣿⢸⢰⡌⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⡾⢱⣿⠀⣿⣿⣿⠇⡏⢸⣿⣏⢸⣿⠀⣇⢹⣿⢸⠀⣿⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣐⢿⣿⠐⢟⣿⣿⠀⠁⣾⣿⡿⢸⣿⠀⣿⠸⣿⢸⠀⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡎⢿⢸⣿⣿⣿⠀⡆⢻⣿⡇⢸⣿⠀⣿⡆⣿⢸⡆⣿⡇⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢻⡇⣸⢸⣿⣿⣿⠀⣿⢸⣿⡇⢸⣿⡆⢿⣇⢻⡸⡇⣿⢁⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣈⣼⣿⢸⣿⣿⣿⢠⣿⠈⣿⡇⢸⣿⡇⣼⣿⠸⢡⣇⣁⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⢸⣿⣿⣿⢸⣿⡄⣿⣧⢸⣿⡇⢿⣿⣧⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⣶⣿⣯⣸⣿⣧⣘⣯⣈⣿⣦⣼⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢂⣠⡤⢶⣶⣿⣧⠉⠀⠉⣱⠆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡴⠁⠈⠀⠀⠰⣅⠍⠙⣃⠀⠁⠁⠀⠃⠀⢈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⢹⠁⠀⠀⢰⣦⢀⠤⠏⠛⠀⠀⠀⠀⠀⠙⡷⠛⠗⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠜⠀⢐⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠴⠿⣷⢬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⢇⠀⠊⡁⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠣⣣⠈⣉⡉⣷⠀⠀⠀⠀⠀⠐⠨
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢒⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠑⠒⠀⠆⠀⢰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠀⠀⠀⠈⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⢸⢄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⢀⠜⡅⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠂⡁⠑⢤⡀⠀⠀⠀⠰⠀⡜⠁⠀⠀⠀⠀⠀⢀⠴⠃⢈⠐⠁⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠀⣡⣆⣀⡀⠀⠠⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⣀⢴⡑⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢈⡦⣀
⠀⣀⣀⡶⠀⠡⠌⠛⠀⠀⠉⠓⠲⠆⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠰⠖⠛⡉⠀⠀⠛⠡⠌⠀⢶⢀⣀
⠀⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠁⠀⠀⠀⣀⣀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⣠⡴⠞⠛⠉⣉⠛⢷⡄⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⡈⠋⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢸⡿⠶⠶⠞⠋⠀⣰⢿⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⠶⠶⠶⠞⠋⠀⠙⢷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡙⠛⠶⠛⣋⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠙⢷⣤⡾⠋⢙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢷⣴⠟⠙⠳⣦⡟⠉⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠈⠃⠀⣀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀⠀⢀⣴⠟⠁⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠈⠻⡶⠟⠁⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡆⣿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡋⠋⠛⠛⠛⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⣿⣿⣿⣿⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⣿⣿⣿⡿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⡉
⠀⠀⠀⠀⠀⢠⣾⣷⣆⠸⡆⠀⡿⠁⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡏⣿⣿⡏⠀⣷⠀⡇⣀⣤⣤⣶⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣶⣧⡘⣧⡀
⠀⠀⠀⠀⠀⠸⣻⣿⡟⢀⡇⠀⣿⢻⣿⣟⣻⣄⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡶
⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠀⠀⣿⣸⣗⣷⣹⣽⣿⣿⠁⠀⠀⠀⢰⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡘⣿⣆⠀⠀⠀⠀⠀⠀⠀⣇⢠⡇
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡘⣿⡄⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠙⠛⠛⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡘⣷⠀⠀⠀⠀⠀⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡘⡇⠀⠀⠀⠀⠀⠙⠙
⠀⠀⠀⠀⠓⠒⠶⠶⠶⢤⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡈
⠀⠀⠀⠀⠤⠤⠶⠶⠶⠟⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⣾⠂⠀⠈⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⡏⠀⠀⠀⢃⠀⠀⠁
⠀⠀⢀⣀⣤⣤⣤⣤⣴⣾⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠚⢃⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠸⠟⠿⠟⣿⣿⠿⠿⠿⠟⠻⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⣀⣾⠁⠀⠀⠀⠈⠛⠿⢿⠿⠿⣿⠟⠛⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠠⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⢁⠀⠛⠋⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢀⡀⠀⠀⠀⠀⣿⣟⠀⠐
⠀⠀⠀⠀⠠⣤⣤⣼⣶⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡄⠀⠀⠀⠀⠀⣒⣶⠶⠶⢶⣖⠀⢠⠀⠀⢸⡏⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠴⠶⠾⣿⣿⣿⣿⣶⣤⣤⣶⣴⣧⣤⠾⠯⠍⠀⠀⠀⠀⠀⠀⠀⡪⠭⠭⠭⠭⠵⠀⠈⢧⡀⠀⠻⠶⠂⠀⠀⠹⣿⣄⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⣽⣯⡭⠭⠳⠶⠞⠓⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⣤⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠹⣀⠀⠐⠒⠀⡈⡁⠆⠢⠀⡩⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠂⠁⠀⠀⣘⠁⣉⢡⠀⡄⠈⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠁⠀⠀⠀⠀⠈⠂⠐⡈⠉⣤⡠⠁⠀⠀⠀⠧⠤⠄⠄⠂⠉⠡⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣮⠀⣀⠀⠀⠀⠀⠀⠐⡁⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠎⢈⠏⠐⠀⠈⠉⠢⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠠⠀⠀⠀⢰⣥⣴⡀⠀⣀⣀⡀⠤⡄
⠀⠀⠀⠀⠀⠈⠍⠑⠒⠤⢄⣽⡀⠘⠷⢦⡦⠀⠤⠊⠀⣀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⡠⢁⢐⡴⠕⠚⠋⠉⠉⠁⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠁⠁⠒⠤⢙⢦⢀⢶⡦⠨⠊⢔⠠⢂⠁⠊⡈⢀⠄⣨⣄⠔⠉⢠⠀⠀⠀⠀⠀⠀⡠⠁⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠙⠺⣆⢔⠨⠂⠄⠈⡂⢐⣀⢀⡴⢺⠔⠁⠀⢠⠂⠢⡀⠀⠀⢀⠔⠀⠸⡀⡇
⠀⠀⠀⠀⠀⠀⠰⠀⠤⠀⠐⠑⢄⠀⠀⠀⠀⠀⠀⠀⠑⢮⠂⢑⠠⠂⠥⠇⠈⡶⠁⠀⠀⠀⡇⠀⢰⠈⠀⡠⠁⠘⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠂⠑⠄⠀⠀⠀⠀⠀⠀⠀⠑⣄⠊⠊⡐⣱⠎⠐⠀⢱⠀⠀⠨⢤⢤⡾⠊⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠁⠀⠢⡀⠀⠀⠀⠀⠀⠀⠈⢷⢈⡸⠃⠀⠐⢤⠏⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⢀⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠤⠀⠀⠊⠲⣄⠀⠀⠀⠀⠀⠘⡷⠁⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢠⢀⣠⠖⠋⠀⢊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠉⢐⣢⡤⠤⠭⣷⣦⡀⠀⠀⠀⠃⠀⠀⢀⣠⣰⡥⣄⡀⡈⠀⠀⣠⠼⠋⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠛⠀⠚⠉⠁⣠⡄⠀⢌⡦⠖⠋⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⢄⡙⠁⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠤⢤⠤⠤⠀⠀⠊⠁⠀⠀⠀⢁⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠉⠁⠀⠀⠂⠀⠒⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢀⠅⡠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠈⠐⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⣶⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣡⠟⠁⠀⢸⠀⠀⠙⢧⡉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢦⣀⣰⠃⠀⠀⠀⢸⠀⠀⠀⠈⢷⣀⣠⠟⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢹⠟⠶⠤⣤⣄⣼⣤⣤⡤⠶⠚⣿⠁⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⡀⣀⣠⣤⠤⠾⠦⠤⣤⣀⡀⣼⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⣤⠞⢿⠉⠀⠀⠀⢸⠀⠀⠀⠈⣹⠿⢦⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⢷⡀⠀⠀⢸⠀⠀⠀⣴⠋⢀⣠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢿⣦⣄⣼⣤⣴⣾⠷⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠉⠢⠀⢄⠀⠄⠀⠀⢀⣀⣀⣠⡴⠖⠛⠉⠉⠉⠑⠂⠀⠀⠀⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡤⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣳⡶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠂⠀⠀⠀⠉



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠙⠒⠲⢤⣀⠇⠠⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠢⣌⠙⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⢄⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠳⡄⢀⠔
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠁⠁⠀⠀⠀⠎⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡠⠤⠶⢄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⡀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣣⠎⠉⠉⠛⠒⠒⠒⠂⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢄⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠚⠁⠀⠀⠀⢳⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢇⢄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠱⣄⠀⠀⠐⠊⠁⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠘⢀⡠⠊⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠈⡗⠀⢄⠀⠀⠀⣾⠠⠒⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⠉⠛⠶⠦⢤⣤⣤⣧⣀⠠⠓⠒⠉⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡈⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⡀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⡃⢀⠀⠀⢀⣀⣀⢀⢀⣀⠀⡀⢀⡀⠑⣀⣀⠀⡀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⢀⡀⢀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣠⣼⠽⠿⠦⠼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠛⡍⠀⢠⠭⠁⠀⢐⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠬⠶⡄⠀⠈⠚⠁⣀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⠢⣄⣀⣀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠈⠊⠓⢾⣆⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⠽⠃⠀⠀⠀⠀⠀⢀⡀⠁⠀⠙⣆⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡞⠁⠀⡤⣶⠻⠀⠀⡔⠁⠈⡆⢠⠀⠸⡄⠀⠀⠀⠸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠳⡀⠀⠳⡇⢀⣀⣼⠔⠂⠀⡇⡾⡁⠀⠽⠦⠄⣀⣠⣤⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠹⣄⣀⠷⢚⡄⠸⢄⣀⡴⠁⡿⣜⡂⠤⢀⡀⢡⠊⣄⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⡋⣁⣤⢴⠟⠲⣄⣀⣀⣀⢧⠀⠉⠙⠲⢆⡽⠤⢿⣤⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡝⠋⠉⢸⠀⢰⡏⢁⡄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠘⠁⠀⠀⠈⠳⡈⢣⣾⠆⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢰⢹
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣶⣄⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠏⡄
⠀⠀⠀⠀⠀⣠⠞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢳⠈⡓⠀⠀⠀⣸⠀⠀⠀⠀⠀⢓⢡
⠀⠀⠀⢀⡞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣇⠀⢀⡌⢠⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⣸⠀⢀⠀⣄
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⣾⢀⡏⣀⣀⣀⣐⣳⠐⢯⠍⣰⠖⠀⢱⠀⠈⢟⣉⡓⢲⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⣳⣜⠯⣝⣓⠠⠤⠬⣓⡦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠴⠋⠀⠀⢈⡉⣉⠍⢥⡀⠀⠀⠀⡤⠶⠋⠛⠒⢲⡄
⠀⠀⠀⠀⠈⠙⠲⢤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⡅⠙⠄⠀⣀⠅⠀⠀⠘⠓⠒⠢⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠐⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠚⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠀⠒⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⠀⠀⠀⠘⠓⠒⠒⠒⠽⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⣠⠞⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⣀⡤⠖⠋⠉⠀⠀⢀⣠⠤⢤⣀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡡⠖⠒⠒⠲⣤⣠⡞⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠃⢼⠀⠀⠀⠀⣿⣯⣿⢀⣀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⠳⣄⣀⣀⣀⡡⢾⡿⠿⠃⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠒⠲⠲⠞⠁⠀⠀⠀⠀⠀⠀⠒⠒⣲⠶⠦⣄⣀⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣅⠀⡿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣏⠁⠀⣽⠈⠙⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⢰⣇⠀⢻⡒⢲⡦⠤⠤⠤⣤⡤⠤⠶⠶⢲⡿⡉⠁⠀⢸⠈⠱⠦⠟⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠘⣿⡀⠀⠑⠞⠙⣄⠀⠀⡎⠳⡀⠀⠀⣸⠀⠙⠦⡤⠃⠀⠀⣀⣀⣀⡖⠒⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⣏⢧⠀⠀⠀⠀⠈⠙⠋⠀⠀⠈⠓⠚⠹⣆⣀⣀⣀⣠⠖⠋⢉⣁⡈⢃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠸⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⡨⠋⠀⠀⠀⡇⠀⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢳⡈⢦⠀⠀⠀⠀⠀⢀⡎⠱⣴⢋⡤⢄⠀⠀⡜⠑⠢⢄⢹⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠳⡄⠀⠀⠀⠈⠢⣄⢳⡞⠀⠀⠱⣀⠀⠀⢀⡤⠟⠁⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⢢⡀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠢⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠐⢄⠀⠀⢸⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⠀⣨⣀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢰⢋⡤⢤⠠⡶⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⠐⡆⡔⠐⢬⠀⠀⠀⠀⠉⠓⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠈⠙⠀⠺⠤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠀⠀⠀⠀⣀⣀⡀⠀⣞⠛⠻⠿⡿⠓⠀⠲⡀⠀⠀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢁⠀⠤⠉⠉⠐⠑⠂⠀⠑⣄⠀⢀⠏⠔⠛⠒⠒⠒⠒⢒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠓⠀⠀⠐⠂⠈⠉⠁⠀⠈⠁⠀⠈⠉⠉⠉⠑⠒⠤⢄⡀⠽⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⠋⠀⠀⠈⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡖⠁⠀⢠⢤⠀⠀⠀⠀⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢚⠀⠀⡜⢀⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣭⠃⠀⠙⠋⢁⠀⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠸⣦⣀⡼⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⡀⠀⡉⠑⠒⡄⢀⠀⠀⠀⡰⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢒⠏⠻⠤⠕⠀⢾⣿⣿⣿⢖⠝⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣴⣶⣤⣴⣿⣿⣿⡷⡍⣴⡁⠀⠀⠀⣀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣯⢟⠞⠱⡄⠈⠓⣖⠉⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⢿⣿⣿⣿⡿⡣⢯⠶⠚⠙⠦⣤⡼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣹⠊⠀⢀⢞⠞⡔⠛⠿⣬⡉⠁⠀⡶⠒⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠰⣇⢀⡰⡻⠃⠀⢸⠀⢀⣨⣿⡆⣸⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠙⢦⠌⡐⣟⠀⠀⢠⠃⠀⢻⣿⡿⠙⠋
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣢⠾⠁⠀⡰⠁⠠⣾⣿⡟
⠀⠀⠀⠀⢠⡏⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠜⠁⠀⢀⠜⠀⠀⣤⣾⣿
⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡡⠋⠀⠀⢠⣾⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⢀⠤⠒⠤⣾⠝⠀⠀⠀⠐⠛⠛⢻⠉⠙⣯⠉⠙⣇
⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⢀⠔⠡⢄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⢇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⠄⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢣⢀⡇⠘⡄⢸
⠀⠀⠀⠀⠀⠠⠴⠚⣉⠄⢀⠅⠀⡠⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⢣⢸
⠀⠀⠀⠀⠀⠀⠠⠭⠒⠭⡀⢄⣪⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠈⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⠀⠀⠀⢠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢻⠀⡄⠀⠀⢀⠈⣇⠀⠀⣸⠃⢰⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣀⠀⠀⠀⠀⠸⣆⠀⠤⠠⠀⠀⠹⠄⢠⡏⢺⡉⠀⠀⢀⡞⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢳⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⣠⠟⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞⠃⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠙⠀⠀⠙⠃⠀⠀⠈⠅⠀⠀⠀⠀⡠⠀⠉⠙⠃⠀⠀⠀⠀⠀⡄⠀⠀⢄⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⢀⠀⣴⡂⠈⠐⠃⠀⢀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠇⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⢤⠤⠤⠀⠀⠀⠀⠀⠈⠯⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⢀⡤⢀⠴⡄⠄⠀⠀⠰⠶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⡈⠀⠀⠀⠀⠸⡊⠀⡀⠨⠆⡖⢒⣀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠁⠄⡀⢀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⣁⡤⠶
⠀⠀⠀⠀⠀⠀⠘⠓⠚⠒⠲⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⡀⠀⠀⠠⠈⠁⠈⠀⠈⠒⢄⡀⠀⠀⠀⠈⠀⣀⠀⠘⠋⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⡀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⡈⠀⠸⠒⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢷⠒⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢌⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠱⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡦⠄⠀⠀⢌⠀⠰⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠐⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠞⢀⠁⠀⡀⠀⠀⠀⢤⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠈⠁⠒⢀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣨⢁⠴⠋⠀⠀⢱⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠴⠋⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⢀⡰⢚⣥⡀⠀⠀⠀⢀⠦⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣠⠔⡩⠞⠁⠀⠈⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⢬⣀⣤⠤⠖⠻⠤⣀⣀⣀⡤⠞⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⣼⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣿⣿⢇⣠⠀⠉⠀⠩⣬⠉⢻⡏⠀⠀⠀⣿⡟⠉⠉⠻⠿⣿⡿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣽⡟⠀⢀⠀⠀⠀⠀⣀⠀⢘⠷⠀⠀⣀⡿⢀⣒⠂⠀⠀⠀⠲⠄⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⢃⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠏⠃⢺⡿⠀⠀⢠⣾⡅⠀⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠤⡀⠀⠀⣦⣤⡶⠀⢀⡼⢿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠙⠆⣀⡀⠉⣀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠐⠈⠀⠐⠄⠀⠀⠀⣤⣤⣤⣤⣤⣖⣂⣨⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠠⡄⠁⢄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣪⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠐⡂⠐⠁⠀⠀⠀⠀⠁⠀⠒⠁⠀⠀⠂⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⡠⠁⢣⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⡠⠖⠀⠀⠀⠀⠀⠘⠦⣄⠐⠀⠐⠂⡤⠚⠀⠀⠀⠀⠀⠓⠤⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣏⠈⠉⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣿⠿⢟⣛⣿⣮⣛⠻⠿⠟⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣾⣿⡟⢡⡾⣫⡿⣿⣿⢿⡿⣿⡿⣯⣻⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣳⣤⣽⣿⡿⢱⣿⣿⡟⣰⢏⣿⣹⣗⣿⢷⡙⢿⣮⣛⠶⣿⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣩⣽⣿⣿⣿⠃⣼⡿⣹⡇⣿⣿⢿⠙⣿⣽⣆⣿⢦⡙⢿⣷⣮⠻⣿⣷⡶⣆⠀⠘⠻⠶⠶⠾⠟
⠀⠀⠀⠀⠀⣠⣤⠖⠛⠉⢱⠞⢻⣿⡽⢟⣡⠞⣽⣿⣿⡇⣿⣿⣿⡆⣿⣿⢿⣧⣾⠻⣆⠹⣎⢷⠘⣯⠻⣟⠛⠛⢶⡄⠀⣤⠶⠖⠛⠻⢦⣄
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠘⠻⣯⣭⠶⣻⣿⠾⢋⡾⣡⣿⣿⣏⣼⠇⣿⣿⡘⣏⢹⣧⣹⠌⣿⢿⡆⢿⡛⠋⠀⣴⣟⣁⠀⠙⠛⠛⠛⠛⠛⠋
⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⣰⣟⣫⡾⢿⡏⣿⣿⡟⣰⡏⣿⣇⢿⡿⣿⣿⠀⣿⣌⢳⣼⣿⡆⠀⠀⠀⠉⢻⡆⠀⠰⣾⣿⠆
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⢻⡆⠀⢾⣿⣧⠾⠷⠞⠻⣷⢿⣟⣱⢿⡇⢿⣿⣎⢻⣿⢿⡶⣷⠾⠀⠉⠋⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣹⣾⠟⠋⠀⣿⣼⠁⣿⢻⡇⠘⠷⠛⢀⣀⣠⣤⡴⠶⠛⢉⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠛⠓⠒⠛⠛⠛⣋⣉⣩⣉⠛⠦⣤⣤⣤⣬⣅⡀⢙⣋⣡⡤⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣤⠴⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠅

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⢤⡀⢀⡠⠐⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣇⠀⣠⠀⠀⠀⢠⣤⠀⠀⠀⠔⠀⠉⠁⠢
⠀⠀⠓⠃⠀⠀⢰⠁⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢁⣀⡀⠀⠉⠉⠀⠀⢀⡀⠈⠀⠀⢘⢀⡄⠀⠀⠀⠀⡔⠁⠉
⠀⠀⠀⠀⢠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⠀⠀⠀⠀⢀⡜⠢⡠⠚⣄⠀⠀⢀⡴⠥⠄⠠⠤⢄⡀
⠀⠀⠀⠀⣈⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠥⢀⠀⠀⠀⠀⠀⠃⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠒⠈⠀⠀⠀⠀⠒⠎⠀⠀⣠⣒⡒⠦⠔⠒⠢⠤⡄⠀⠈⠑⢄⠒
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡇⠰⡞⡵⣶⡦⠀⠀⣬⣭⣁⠁⠀⠀⠀⣸
⠀⡏⢉⠉⡉⠉⡉⢉⠉⣀⣀⡄⠬⠤⠄⢀⡀⠀⠀⠁⠀⠇⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⢹⢶⠀⢏⡻⡇⠀⢸⡸⣿⠁⢃⠒⣄⡴⠃⡖
⠀⡇⠀⠀⢀⢸⡀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠛⢭⠭⠍⠀⡥⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⢸⠈⢆⠀⢰⡥⠤⣴⠉⠁⢀⡌⢴⠉⠀⠆⡗
⠀⡇⢀⠀⡰⠊⠀⠀⠤⠤⢤⣄⠀⠐⠒⣠⢄⡀⢣⡠⠀⡇⠰⠐⠒⠐⠂⢲⠒⠂⠀⠀⢸⠀⠨⠷⡦⢭⣨⡥⡴⢚⠉⡹⢋⢧⣁⣤⣷
⠉⠀⠉⠀⡇⠀⠀⠀⠉⠐⣚⣧⠀⠀⢴⣻⡄⢃⡿⢤⠀⡇⢀⠀⠀⠀⠀⢸⠀⢀⠀⠖⠁⠁⠐⡞⠀⢰⠀⠅⢀⢸⠊⠐⠁⠈⡇⡐⡒
⣀⡄⠉⠁⠳⢦⠃⡵⠇⠀⣌⢫⠇⠀⣩⡛⡣⢸⠃⠜⠀⠃⢸⠀⠀⠀⠀⢸⠀⠈⠀⠐⠂⠈⠀⠳⠄⣨⡀⢘⢇⣀⠉⠒⠒⠘⣧⠆⢇
⢀⣠⣤⠦⠄⠠⠛⢦⠀⠀⠈⡵⢦⣤⣷⠍⠀⠌⠀⣁⠀⡁⢸⠀⠀⠀⠀⢸⡔⠁⠠⠔⠀⣰⢯⢻⡄⢙⡷⢡⠞⡀⠈⠑⠒⠒⠙⡀⢸
⠈⡆⠀⡬⢤⢰⣪⠞⠓⢤⣀⠘⠂⢐⣋⣤⠞⢋⡡⠜⡇⡀⢸⠀⠀⠀⠀⢸⠐⠤⢄⣀⣄⣀⡄⠀⣠⢈⣱⡁⠀⣣⣀⣀⣀⠠⠔⡇⠸
⣀⣿⠀⠇⠲⡼⡅⠀⠀⡇⠉⢛⠫⠚⡩⠔⠊⠁⠀⠰⠁⡀⠗⠠⠦⠠⠄⣸⠄⠂⠌⠣⠸⠄⢤⠔⡹⡏⢸⠁⠀⠀⢳⠀⠀⠀⠀⣭⢉
⠤⠘⠀⡇⡘⢰⣀⡀⠠⢼⢠⠋⡝⠁⠀⠀⠀⢀⠠⠺⣒⣊⡉⠔⠓⡄⠢⠔⠢⡀⠈⡉⠤⠶⣭⠊⠀⡆⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⠄
⠒⠉⠀⢹⠁⠈⠲⠒⠛⢋⡇⠸⠀⢀⡠⠔⢊⡡⢐⠩⠐⠉⡠⠔⠊⢳⠴⠒⠛⠩⠀⠀⠀⠀⣿⠈⠀⠉⢸⠀⠀⠀⡞⠹⡄⠀⠀⢸
⠀⠶⠄⠱⢤⣀⡀⠑⠢⢄⡑⠦⣮⣅⠴⠮⡔⠊⣀⠤⠂⠁⠀⠀⠀⠸⡄⢀⣀⠀⠀⠀⡐⠀⢸⠠⠶⠄⠸⣽⣖⣱⠇⠀⢳⡁⢮⡼⢀
⠀⠀⠀⡐⠁⠀⠈⠉⢲⠚⠻⣄⣠⣏⠀⠂⠓⢎⠀⠀⢠⠊⣿⠽⠂⣄⢗⠝⠁⠀⠀⠠⠀⠀⣴⠀⢀⣄⢰⠃⠄⢇⠀⠒⣂⢇⡀⣇⠈
⠀⠀⠀⡇⠀⠀⠀⢰⡟⠈⠀⠘⢟⠋⠀⠀⠀⠈⠄⠀⠠⢡⠀⢀⡶⣼⠚⡤⠖⠤⠒⣦⣐⠊⡿⠴⣥⠤⠥⠤⠤⢬⡖⠛⠚⠀⠀⢈⡆
⠀⠀⠀⡇⠀⠀⠀⠘⢹⠀⠀⠀⠘⡣⡀⠀⠀⠀⠈⠀⠘⢯⣉⡜⠂⠁⠀⡛⢄⢠⡾⠜⣹⡦⣤⡔⠉⠉⠈⠈⠁⠉⠓⠀⠈⠉⠓⠒⣁
⠀⠤⡄⡇⠀⠀⠀⡇⠈⡆⠀⠀⠀⡗⠓⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠜⠉⠛⠉⠙⢎⠀⠀⢙⢆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⡧⠤⠤⢤⡇⠀⢸⡄⠀⠠⡇⠀⠈⢢⡀⣀⠀⠈⡄⠀⠀⠀⠀⠎⠀⡘⠀⠀⠈⡈⢣⠀⠀⠁⢻⠉⠙
⠀⠀⠀⢹⣁⣹⣉⡀⠀⠀⠹⠤⠽⡥⢄⠀⠋⣕⢄⠱⡀⠘⣄⣀⠤⢸⠀⢠⠀⠀⠀⠀⠰⠈⡆⢀⠈⠈⡆⠀⠀⠀⠀⠀⠐⠓⠶⠳
⠀⠤⠤⢾⣀⠀⠁⣈⣧⠒⢷⢄⣀⣀⠠⡧⠡⣑⣀⡤⠋⠀⠉⠀⠀⢸⠀⠘⠄⠀⠀⠀⠀⠀⢡⣀⣙⣀⣱⣄⡀
⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣐⣲⣆⣀⣀⣀⣀⣀⣘⣙⣁⣘⣒⣒⣔⣒⣒⣚⣒⣒⣚⣃⣀⣀⣈⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢹⠠⠀⠀⠀⢹⡀⢀⣏⣰⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠲⣄⠀⠀⠈⠃⠐⠀⠀⠀⠃⠘⠈⢇⠀⢠⠎⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠣⡌⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⣠⠞⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢄⡙⠀⠘⠁⠀⠀⠁⠀⠠⢀⠤⠈⠙⠀⠀⠀⠀⡀⠀⠠⠀⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⠂⠀⠀⠀⣤⠠⠗⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⣀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠈⠠⠉⠁⠀⠀⢀⣀⣡⣀⡀⠀⠠⢄⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⣀⡔
⠀⠀⠀⠀⠀⠤⠤⠤⡌⠀⠀⠀⠜⠅⠀⠘⠲⠺⡤⡈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠌⠁
⠀⠀⠀⠀⠀⣄⣤⣀⡀⠀⢀⠈⠀⠀⠀⠀⠂⠀⢠⡀⠀⠐⠂⠄⠀⠀⢄⡀⠀⠀⠑⠀⠀⠀⢠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢀⠀⠀⠀⠑⠄⠀⠀⢀⡑⠀⠤⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⡀⠠⠀⠀⠀⠀⠀⠀⠷⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠰⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠠⡋⠠⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠐⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠤⡀⡀⠀⠀⠈⡧⠔⠀⠀⠀⠀⠀⠂⠀⠀⡀⠃⡌⠀⡄⠀⠀⢦⠼
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⢂⣀⡴⠁⠀⠀⠀⢀⠔⠀⠀⢀⠰⠲⠊⠀⠀⡀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠁⠀⣠⢔⠕⠊⠑⠤⠤⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠴⠶⠚⠢⠤⠠⠤⠚⠋⠁


⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠈⠈⠀⠀⠀⢀⠠⠐⠈⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠠⠂⠁⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠁⠄⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢂⡀⠀⠀⣀⠀⠀⠀⣄⡤⠀⢀⣾⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠠⠀⠀⢀⡇⠠⠴⣧⡔⠂⠘⣅⣆⠿⠻⣛⡛⠛⣇⣄⢲⠶⠳⠢⣆⡀⠀⡇⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠤⠴⠋⠀⢩⡾⠁⠀⠀⢠⠟⠉⠙⢿⣷⡿⠾⣿⣟⣿⣄⠀⠀⠀⠑⢦⣳⣄⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡆⠀⢀⠔⠉⠀⠀⠀⡰⠃⠀⠀⠀⡸⢛⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠈⠛⠧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⡠⢁⠒⠳⣄⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣶⡄⠀⠀⠀⡴⠋⠀⠀⠀⠀⡰⠁⠇⠀⠀⠀⠙⢄⠀⠀⠀⠀⠉⠻⣷⣴⡁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠉⠁⢀⡠⠞⠀⠀⠀⠀⣠⠎⠀⠀⣈⠦⣁⠀⡀⠀⠑⣄⠀⠀⡀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠐⠾⠲⠀⠀⣰⠃⠀⠀⠀⡃⠀⠈⠳⡀⠀⠀⠈⠑⠾⣁⡠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⡤⠴⢟⣅⠃⠀⠠⠞⠛⠒⠤⣀⣨⡳⣴⠶⠴⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠦⠖⠦⡀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣷⠀⠀⡷⡇⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⡯⡀⠄⣐⡑⡘⢦⡀⠀⠀⠀⠀⡼⢡⣤⡌⣧⠀⡇⡇⠀⠀⠀⠀⠀⣿⣿⣶⣄⣠⢤⣼⡟
⠀⠀⠀⢀⣰⠛⠉⠙⢦⡄⠀⠀⠀⠀⠀⠙⢶⣄⠉⣡⠽⠊⠀⠀⠀⠀⠀⡇⠈⢭⠀⣿⠀⣱⡇⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠙⠓⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⠛⠚⣿⣤⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠉⠉⠛⠋
⠀⠀⣠⠔⢒⡒⠒⢤⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢶⣶⣤⣤⡄
⠀⢸⡇⡈⠀⠒⡃⠴⠃⠀⢸⠀⠀⠀⠀⣀⠴⢊⠅⣢⢟⠎⠳⡄⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡛⢑⡀⢃⢲⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢐⡧⢀⠋⠾⠓⡁⠔⣨⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⠈⠀⢸⢸
⠀⠸⡇⠀⠀⠀⠀⢠⣄⣀⡟⠀⠀⠀⠀⡷⣄⠑⣖⣡⠴⠋⠀⠀⠀⠀⠀⢀⣠⠔⣒⣿⡟⠉⢳⡆⠀⠀⠀⠀⠀⣷⣽⢀⠀⠀⣿
⠀⠀⠈⠒⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣳⣄⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠙⠾⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢠⣴⡳⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠞⠓⡆
⠀⠀⠘⣎⢳⠘⠉⠸⣿⡀⠀⠀⠀⢀⡤⠴⠉⠀⠀⠀⠀⠈⢓⣢⠀⠀⠀⠀⡶⣯⣶⡯⠕⠒⠢⣄⠀⠀⠀⠀⠀⠀⡨⠷⠾⣄
⠀⠀⢴⡚⠂⠀⠀⠀⢻⠃⠀⠀⠀⢸⡕⠀⢄⡀⠀⢀⣠⠒⢁⣼⠀⠀⢀⡴⢇⣻⠀⠀⣀⣴⣾⣿⠆⠀⠀⠀⡴⠋⠀⠀⠀⠀⠳⡀
⠀⠀⠀⢹⠓⢄⠀⠀⠈⢳⡀⠀⠀⠸⣧⣄⠀⠈⢙⠁⣀⣴⠟⠋⠀⠀⣸⣻⣦⣤⣴⡞⣣⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢼⣀⣈⣆⣀⣤⠾⠁⠀⠀⠀⠀⠙⠻⢶⣶⣶⠞⠁⠀⠀⠀⠀⠈⠙⠾⣽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⢀⢀⡞
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣠⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠘⣇⣀⡼⣏⠀⠀⠀⠀⢰⠛⢦⣀⣀⡀⠀⠀⠀⣠⢶⡄⠀⠀⢀⡤⠖⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢀⡿⠛⣧⣞⣲⣦
⠀⠀⠀⠀⠀⡿⠙⡇⠈⠀⠀⠀⠀⠈⣧⡾⠀⠈⠉⠉⠉⠉⢧⢸⠇⠀⠀⠙⡟⠒⠶⠶⠶⠒⡿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⡄
⠀⠀⠀⢠⣎⠀⠀⢙⡆⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢻⠢⠤⠤⠴⢺⡇⠀⠀⠀⠀⠀⢸⡏⠈⠉⠉⠁⠹⡇
⠀⠀⠀⢸⣇⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠈⠳⠤⢤⡤⠞⠀⠀⠀⠀⠀⠀⢫⠢⠤⠤⠤⠤⠒⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠕⠆⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⡏⢡⡀⠑
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠉⠒⠉⠉⡠⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢐⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⢠⠂⠂⠒⠀⠀⠀⠀⠀⢤⢀⡗⠈⠢⠤⠄⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠉⢀⠽⡽⠋⠒⠂⠀⠀⠀⠀⠤⠐⡇⠀⠀⠀⠀⠀⠀⠈⠆⢄⠀⢄⢀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠲⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢠⡃⠀⢱⠂
⠀⠀⠀⠀⢬⠇⠀⠀⠀⠀⠀⢸⠌⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡶⢫⣜⠒⠊
⠀⠀⠀⠀⠂⠲⢁⠀⠀⠀⠀⠇⠀⠠⠒⠎⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡰⠡⠃⠀⠉⡆
⠀⠀⠀⠀⠀⠃⠈⡄⠲⠀⠴⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠰⠖⡐⠠⠁⠀⠀⠠⠁
⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⡰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠏⡐⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⡠⠄⠒⠀⠈⠀⠈⢸⠄⠀⡠⠂⢸
⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠀⢀⠼⠠⣀⣀⡀⠀⢠⡁⠊⠆⠀⠠⠀⠀⣉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠄⠆⠄⠀⠀⠀⠀⠀⢶⣿⢏⣀⡀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣺⣀⠀⠀⠀⠀⠀⢰⡶⠶⠶⢶⡆
⠀⠀⠀⠀⠠⠅⣾⣿⠎⠥⠀⠀⠀⠀⡏⢱⣿⡆⢹⠀⠀⠀⠀⠀⣻⡥⣩⡇⠀⠀⠀⠀⠱⡶⢵⣛⣦⢴⠎⠀⠀⠀⢸⡇⠂⠐⢸⡇
⠀⠀⠀⠀⠀⠁⠆⡅⠎⠁⠀⠀⠀⠀⠳⣄⣀⣠⠞⠀⠀⠀⠀⢠⡿⠿⠿⢧⠄⠀⠀⠀⠀⠸⠿⠃⠯⠏⠀⠀⠀⠀⠘⠿⠶⠶⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠠⡰⢠⣄⢆⣤⠶⡀⠀⠀⠀⣀⡴⠒⢦⡀⠀⠀⠀⠀⢠⢾⡷⠉⢳⡄⠀⠀⠀⢀⣴⡿⣛⣿⣦⡀⠀⠀⠀⢀⢻⠽⡮⡿⡀
⠀⠀⠀⠀⣹⡇⢸⣯⢀⣿⡁⠀⠀⢰⠃⠀⠀⠀⢉⡇⠀⠀⠀⢳⠈⢰⣦⢀⡇⠀⠀⠀⠀⣿⠲⠻⣌⡇⠀⠀⠀⠀⠠⠽⢭⡯⠯⠅
⠀⠀⠀⠀⠃⠘⠋⠘⠚⠀⠃⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠑⠚⠓⠊⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠚⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⡤⠤⡀
⠀⠀⠀⠀⠀⠰⢻⣷⣀⠀⠀⠀⠀⠀⠀⢴⡞⠦⠀⠀⠀⠀⠀⢿⣆⣀⣀⣸⠷⠀⠀⠀⢰⣿⡋⠉⢹⣿⡀⠀⠀⠀⠀⣼⣀⣀⣵
⠀⠀⠀⠀⠀⠀⢨⢳⡀⠀⠀⠀⠀⣞⠉⣧⠹⣞⠉⣣⠀⠀⠀⢘⣯⣿⣿⣽⠀⠀⠀⠀⠘⢿⣿⣿⣽⡿⠀⠀⠀⠀⠀⣯⣿⣿⣽⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⢠⣤⣼⣽⣤⣤⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⡄⠀⠀⠀⠀⠀⢀⣤⢶⡄
⠀⠀⠀⠀⠀⣿⢏⣍⢻⡇⠀⠀⠀⢀⢿⣶⠦⣶⣷⠀⠀⠀⠀⢠⣀⣿⣿⣠⡆⠀⠀⠀⢰⣿⠇⠉⢻⣷⠀⠀⠀⠀⢠⡮⠁⠈⢫⣄
⠀⠀⠀⠀⠀⢻⣌⣫⣾⠁⠀⠀⠀⠨⡿⠷⠲⠿⢿⠀⠀⠀⠀⠼⠥⠼⠧⠬⠯⠀⠀⠀⠀⠉⠇⠀⠟⠉⠀⠀⠀⠀⠙⠵⠆⠴⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡸⣆⣇⡇⠀⠀⠀⠀⠀⢀⡀⠀⣤⣤⡄⠀⠀⠀⠰⣆⠐⠿⠀⠀⠀⠀⠀⠴⢤⠤⡒⠤⠴⠄⠀⠀⠀⠀⠰⢶⡶⠆
⠀⠀⠀⠀⠀⢿⡿⠻⣧⡴⠃⠀⠀⠈⠻⠿⠖⠛⠋⠀⠀⠀⠀⠀⠉⢻⣿⣿⡆⠀⠀⠀⠰⣨⣍⠉⣩⣡⠆⠀⠀⠀⢸⣶⣾⣷⣶⡄
⠀⠀⠀⠀⠀⠘⢧⢀⠟⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⠉⠛⠐⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣸⠆⣴⣼⣧⣠⣶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⠿⣿⠾⣿⢏⠑⠎⣵⣿⡇⣴⢖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠎⠛⠿⢃⠲⣶⣶⣭⣾⣧⣆⠻⣫⡄⣠⣿⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣻⡗⣼⡇⢿⣧⣩⡻⠿⡻⡭⠯⢸⣿⠟⠿⠛⢅⣻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠎⠻⢿⢯⡴⣶⣿⡾⣃⣾⠇⣿⣠⣾⣋⣾⠃⢸⣿⡿⠋⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣿⣃⣛⣦⣄⣿⣄⣚⡷⢿⡇⢦⣿⣋⣤⡼⢿⡷⢏⣿⡃⠸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠹⠿⠟⠰⠟⠀⠈⠙⠿⣿⣿⣿⣿⠛⠁⠀⠈⠉⠈⠻⠿⠄⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣿⣫⣤⣾⣾⣋⡛⠛⠲⢶⣿⣷⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣦⣿⣿⣿⣿⡿⢎⣡⣄⠀⠀⠀⠙⢿⣿⠋⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣾⣿⣿⣿⣿⣿⣿⠗⠈⠉⠙⠛⠛⠃⠀⠀⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠱⣄⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣀⠀⠀⠀⠀⠈⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣾⣿⣿⡇⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣠⣟⣿⣿⠃⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢺⣿⣿⡄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠉⠹⢿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠛⠻⢿⣿⡋⠛⠻⠟⠻⢟⣻⡿⠟⡧⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⣿⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠐⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢰⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⣦⢤⡀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠓⠳⡀⣾
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⣀⠇⠀⠀⠘⣏⠀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡤⣄⡀⠀⠀⠀⠀⠀⠀⣸⠘⠦⡤⠔⢒⣿⣇⢀⡀⠀⢸⡇⢰⣙
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠼⠤⠀⠈⢉⠋⠉⣩⣿⣯⠀⠀⠰⡀⠀⢿⣿⣿⢸⡘⡄⢸⡇⢠⠏⠀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠢⣄⠀⠀⢠⠀⠀⢿⣿⣿⠀⠘⢒⠕⠂⠄⣛⡟⠀⠙⢇⣾⡷⣃⠼⠭⠋
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠙⣄⠀⠀⠑⠂⠀⢛⡁⠀⣄⢁⠆⠐⠀⣴⠁⠀⠀⠈⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⠀⢀⣀⡨⢦⠀⠀⠠⠈⠀⠈⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⠒⠤⠤⠤⠤⠤⠤⢶⠛⠒⠒⠒⠒⠒⠘⡏⣤⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⠷⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⠑⠤⣀⠀⢸⠖⠒⠒⠊⠉⠁⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⡀⠀⠀⠀⠀⠈⠉⠚⠲⠤⡴⠊⠷⢴⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⠀⠀⠀⣷⠀⠀⢩⡾⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡏⠉⠉⠉⠉⠉⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢄⣀⣀⣀⣀⠤⠤⠤⠖⠒⠴⠧⣀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⢀⡤⠺⠉⠉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠿⠋⠉⠉⡇⠒⠂⠉⠉⠉⠀⠀⣀⠜⠀⢠⠊⠀⠀⠀⠀⠀⠀⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⠶⠦⠐⠒⠧⠤⠤⠤⠤⠒⠒⠉⠁⠀⠀⠘⠒⠒⠤⠖⠒⠢⠒⠂⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⢰⣧⢀⣤⢰⣟⣄⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡃⣼⣿⡧⠿⢃⡿⠟⣡⣶⡎⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⣿⣷⣶⣿⠍⠛⠿⠋⠻⣿⢣⡄⠈⠃⣾⣿⣿⠇⡚⢛⣥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠳⡙⠛⠿⢋⠈⢻⣿⣿⣷⣦⣿⣿⢰⣆⠹⠛⣡⡖⢀⣿⣿⣥⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⣿⣷⣀⣾⡇⢸⣷⡄⠙⠿⣿⣿⡿⡟⣹⣟⠀⣾⣿⠗⣿⣿⠿⡣⠾⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⡟⢷⣶⣷⣤⠿⠃⢈⣻⣟⢸⣧⢀⣠⡆⢻⡅⠉⢀⣿⡯⣠⡆⠀⢨⣴⣾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢾⣧⡝⠄⣙⠿⠟⢷⡛⠿⣿⣿⠟⢧⣸⣿⠇⢸⣿⣴⣿⣥⣴⣻⡁⠀⣼⣻⣟⣋⣀⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⡟⣒⡛⢦⣄⣀⣿⣆⣀⠻⣿⣾⣿⡔⣦⣼⣿⢋⣀⣠⣾⣭⣷⠿⢋⣷⡶⠀⠸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠿⢋⣾⣿⡿⠉⣽⡿⠉⠙⠛⢿⣷⣦⣿⣧⣼⣿⣿⡿⠛⠉⠀⠘⠻⠗⠻⣿⣿⣆⠀⠙⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠛⢛⣿⣿⣿⠿⢷⣦⣤⣀⣀⣤⣤⣤⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢹⣶⣷⣾⣿⣿⣿⢻⣥⠴⠆⠀⠀⠉⠛⢿⣿⣿⣿⣿⢦⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣤⣷⣾⣿⣿⣿⣿⣿⡿⠇⣠⣤⣤⡀⠀⠀⠀⠀⠙⢿⣿⡏⠀⠸⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠚⠉⠉⠛⠿⠿⠶⠆⠀⠀⠈⠻⣆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢲⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠈⠓⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣾⢡⣿⣿⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⠀⠀⠀⠟⠛⣿⣿⡄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃⠙⠉⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⠁⠙⠻⢿⣟⣉⡈⠉⠛⠛⠙⢛⣋⣹⣿⠟⠛⠵⠂⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⡏⢻⡏⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⡄⢀⠀⢠⡀⠀⠀⠀⣀⢀⣀⡀⠀⡔⠸⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠄⠈⢻⠀⠈⢁⠆⠈⠢⡀⡎⠀⠁⠀⠈⠤⡣⢤⠤⠃⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠉⠀⠀⠣⢄⢸⡄⢠⣊⠀⠀⠀⣬⠇⠀⠀⠀⠀⠀⡄⠠⡒⠈⠀⠀⡄⠀⠀⠤
⠀⠀⠀⠀⠀⡔⠀⠈⡀⠘⠁⠀⠀⠀⠀⠀⡈⡆⠀⠌⠀⠀⠀⠀⢑⠤⠀⠀⠀⠠⣘⠂⠁⠀⠀⢠⢀⢀⠀⠄⠔⠀⢀
⠀⠀⠀⠀⡎⢀⣀⠄⠀⠐⢢⠀⠀⠀⠀⣀⠃⣙⣁⠰⠦⠄⠐⠚⠓⠀⡤⠄⡤⠚⠠⡉⡢⠀⠀⠘⡆⢉⠦⠄⣀⡤⠊
⠀⠀⠀⠀⢈⠁⠀⢒⠀⠠⢈⡂⠀⠒⣏⠤⠒⠉⠀⠀⠀⡠⠀⠀⠐⠊⠀⠀⠈⠦⠬⠠⢇⡀⢩⠙⠫⡌⢀⡴⠋⠑⡀
⠀⠀⠠⠀⢀⢑⡀⠀⣆⡠⠜⠀⡩⠋⠁⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⢠⠂⠀⠀⠀⠀⠀⠘⡡⠉⡠⠷⡛⠉⢨⠁⠃⠄⡀
⠀⠀⠁⠀⠀⠈⠄⠉⠹⠆⠖⠺⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⡱⠄⢠⣣⡀⠃⢄⠂⠀⠁⠀⠐
⠀⠀⢀⣐⣾⠧⡈⡖⠁⢰⢈⢀⠇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡠⠁⠀⠣⠤⠔⠈⠐⠒⠈⠀⡌⠀⠀⠑⣀⠎⠀⡠⠬⣧⣆⡀
⠀⠀⠈⠫⡅⢐⡽⠐⣤⠁⠀⠀⠀⠀⠔⠁⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠘⠀⠀⢯⡆⢨⠝⠁
⠀⠀⠀⠀⢀⠨⡀⠀⡅⠀⠀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢃⠀⢀⠇⡌
⠀⠀⠀⠀⠀⢂⠈⢰⡄⠀⢘⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄⠁⠢⢄⠀⠀⠘⠔⠃⡔
⠀⠀⠀⠀⠀⠀⠑⢼⠈⠂⡈⠂⠄⣀⠀⠸⠦⣀⣀⠠⠎⠀⠀⠀⠀⠀⠀⠈⠦⢀⣀⡠⠎⡠⠤⡀⠀⠑⡀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⢂⠀⠀⠀⠈⠀⠀⠀⠀⢃⢀⠀⠀⡀⠀⠀⠀⠀⠔⠀⠀⠈⢂⢀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠑⠠⠄⡀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠢⢀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠆⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢁⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠐⠤⠤⠀⠠⠤⠤⠂⠒⠈⠁

⣟⣿⣿⣻⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣟⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠓⠦⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⣝⠻⠖⣲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠞⠀⠀⠀⣠⢾⡷⡾⢀⡜⠙⣆⠀⠉⢫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣃⠀⢀⡠⢞⣁⠀⠀⠷⠋⢀⣀⠘⢆⣦⢀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⡹⡴⠋⠀⠈⠈⠁⠀⠀⠀⠈⠈⠀⠈⠙⡶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇⠀⠀⠀⢠⠄⠀⠀⠀⠰⡦⠀⠀⠀⡟⠱⡄⠀⢀⠜⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣇⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡷⠚⢁⡴⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠢⣤⠔⠀⠀⠀⢀⡴⠓⠋⠻⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣀⣀⣀⣀⣠⣤⡖⠻⡇⠀⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢙⠲⠋⠀⠳⠋⢘⡶⡹⠓⠒⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⢸⡀⠀⡠⠔⠶⣯⢾⣁⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠙⠲⣇⠀⠀⣸⠘⡍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢤⣀⠜⡽⠋⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⣄⣀⠀⠐⣏⠙⠒⢢⠀⠀⠀⠀⠀⣿⣷⡶⣫⣾⣶⣶⣶⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠉⠰⢧⡐⢥⡄⣰⠇⢀⣤⢖⠒⠒⢿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡀⠀⢀⣠⠇⠀⠉⠁⡴⠋⠘⠦⣳⢄⠀⠹⡟⢻⠛⠉⠛⢿⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠱⠤⠞⠁⠀⢀⡤⢊⠀⠀⢀⠀⠉⠻⣷⣤⠇⢸⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣔⠋⠀⠀⠀⡸⡏⠉⢹⡀⠀⠀⣸⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠴⣗⣋⣉⣹⠇⠀⠀⠿⢝⣛⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠑⠢⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠔⠀⠀⠠⣀⡄⠀⢠⠒⠀⠀⢠⡒⢒⡄⠀⠀⣠⠒⠒⠒⠒⠒⠲⠂⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡠⠾⡀⠀⠀⡄⠀⠈⠲⡇⠀⠀⢠⠀⠀⠀⡴⣁⢢⠉⠈⠉⠁⠲⢄⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⡉⠆⠀⡍⠀⠀⠀⠰⡀⠀⠈⠐⠓⠀⢬⡤⠔⠃⠀⠀⡘⠀⠁⡏⠀⡀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢄⠀⢀⢶⡷⡤⡗⠈⣀⢀⡜⢀⡀⢠⠀⣜⠀⢸⠤⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠈⣣⣄⣰⡀⡀⠀⠈⠀⠀⠀⣀⠀⠄⠓⡷⢄⠹⠧⠖⠉⠈⠁⠑⠼⠀⠂⠐⢇⣔⡋⠀⠲⠐⠂
⠀⠀⢀⠤⣀⠀⠈⠁⠀⠀⡉⠝⢣⡀⡖⠒⢊⢁⡠⠄⠒⢈⡡⠤⠤⠒⠐⢠⣀⠀⡀⠀⢹⠀⡠⠊⠀⠘⠁⠒⢂⡀⢀⣀⡀
⠀⠀⠓⠒⠊⣖⠉⣉⠇⣈⢄⣀⠠⢵⠓⠨⠀⠊⠑⠀⠀⠈⠂⠤⡀⠀⠀⡜⠀⠀⠈⠉⢁⡈⣧⡤⡆⠀⠀⢎⠁⠀⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠉⣠⠎⡁⠄⠁⣞⣻⠀⠈⢂⣠⠎⠀⠀⠀⠀⠀⢡⠀⠘⠀⠀⠀⠀⠀⠉⢑⡤⢤⢾⡁⠀⠘⠀⠤⠀⠄⠸
⠀⠀⠀⢀⣠⠀⢄⢣⠀⡤⣄⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠰⢄⠠⠐⠒⠠⠐⠁⢰⠉⠀⠑⡄
⠀⠀⠀⡣⠀⡐⠲⠤⠿⡶⠊⠀⠀⠀⠠⠂⠉⠀⢉⠁⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⡄
⠀⠀⠀⠣⠜⠀⠀⠀⠰⠀⠀⢀⠤⠤⠃⢠⠄⠃⠈⠘⠳⢆⠀⠀⠀⠀⢀⠄⠛⠈⠑⠣⣄⠀⡔⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠃⠀⠀⠀⠎⢠⣾⣿⣿⣦⠈⡆⠀⠀⠀⠇⢠⣾⣿⣿⣦⠈⡄⠑⠢⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⡀⠑⠤⠀⠠⡄⠘⣿⣿⣿⡿⠀⡆⠀⢄⠀⡄⠘⣿⣿⣿⡟⠀⠗⠤⡀⠀⢱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡗⢄⠈⠂⠀⠀⣀⠈⠢⣀⡉⢉⡠⠊⠀⠁⠀⠁⠘⢤⣀⠉⢁⠠⠊⠀⣀⡀⠁⠁⢀⠞⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠑⠢⠤⠊⠘⣀⡠⠀⠙⠤⢄⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣀⡐⠈⠐⠈⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠒⠂⢤⡀⣀⠭⡔⠂⠀⠀⠀⠀⠑⡄⠀⠀⢠⠀⠀⠀⠀⠀⠰⣭⢔⡀⡠⠊⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠳⡚⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠱⢀⠀⠀⢀⡀⠉⠁⠊⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢁⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠔⠊⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠧⠀⢀⣀⠀⠠⠼⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡀⠠⠄⡀⠀⠀⠠⠀⠤⠀⠠⠀⡐⠐⢂⠐⣆⠐⢀⠀⠀⣂⣑⠦⠀⠠⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣀⡍⢘⢶⠌⠉⠍⠫⢝⠒⡒⢁⡥⠤⠖⠢⠗⠢⠖⠀⢉⠉⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠈⢻⣾⢝⠀⣀⢀⠀⡈⢍⢉⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⣀⠠⠄⠀⠁⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠈⠀⠀⠀⠀⠈⡀⠀⠻⠈⠈⠙⠉⠋⠅⢀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣀⠀⠰⠷⠀⠐⠶⠃⠨⠄⠁⠂⠐⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠈⠠⠀⠀⠀⠰⠲⠚⠀⠀⠀⠄⠀⠈⣀⣀⠂⣉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈⠀⣦⢀⠘⣑⠢⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⠤⠠⡆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠉⠀⢠⢈⡌⠀⢀⣀⠊⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠀⢨⡶⠓⣃⢄⠀⠀⡀⠀⠠⠠
⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠹⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠓⠒⠆⠀⠂⠠⠇⠀⢈⠀⠡⠀⠀⠀⠀⠄⠀⠀⠁⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⣖⠲⣄⠐⠀⠐⠀⢀⠄⠼⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠑⠄⠀⠒⠊⠀⢀⠄⠀⠀⠑⠀⠠⠀⡄⠀⠀⠁⢢⢰⡏⠐⠈⠀⠉⢙⡃⠲⡀⢄⣠⡄⣐⠐⠂⣀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⢀⡀⠀⢌⡁⠠⢄⠀⠀⠀⠀⠀⡁⢠⠀⠀⣄⠀⠀⠁⠀⢲⡏⢙⡀⠠⣙⠐⢒⣄⡀⢀⡐⠹⠉⠒⠫⠜⠡⡤
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠈⡇⠂⣬⠀⠀⠀⠁⠀⠀⠒⠈⠃⠀⠀⠀⠀⠦⠀⠀⠠⡦⠀⠀⣖⠀⠉⠉⢑⣶⡌⠉⡀⠀⠠⢘⠐⠅⣴⠀⡈⠑⡀⠂
⠀⠀⠀⠀⠀⠀⠀⡂⠀⣸⡀⢰⠀⠖⣧⠀⠟⡄⠀⠀⠈⠉⠀⠀⠘⠀⣀⠀⠐⠆⠀⠈⠀⢀⡄⠀⠂⠀⡤⠹⠀⡮⢬⡀⠒⢥⡀⢠⠙⣝⢢⡀⢀⡛⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠘⠆⢰⣃⣰⣲⣾⣶⢀⠠⠀⠀⢛⠂⠀⡐⠄⠀⠈⠀⠀⢀⠀⠀⠠⠄⠐⠂⢀⡀⠁⠄⠄⠐⠈⠇⠁⢈⠠⠄⠈⠉⡀⣈⠺⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠨⠀⠈⠉⢉⠁⠀⠈⠘⠀⠀⠀⠸⠂⠀⡶⠀⠄⠒⠓⢠⡤⡜⠋⠕⠁⠀⠀⢀⣼⠀⡒⠤⢠⠰⢤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣤⠀⠬⠀⠀⠁⢁⣄⡄⣴⠆⠀⡶⠦⠀⠁⠓⠀⠀⠀⢘⡂⠊⣠⠂⠀⠀⢠⠏⢀⠐⠬⣀⠘⠀⠰⠆⠈⠵⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠋⡘⡍⢀⠀⠁⢠⠀⠀⠀⠆⣤⠇⠀⠀⠹⡄⠀⣰⡽⢃⠐⠤⡉⠓⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⣲⠾⠏⠀⠈⠀⠀⠀⢠⠈⢀⢭⠑⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠐⠊⠁⠀⠀⠀⠀⠀⠀⠔⠉⠀⠘⠓⠂