Water sport Emojis & Symbols

⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⢠⡿⠿⡝⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠁⣀⡀⠀⠀⠀⠀⠀⠒⠛⣿⡓⠻⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢡⣀⣀⡀⠀⠀⠀⠀⠀⢸⡗⢄⣀⡀
⠀⠀⡀⠤⠤⡿⢠⠣⠤⡀⠀⠀⠀⠀⣠⣤⣬⣝⣛⣻⣃⠀⠀⠀⠀⠀⣀⡰⠯⠷⠀⠀⡀⠀⠀⠀⢰⢴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣺⣾⣛⣺⣿⣟⡆
⠀⠀⠁⠀⠀⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠈⠁⠈

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⣂⠱
⠀⠀⠸⠏⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢺⣮⠄⠰⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠛⠂⠀⠀⠀⠀⠀⠀⠎⣥⠒⣿⡷
⠀⠀⠀⠀⠀⠐⢻⣟⡂⠀⠀⠀⠀⠀⠀⡘⣿⡿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣝⠳⠀⠀⠀⠀⠀⢀⣀⣼⣧⢤⣤⠀⠀⠀⠀⠀⠀⠀⢈⡿⠯⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠑⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡬⢷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⢄
⠀⠀⠀⠀⠠⡾⡟⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡿⣿⣶⣦⠀⠀⠀⠀⣠⣼⣟⢊⣰⣟⣻⣄⠀⠀⠀⢀⣀⣀⣸⣛⣖⡈⠀⠀⠀⠀⠀⠠⣶⣶⣶⣦⣤⣤⣥
⠀⠀⠀⣐⣈⣤⡴⡶⠧⠀⠀⠀⠀⠀⠀⢰⠇⢻⠀⠀⠀⠀⠀⠀⠀⠛⠛⠫⠟⠛⠛⠛⠛⠀⠀⠀⠈⠻⠟⠛⠿⠟⠛⠂⠀⠀⠀⠀⠙⠋⠙⠿⠿⠿⠋
⠀⠀⠀⠈⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠴⠧⠂⠀⠀⠀⠀⠀⠀⣴⣾⡿⣋⢉⡄⠀⠀⠀⠀⠀⠛⠶⣿⠇⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⠀⢀⣤⡀
⠀⠀⠀⠀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠸⢹⣿⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⡙⠃⣀⠀⠀⠀⠀⢀⣀⣻⡿⣏⣿⣿⣟⠁
⠀⠀⠀⠶⠿⠶⠿⠷⠖⠀⠀⠀⠀⠀⠠⡤⠟⠛⠚⠛⠁⠀⠀⠀⠀⠀⠈⠛⠷⠉⠍⠠⠄⠀⠀⠀⠀⠰⣈⠉⠩⠑⠂⠁⠀⠀⠀⠀⠉⠹⠿⠋⠙⠉⠉⠁


⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣹⡅⠀⢀⣀⡀⠀⠀⠀⠀⠐⠊⠳⣄⣸⣿⣦⡔⠀⠀⠀⠀⠀⠀⣠⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⢘⣌⣢⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣶⣟
⠀⠀⢰⣉⣛⣞⣉⣙⣏⠀⠀⠀⠀⠀⡴⠉⢋⠉⢻⡷⡶⠀⠀⠀⠀⣾⣶⣯⣄⣼⣤⣶⣷⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⡼⠉⣹⠟⠀⣩⣬⣁
⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠈⠈⠁⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠃⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣤⣤⡇⡁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡠⠃⠀⠀⠀⠌⡃⠈⠁⠋⠐⠿⠶⣶⣾⠗⠀⠀⣶⣃⣲⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⢀⡀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢾⣤⣤⡇⠈⠀⠀⠀⡠⠞⢉⡝⢀⠞⠤⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠎⠸⣗⣠⢟⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⡵⢦⠐⡠⠔⠁⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡲⠅⠈⠀⠀⠀⠀⠀⢺⠇⠀⠀⣀⡲⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⠳⣌⠱⢄⠀⠀⠈⢶⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣦⠞⠉⣀⣍
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀⣠⣤⣠⡀⠀⠀⠀⠀⠀⠸⡅⠀⠈⠳⠀⠙⢦⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣍⣸⣗⢒⢉⣿⡏
⠀⠀⢀⣠⠟⢹⠓⠶⠖⠰⠶⢶⣶⢾⠎⡄⠀⡀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠸⢿⡇
⠀⢦⠈⠙⠒⢃⠀⠖⠶⠠⠤⠾⠶⠯⠚⠁⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠚⠚⠛⠲
⠀⠀⠑⠒⠀⠀⠀⠳⣤⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⣴⠃⠀⠀⠀⠀⢐⠉⢉⢹⠋⠀⠚⡿⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠒⠈⠙⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⡨⠉⠐⠒
⠀⠀⢀⠄⠀⢉⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠉⠄⣰⣄⠀⠖⡀
⠀⠀⠇⠀⠀⠀⠀⢱⠀⡂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠒⠂⠀⠀⠀⠝⠒⠂⠀⢀⣀⣠⠄
⠀⠀⣄⠘⡀⠀⢀⠄⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠄⠈⡁⠀⠀⠀⢳⠶⠆⠤⠤⠶⠖⠒⢚⣻⡿⠿⠛⠁
⠀⠀⠈⠀⠠⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠐⠖⠀⠀⠖⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣻⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢃⣭⡋⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀
⠀⠀⠀⠈⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠸⠿⠇⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣠⣬⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠲⠘⠂⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣥⣤⣤⣦⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣶⣆⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠦⡼⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⣿⣭⣱⣿⣿⣀⣀⣀⣀⣠⣠
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⣶⣶⣤⣤⣘⣿⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣀⣀⣀⣀⣀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡀⢸⡄⢸⣅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣤⣴⣾⣷⣦⣤⣤⣤⣤⣀⣀
⠀⣠⣤⣤⣤⣀⣤⣶⣶⣾⣿⣾⣿⣾⣿⣶⣶⣾⠟⠀⠀⠀⠀⠀⢀⣤⣠⣤⣀⣀⣶⣴⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⡀⠀⠀⢀⣯⡀⣤
⠀⠀⠀⠀⠀⠀⠘⢶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⣩⣭⣤⣤⣬⣷⣤⣿⣦⣤⣤⣤⣤⣶⣶⣾⠿⠃
⣤⣤⣾⣿⣿⣿⣷⣶⣮⣷⣶⣯⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣷⣶⣤⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣅⣅⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠩⠑⠤⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠈⠉⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⢀⡀⠠⠐⠈⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡈⠀⠰⠁⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠓⠤⢆⡀⠀⠀⠀⠀⣠⠞
⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡇⠀⠀⠀⠁⠀⠒⠀⠤⠠⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⣶⣶⣆⠀⢠⡞⠉⢀⣀⠀⠀⠄⠤⠀⠂⠀⠈
⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣤⣀⣀⣀⣸⣿⣿⠏⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂
⠀⠢⡀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢀⡼⠁⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠉⠀⠀⠀⢀⠔
⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠦⠤⠤⣤⣤⣤⡄⠀⣰⢿⠤⠴⠶⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠁⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠠⠄⠀⠀⣀⡠⠂⠀⠈⠁⣐⣁⠀⠀⠠⠄⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢴⡀
⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠈⠘⣧
⠀⠀⠀⠀⠀⡇⠘⣧
⠀⠀⠀⠀⠀⡇⠀⠘⣧
⠀⠀⠀⠀⣀⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠉⡇⠙⠛⠛⠙⣧
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠐⠻⠐⠦⠤⠤⠴⠖⠂⠹⣧
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⡇
⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠢⠇
⠀⠀⢩⠁⠈⠒⠲⠤⠤⠤⠶⠖⠚⠉⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠈⠁⠀⡶
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⠀⢀⣄
⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢀⠜⡀⠀⠀⢩⠀⠑
⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠤⠀⠒⢁⠔⢣⠀⠀⠀⣷⡄⠠⡀
⠬⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⡶⠶⠛⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠆⠐⡄
⠀⠀⠉⠑⠠⠌⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⢇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠄⠀⢀⠄⣰⠏⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⠀⠀⣆⠄⢠⡞⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠢⢄⠀⠀⠀⠀⢻⡌⢀⠘⡂⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⠤⡀⠈⢿⣆⣻⣙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⢮⣿⣏⡻⡶⠖⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣾⣿⣷⠤⣘⠛⠻⠆⠉⠐⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⢄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠳⣤⣀⣀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⠀⠀⠉⠙⠓⠲⢦⣀⠙⠦⣤⣤⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣲⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠛⢦⣀⠀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠳⣤⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⠳⢤⡀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⣿⠀⠀⠙⣆⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⣀⡤⠶⠃⠀⠀⠀⡇⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣤⢤⣤⣀⣷⣄⣤⠴⠒⠉⠁⠀⠀⠀⠀⠀⢸⠃⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠘⢧⣄⣀⡀⠈⠉⠉⠙⠛⠓⠲⠶⠤⠤⣤⣄⣽⣀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠙⣳⠶⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠶⠶⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠥⠤⠶⠚⠁⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠲⠶⠶⠤⠤⠤⣤⣤⣤⣀⣀⣀⣈⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⣤⡤⠴⠞⠋⠉⠉⠉⠉⠙⠓⠦⢤⣤⣤⣤⡤⠶⠛⠉⠉⠉⠉⠉⠙⠲⠤⣤⣤⣤⣤⠴⠞⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠠⠤⠴⠖⠋⠉⠀⠀⠀⠀⠉⠙⠓⠶⠤⠤⠤⠶⠚⠉⠁⠀⠀⠀⠈⠉⠛⠲⠦⠤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠰⠶⠶⠚⠋⠁⠀⠀⠀⠀⠈⠉⠓⠲⠶⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠶⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣶⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣉⡛⠒⠖⢛⣉⣭⣭⣙⠻⣿⠚⣋⣩⡅
⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠉⠛⣿⠛⠉
⠀⠀⠀⠀⠀⢿⣿⡿⠃⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠿⠷⢤⡀⣿
⠀⠀⠀⠀⠀⠀⣰⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⢀⣿⣿⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⣦⡀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⣼⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠾⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣬⣧⣄⠀⣠⣿⣿⣿⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣿⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣿⣥⣿⣿⣿⣿⣿⣟⣉⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠻⣿⣿⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⣼⣿⣿⣿⡆
⠀⠠⣶⣚⠋⠉⠉⠀⠀⣿⠏⠀⠟⠋⠉⠀⠀⠀⠈⠉⢻⡆⠀⠀⢼⡟⢹⣿⣿⣿⠀⠈⣿⣿⣿⢸⣿⣿⡇⠀⠀⢠⣶⡿⠟⠛⠻⣿⣿⣷⣦⣄⠹⢿⣿⠿⠃
⠀⠀⠀⠉⠉⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠛⠉⠀⠀⠀⠀⠀⣾⣿⢻⣿⠀⠀⢿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠁⠀⢠⣴⡿⠟⠛⠻⢿⣿⣷
⠀⢈⣛⠓⠶⣤⣤⣤⡴⠞⢛⣛⡛⠳⠦⣤⣤⣤⠴⠞⢛⡃⠀⠀⠀⠀⣿⣿⢸⣿⡀⠀⠘⣿⣿⢸⣿⠏⠀⠀⠀⠛⠳⠦⣤⣤⠴⠞⠛⠛⠶⢤⣤⣤⠶⠛⠃
⠀⠈⠉⠛⠲⠦⣤⡤⠶⠛⠉⠉⠉⠛⠶⢤⣤⡴⠶⠛⠉⠉⠀⠀⠀⠀⠻⠿⠸⠿⠁⠀⠀⠘⠿⠸⠋⠀⠀⠀⠀⠙⠛⠶⠤⠤⠶⠛⠉⠙⠳⠶⠤⠴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣥⣤⣤⣤⣤⣤⣤⣤⢤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠙⠛⠻⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣍⡉⠁⠀⠀⠀⢠⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣄⣠⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡇
⠀⠀⢰⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣀⣤⣤⣤⣤⡤
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⢀⣀⣀⡉⠉⠉⣉⣽⣿⠋⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠛⠛⠛⠋⢉⣉⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⢠⣬⣍⠙⢃⣾⣿⣿⠏⢈⣩⣥⣤⣍⣙⠛⠶⠶⠶⠚⣋⣩⣥⡄⠀⠀⠀⠀⠀⣨⣭⣉⡛⠳⠶⠶⠶⠛⣋⣉⣥⣬⣍⣙⠛⠳⠶⠶⠞⠛⣉⣩⣥
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠃⠘⠋⠁⠀⠀⠀⠉⠛⠓⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠒⠛⠉⠁⠀⠀⠈⠉⠛⠓⠶⠶⠚⠛⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⠛⠻⠿⠻⠿⠿⢿⠛⡹⠿⠿⠿⠿⠛⠿⢿⠟⠻⣿⠛⠿⠿⠛⠙⠿⠋⠛⠋⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠤⠤⠤⠤⠄⠤⠿⠄⠄⠠⠤⠠⠤⠦⠤⠼⠤⠤⠧⠤⠤⠨⠄⠤⠤⠤⠤⠤⠄⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⣿⢀⣿⢀⡟⢨⣧⠀⠀⠚⠚⠛⠛⠛⠛⠛⠀⠀⠀⣠⣈⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠠⣶⣶⣮⣿⡅⠀⣠⣶⣿⣿⣷⣦
⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⣤⠀⠀⠀⠶⣾⣿⣿⣿⣿⣤⡄⠀⠀⠻⠶⠴⣤⡄⠀⠀⡈⠉⠙⠛⠛⠀⠙⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣀⡤⠤⠔⠀⠀⠀⠀⠀⠰⠛⣿⠐⠀⠀⠈⢉⡉⠉⠉⠛⠁⠀⢀⣤⠀⠀⠀⠀⠀⠈⠿⣦⠀⠀⠀⠀⠀⡀⠈⠛⠻⠿⠇
⠀⠀⠀⢠⠞⠁⠀⣀⡀⢀⣴⣶⣶⡄⠀⢸⣯⣀⠀⠀⠀⠈⣿⣶⠀⠀⠀⠀⠀⢛⡇⠀⠀⠀⠀⠀⠰⣭⡤⠀⠀⠀⠀⠁
⠀⠀⠀⢀⣠⠖⠛⠉⠀⢸⣿⠃⠘⠃⠀⠀⠈⠉⠀⠀⠀⣀⣨⡭⠶⠖⠀⣀⣀⣭⣤⡤⠆⠀⣀⠀⠛⠋⠀⠀⠀⢠⣾⠃⠀⠐⠛
⠀⠀⠀⠋⠀⠀⠀⢰⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⢠⠀⠀⠀⠀⠀⡀⠀⢀⣀⣤⣤⣹⣄⠀⠀⠀⠠⠋⠛⠉⠀⠈⢠⠁⡀
⠀⠀⠀⠀⠀⠀⣬⠿⠁⠀⠀⡀⠀⠀⠀⠀⣠⡾⠿⠀⠀⠰⣾⡆⠀⠀⠀⢼⣧⠀⠈⠻⠿⠿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⢂⢋⣹⠃
⠀⠀⠀⠀⠛⠒⠛⠒⠂⢀⣼⠁⠀⠀⠴⠶⠓⠀⠀⠀⠀⠀⠿⠇⠀⡀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠒⢑⣷⣸⡀⠀⠠⡽⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠃⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠰⠟⠋⠀⠁⠠⠴⠾⠂⠘⠃⢀⣴⡆⠀⠀⢰⣶⣿⣿⣷⢀⠀⢀⡤
⠀⠀⠑⡧⡀⣀⡀⠀⠉⠁⢰⣆⣤⠾⠋⠀⠀⢀⣴⡾⡇⠀⠀⣰⣧⣄⠀⠀⠀⠀⠀⠀⡜⡿⠁⠀⣶⠀⠉⠉⠉⠀⠈⠀⠄⡌
⠀⠀⠀⠉⢻⠾⠧⠀⠀⠀⠋⠉⠃⠀⠀⠉⠩⠏⠟⠀⠀⢀⠀⠁⠙⠛⠷⠚⠧⠀⣀⣞⣸⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠢⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀⢸⡄⠀⠀⢠⡀⠀⢀⣇⡞⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠸⠿⠿⠿⠗⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠛⠛⠛⠁⠀⢀⠀⣀⢀⡀⢠⠀⠀⠾⠷⠄⠀⢸⣿⣄⠉⠉
⠀⠀⠀⢀⣿⣥⣶⣦⠀⠀⠀⠀⢀⣀⣈⣧⣀⣀⠀⣀⣀⣸⣆⣀⡀⠀⢠⣤⣽⣧⣿⣼⣧⣼⣧⣤⠀⠀⠀⠀⢸⡿⠿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣰⣤⣤⣴⣶⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡙⠛⠛⠛⠛⠉⠀⠹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡀⠁⠙⠿⣿⣿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣀⡼⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣙⡛⠁⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠛⠉⢙⣧⣤⣾⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢇⣾⡇⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢰⣤⣿⣿⣿⣿⣿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⠀⠀⠠⠀⠀⠀⠤⢌⡈⠙⠛⠛⢿⢹⣿⡆⠁⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠐⠀⢠⡾⠁⢀⠂⠠⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⡁⠀⠀⠈⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠂⠁⠀⠂⢁⠀⢀⣴⡏⠁⠀⠀⠁⠀⠀⠀⢀⡀⠀⣠⣿⠇⠀⠀⠀⣸⠒⡀⠔⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠁⢀⣾⡿⠓⠀⠀⠀⠀⠀⠈⡀⠀⣠⣾⣿⠟⠀⠀⠀⢠⡟⠈⠀⢀⡼⠀⠀⢀⠄⠂⠀⠀⠀⠀⢀⠀⠄
⠆⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⢱⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠈⢀⣠⣾⣿⣿⣿⣄⠀⠀⢀⣾⣀⣤⣶⡿⠁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⢇⣾⣿⣿⣇⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠿⠛⠛⠓⠒⠉⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠀⠀⠀⠄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⣼⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣦⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠓⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡄⠀⠋⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⢀⠠⢆⠁⠀⠀⠀⠀⠀⠀⢀⠈⠀⠐⠂⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠃⠀⠕⢀⠜⠀⠐⢊⣁⠠⢚⠀⠀⠀⠀⠔⠐⠀⢨⠂⣠⠃⠠⠤⠤⠒⣲⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠒⠒⠉⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢄⠚⠄⠈⠁⠀⠀⠴⠃
⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠓⠒⠚⠓⠒⠒⠂⠀⢰⠇⠐⠒⠒⠒⠒⠒⠚⠓⠛⠒⠒⠒⢒⡞⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠤⡿⠄⠤⠤⠄⠐⠒⠒⠒⠒⠒⠒⡲⠋⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡇⠈⠀⠀⠀⠀⠀⠀⠀⡠⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠂⠀⠀⠀⠀⠀⠀⡔⠁⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⢩⣥⣤⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⣈⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠈⣻⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⡍⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣶⣤⣴⣾⣶⣷⣶⡆
⠰⠤⠭⠿⠭⠽⠯⠤⠴⠀⠀⠀⠀⠀⠀⠀⡹⠆⠛⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣼⣴⡤⠀⠀⠀⠀⠾⠭⠖⠶⠭⠶⠲⠭⠶
⠈⠙⠋⠉⠛⠋⠉⠛⠉⠀⠀⠀⠀⠀⠸⠽⠿⠽⠿⠽⠃⠀⠀⠀⠀⠀⠰⠶⠲⠷⠲⠷⠒⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣴⡇
⠀⣀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠘⢿⣀⣀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⣿⣤⢹⣿⣿⣹⣿⡄⠀⠀⠀⠀⠘⣿⡏⠉⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣽⣥⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠀⠘⠋
⠀⠿⢭⡘⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠙⠷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⡾⣿⣼⡿⣶⣶⡶⠀⠀⠀⢠⣤⣤⢿⣽⣯⣤⣤⡀
⠀⡦⠴⣓⠯⢴⣲⠤⡆⠀⠀⠀⠀⢐⠶⢖⣒⠶⣖⣲⠶⣖⠀⠀⠀⠀⠲⠶⠚⠲⠶⠚⠒⠶⠒⠀⠀⠀⠒⠶⢲⣶⠱⠒⠒⠶⠒
⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡀⠀⠁
⠀⠀⠀⠐⣟⣀⡀⠀⠀⠀⠀⠀⢠⣤⠤⣄⠀⠠⣤⡄⢂⣀⠀⠀⠀⠀⠀⠀⠀⣼⣄⣀⣀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣿⣧⣤⡦
⢠⣤⣤⡾⣫⣽⣥⣤⣄⠀⠀⠀⣠⣤⠶⢮⣿⡿⠿⣷⣜⡛⡀⠀⠀⠀⣽⣿⣿⣿⣾⣿⣿⣿⣦⠀⠀⠀⠲⠭⠖⠲⠭⠖⠲⠤⠖
⠲⣯⡢⠞⠯⠖⠒⠮⠷⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠎⠉⠉⠀⠀⠀⠭⡭⠴⠮⡭⠷⠮⣭⠵⠀⠀⠀⠀⠀⢤⣤⣶⣦⠄⠀⡀
⠈⠉⠁

⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶
⠀⠀⢀⡣⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢲⡀
⠀⠀⠸⣇⡀⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⣷⡀
⠀⠀⠀⢨⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠰⠶⢰⠿⠿⠿⠘⠛⠃
⠨⢛⡫⠭⣟⡯⢭⣛⡭⠀⠀⠀⠀⠨⣟⣫⢭⣛⡯⢭⣛⡭⠀⠀⠀⠀⣒⠶⣒⣒⠶⣚⣲⢶⡂⠀⠀⠀⣀⡙⣛⣛⡻⣛⣛⡛⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⢳⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⣀⣀⣀
⠀⠀⠠⠿⠶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠿⠛

⠀⠀⠀⢀⣤⡤⠄⠀⠀⠀⠀⠀⠀⢀⣦⠔
⠀⠀⣰⣿⣿⣇⠀⡄⡀⠀⠀⠀⠀⠀⣾⣤⡶⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣤⣤⣤⣤⣤
⠒⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀
⠀⠀⠀⠀⢀⡀⠀⠚⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧
⠀⣠⣤⣤⣾⣭⣥⣤⠀⠀⠀⠀⣴⣾⣧⣿⣶⠄⠀⠀⠀⠀⣼⣷⣦⣴⣶⣶⠄⠀⠀⠀⢀⣀⣤⣭⣿⣟⣭
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⢄
⠀⣤⠄⠸⠷⠆⠰⡤⠀⠀⠀⠀⠀⠙⣿⠶⠦
⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠶⢦⣠⡤⣤⣤⠀⠀⠀⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠀⠉⠀⠀⠀⠀⠰⠒⠺⠗⠿⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣆⣼⣏⣝⣻⣶⣄⣶⣤⣴⣦⠀⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⣿⣯⣿⣿⣿⣿⣿⣽⣿⣧⠿⠃
⠀⠀⠀⢀⠊⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⠃
⣢⡬⠞⠉⠀⠀⠀⠀⠸⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣥⡴⠃⠀⠀⠀⠀⠀⢠⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⡇
⠁⠀⠀⠀⠀⠀⠀⠂⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠹⣷⣀⡀⡒⣴⣿⣻⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠃⠀⢀⢄
⠀⠔⢸⣖⣷⣻⣍⢻⣿⢹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⣀⠃⠀⠀⠀⠈⠱⠀⠄⠂⠀⠂⠨⠒
⣤⣤⣼⣿⣽⣧⣿⣟⣿⣾⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⡄⣀⣸⣿⣿⢻⣿⣿⣶⣴⣶⣶⣤⡆⢶⡆
⣿⣾⣿⣽⣿⠽⠗⠛⠛⠛⠉⠛⠛⠛⠿⣿⣿⣿⠟⠁⠀⠀⠀⠄⠀⢀⢀⡹⣿⣿⣿⣿⣿⣻⣿⣿⣟⡿⠟⠉⠁⠈⠀⠁⠀⠀⠈
⣿⡯⠝⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⢉⠀⠀⠀⢤⡀⢦⣀⢀⣄⢳⣻⣿⣿⣿⣿⢿⣷⣷⡟⠁
⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⡘⢤⣰⣀⡀⠴⠄⢀⡀⠰⣦⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⡷⣿⡇
⠀⠀⠀⡀⠀⠒⢑⣆⣾⡟⣿⣿⣿⣿⣿⣿⣷⣀⣨⣽⣷⣿⣿⣿⣿⢿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡦⡀
⢀⣀⢀⡁⠀⠀⠒⣌⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣷⠦⠄⠀⠀⠀⣠⣤
⢷⣿⣿⣿⣷⠎⣯⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠙⠙⠛⠛⠛⠛⠻⠟⣋⡉⢉⣀⣀⣉⣩⣅⣀⡀⢶⣦⣐⠷⣶⣮⣽
⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⣀⣤⣴⣦⣄⡀⣷⣶⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣦⣭⣻⣿⣿⣿⣿⣿⣿⣮⣝⡛⢶⣭⡙

⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠀⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠉⠁⠀⠀⠀⠀⠀⣈⣉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⠦⣈⠛⢦⠀⠀⢀⠴⣶⠶⢤⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠁⡎⣸⣿⣿⣆⠙⣿⣞⡾⣥⣿⣍⣉⣙⣒⠲⢤⣤⣄⢂⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡆⢫⠙⣿⣟⠛⢋⢿⣝⢿⣿⣶⣌⠙⢷⣶⣖⠚⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⣹⢿⣿⣷⠘⢧⡀⠛⠃⣸⡼⣯⡼⡟⢻⣿⣿⣦⣮⡻⣿⣃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣱⣾⣃⣏⣻⣿⣇⢀⣹⣧⠀⢡⠄⡏⠃⣿⠇⠟⢉⣿⣿⣿⣮⡻⣤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠴⠶⠶⠦⢬⡻⠿⢿⣶⡶⠚⡈⠀⣼⣿⡿⠄⠀⠉⢹⣿⣷⣽⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣤⣒⠢⡀⢀⡀⢄⠒⠤⠄⡴⢺⣿⠟⠋⠀⢀⣴⢻⡿⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣌⡑⠛⠦⠕⠒⠊⠀⠀⠈⠓⠂⠒⢫⡍⣨⢁⣾⢻⣿⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⡏⣼⢿⣿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡞⢆⠰⣤⣄⣀⠀⠀⠀⠀⠀⣉⣾⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢧⡀⠳⣜⠿⣮⠙⢶⣄⠀⠀⢈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠋⣻⣷⣦⡈⣆⣼⣿⣷⣬⡛⠿⣄⢼⣿⣷⡄⠈⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠿⢿⣿⣿⢿⣿⣿⣿⣾⡿⡟⠿⣹⣷⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⡀⢀⡀⠀⠀⠛⣦⣹⣿⣷⠻⣿⣿⡈⠁⠉⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⣷⠀⠀⣿⣿⣿⣿⣯⠈⢉⣟⣿⡶⠒⢹⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⢀⣮⣿⠀⣷⣿⣿⣿⢿⡟⢰⠿⣫⣟⣡⣤⣼⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⠏⣼⣿⢇⣿⡟⣼⡠⠴⣺⢿⣻⣿⣿⣿⠻⣿⣟⠀⠙⠆
⠀⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠶⠀⠀⠀⣠⣴⣶⣿⣿⡿⠋⣰⡿⢋⣾⠟⡼⠉⠀⢘⣵⢿⣿⣿⠿⠏⠙⠈⠛⣿⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⢂⣼⡿⣛⣽⣾⣿⠁⡈⠉⣴⡿⠃⠈⠀⠀⣰⠟⣵⠿⠟⠉⠀⠀⠀⠀⠘⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠫⣾⣿⠿⠋⠛⠛⠁⠸⠋⠀⠀⠀⠀⠈⠁⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣻⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣾⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣾⣿⣿⡿⠿⠿⢃⣀⣀⣀⣀⣤⠴⠶⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⢟⣩⣴⣶⣶⣾⣿⡿⣻⣿⡟⠡⡜⢿⣼⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣀⠸⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⢷⢹⢸⡿⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣮⡉⣸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⠀⡟⠀⡟⡾⡇⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣇⢹⣿⡇⣿⣿⣧⣈⣉⡙⢿⣷⣶⣤⣀⡀⠀⢙⣦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣻⣽⡔⢮⣅⣈⣛⣛⣫⣥⣾⣷⣮⣝⠻⢿⣿⡿⠿⠛⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠿⡿⣦⣝⡛⠿⠟⠛⢋⣛⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⠉⠉⢉⣴⠟⠉⠉⠀⠙⠃⠀⠀⠀⠐⠳⣶⣶⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣼⡿⠿⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡤⣤⣤⢀⣤⣤⣤⣤⢠⣤⡄⣤⣤⡤⣤⣤⢠⣤⣄⢠⣤⡄⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡌⠁⢸⣿⠘⢿⣷⣬⣉⠀⣿⣦⣼⣿⠀⣿⡇⢸⣿⣿⣦⣿⠀⣿⡏⢈⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⣾⣿⠼⡿⢶⣿⠿⢰⣿⡆⢼⣿⠤⣿⣧⢼⣿⠌⠿⣿⠀⠻⣿⡶⢿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢒⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⢤⡀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢼⣆⣀⠀⣀⣤⣶⣿⣟⣛⣿⣿⣿⣿⣿⡟⢿⣷⣶⡅⠀⠀⠀⠀⢀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣼⣷⡘⢷⣽⡿⠿⠿⣛⡋⡉⠛⠛⠻⣾⣿⠏⣴⣿⣶⣄⠀⠀⠓⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣞⠉⠀⣴⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⠀⠈⣉⣉⣉⣡⣄⣜⣷⣿⣿⣿⣷⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡁⢈⣧⣾⣷⣾⣿⡯⣄⡀⠀⠀⣠⠴⡒⡋⠉⠉⠀⠈⠠⠀⠀⣉⣻⣿⠿⢿⡿⢿⡿⣿⡿⢟⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢍⣉⣿⣿⡿⠋⠀⠀⠉⣽⠟⠉⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠞⠐⣛⠛⠈⢀⡼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⢠⠀⣱⠟⠇⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠠⣄⡈⣿⣦⣾⣥⣇⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢫⠀⣒⠿⡈⠠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣛⠶⣄⠈⠁⠉⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢦⣄⡠⠀⠀⠀⣤⠀⠀⣰⡦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢖⣛⣿⡦⠖⢻⣿⣿⣿⠦⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡿⠉⣹⠃⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⡀⢰⢖⡓⢲⠶⠚⠁⠀⢰⠇⣰⠏⢇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣷⣀⠀⡀⡠⠚⠙⡟⡇⡿⠀⠀⠀⠀⢸⢞⣅⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢻⣿⣿⣿⣷⣾⣄⡜⡇⢀⣿⠇⠠⣀⠀⣀⡄⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⡱⢄⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣆⠀⢹⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡐⠀⡄⡌⠙⢻⣶⣯⣿⠿⢿⣿⡿⠿⠿⣿⣿⣿⠿⠛⡿⠲⠁⠀⡠⡀⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢳⠮⠥⡘⠃⠀⠀⠀⠙⢿⣷⣆⠈⠚⢿⣿⣿⣿⡿⠁⠀⡰⠃⠀⠀⠀⠈⠛⣀⠭⢶⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⣤⠀⠀⠀⠀⠙⢻⡄⠀⠈⠹⣿⣿⠀⠐⡏⠀⠀⠀⠀⢀⡔⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣥⠀⠀⠀⠀⠀⠀⠿⠒⠦⣤⣿⢟⠁⠀⣧⠀⠀⠀⠀⢤⡁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠻⣄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣳⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣩⣾⣿⣫⣽⣭⡽⠁⢻⣿⣿⢷⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⣿⣿⠓⠋⢥⣁⢠⣲⣮⣭⣟⡋⠙⠾⣯⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣿⡿⢡⣬⣻⣿⣿⣿⣿⠋⠁⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣠⣾⣟⡵⢈⠻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣯⣿⠏⠀⠾⢽⣿⣿⣿⣿⠀⣠⣴⣶⡲⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣠⣿⣿⣗⠀⠉⣤⣿⣿⣿⣿⡻⡿⠛⠋⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠔⠉⠤⣲⡞⠿⠛⠉⠀⣄⢀⢶⣿⣿⡿⢇⣁⠤⠤⠴⣿⣿⣿⣷⡀⠠⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢀⠀⢶⣎⣷⣿⣿⣿⣿⡏⡓⠀⠀⠀⠀⠀⢨⣭⣻⣿⣿⣷⣶⣶⠟⢛⡿⢟⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⡧⢋⠠⠀⠀⢼⣿⣧⣶⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠈⠝⢋⣤
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣯⣭⣽⣿⣷⣶⣟⣃⡉⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⡿⠷⠉⠉⠀⠀⠀⠤⠶⣺⣿⠟
⠀⠀⠀⠀⠀⠈⢻⡿⠿⢿⣛⣿⡿⣿⠿⣥⡐⠀⠀⠀⠈⢻⣿⣿⣾⢿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁
⠀⠀⠀⠀⣴⣶⣦⣀⠀⠀⠨⠈⠃⠀⠀⢀⢠⡄⢀⢰⣶⣿⣿⣿⣟⠷⠉⠻⠿⣖⠀⠀⠀⠀⠀⢀⣤⣴⣿⠇
⠀⠀⠀⢸⣿⣿⣿⣿⣯⠄⡤⣸⣖⣶⣦⣼⣿⣿⣼⣷⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠠⠖⣛⡛⠉
⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠻⠍⠛⠛⠛⠓⠒⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠿⠿⠿⠿⠿⠟⠋⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⢉⡁⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠉⠉⠉⠁
⠀⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠀⠠⠤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠔⠊⡛⢻⣷⣦⣰⣄⡀⢠⣀⠀⠀⠀⠀⢀⣀⡀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠡⠠⠼⠂⠀⠐⣂⡐⢀⠴⠄⠀⢠⣄⣤⣤⠧⢙⣵⢿⡿⣻⣿⣿⣿⣶⠈⠳⠀⠀⠀⠀⠉⠁⠤⣤⣶⣶⣤⣴⣿⣦⣄⣴⣦⡈⣩⣥⣆⡀⣀
⢤⣴⣶⣶⣷⡴⠈⣤⣤⣶⣴⣦⣤⣠⣼⡽⠁⡡⢖⣫⣾⣿⠟⣫⣿⣷⠀⠈⠲⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣛⡏⡠⣊⣝⠙
⠀⠈⠁⢀⣠⣤⣄⣀⠙⢁⠉⠙⠉⣁⠤⢚⡩⠔⣪⡷⣛⣵⣾⣿⣿⣿⣿⡄⠀⠀⢮⣧⣀⣦⣳⣰⣤⣀⣠⡀⠈⢉⣙⡛⠛⠛⠛⠛⠛⠛⠋
⠤⠤⢒⣛⠩⠥⢚⣛⣭⡅⠤⣒⣩⠔⢊⣭⠶⣛⣵⣾⣿⣿⡿⣿⣿⣿⣿⢃⠄⠀⠀⠒⠯⠹⠧⣦⡂⢥⣠⡬⠍⡉⠈⠍⠋⣠⢾⣤⡦⡤⡚
⣂⣉⠡⠴⢒⣛⣭⣴⠴⠞⣋⣥⠴⣚⡭⢖⣫⢗⣫⠟⣛⣥⢞⣫⣟⡿⣻⣷⣙⠏⠢⡀⠀⠈⠁⠪⠉⠉⠉⠚⡉⠍⠓⠈⠙⠁⠀⠀⢛⡯⠭
⠵⢖⣚⣛⠯⣉⣠⠤⢒⣫⣽⣶⣿⠵⣚⡿⢞⡋⣀⢜⣫⣕⡿⣛⣵⣿⢟⣻⣿⣿⣿⣈⣀⠈⠷⠀⢀⣀⢒⣀⠒⣓⠒⠢⠠⠤⠤⣠⣤⣤⡴
⡭⠿⣒⣛⣭⠷⠖⣛⡭⢖⣛⠭⠖⡫⠁⠾⠋⢝⣒⡽⠚⢁⣮⠟⣫⣵⠿⣫⣿⡿⢋⣽⣿⠟⣿⢿⣿⡿⢟⣿⣿⣿⣷⣾⣷⣷⣿⣿⣡⡟⣰
⠘⠋⢉⠡⢐⣂⡥⠔⣚⡭⢗⣢⡴⣖⣡⣴⠾⢋⣡⣴⠞⠋⣰⠞⣩⣵⡻⠛⣡⣶⠿⢋⡠⢊⡥⠞⣩⠞⣡⣿⣿⣯⣞⣿⣿⠟⢩⡾⠉⣡⣯
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⢡⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠎⡐⢁⠞⡠⣊⢔⡁⢒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣰⣘⣃⣃⣊⣐⣡⣊⣊⠕⡰⠲⠕⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣲⠟⢹⣿⡿⡪⠋⠛⣽⣽⡝⡟⠹⣷⣷⣯⣀⣠⡾⠪⣂⢐⢌⢂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⢀⣤⠔⠛⠿⠱⠑⡀⡢⠙⣿⡇⡄⠜⣾⣿⣟⣄⣜⣿⣿⣻⡟⠊⠻⣿⣷⡶⢵⣯⡇⠀⠀⠀⠀⠀⠀⣠⣶⣫⡂
⢀⣠⠖⣁⠣⠖⠇⠀⠀⠀⠀⠍⠉⠎⢅⢄⠌⢜⣿⣞⢀⠈⠜⣿⣽⡟⠔⠴⣽⣽⣟⣔⢜⣿⣿⢁⣦⣿⣷⣘⡮⣿⣥⠂⢀
⠫⣁⠑⢬⡁⣧⢠⠆⠀⠂⡙⠂⠃⣀⢂⡎⠊⠊⠻⠏⠔⠐⡠⣻⣿⠏⡊⡀⣾⡿⣫⠎⠨⠛⠋⠉⣉⢉⢩⣉⡡⣿⣆⠡
⢀⠈⣢⢤⠳⡈⠜⣠⠤⠈⠀⡠⢠⡾⠛⠇⠀⠀⡐⠄⡸⡈⢀⡿⠋⠈⢁⠁⠙⠈⢄⢠⣢⣥⢾⣉⠀⠀⠀⠀⠙⠯⣍⠒⡠
⠀⠀⠈⠁⠉⠐⠲⠤⢤⡄⠀⠐⠰⡋⠅⠲⡀⠄⡠⢑⠀⠀⠎⡈⣖⣱⣕⡤⠴⠚⠻⠛⠈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢺⣷⠖⣚⣒⠛⠒⠓⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣲⡽⡟⢌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠭⢉⡁⠀⠀⠀⡀
⠀⠠⣂⠁⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣢⣄⣰⣤⢻⣿⣴⣶⡴⡀⠴⠀⠀⠠⠐
⠀⣲⠿⣗⠁⠀⠀⠄⠀⡠⠀⠀⡀⢯⡻⣽⡿⢏⣵⣬⠏⠙⠁⠐⠈⠄⠀⠀⠈
⣾⠁⣶⡹⣦⣀⠂⠀⠈⠀⠀⠸⡏⣮⡇⡷⠃⢈⢱⡇⠌⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⢀⣐⢀⠠⠈⠠
⠙⠞⢿⣿⡿⠟⠋⣠⠤⢤⣿⡁⢿⡟⢧⣇⢰⣾⡀⠸⡦⠀⠠⠀⠂⣤⠐⣄⠀⡀⠀⢠⣶⠆⢛⠣⠀⠀⠐
⠀⠀⠀⠈⠰⣖⠊⠁⠀⢩⠧⠍⠰⠂⠉⣅⢨⡀⢄⣲⣽⢷⡴⣷⣤⣿⣻⠿⠋⠀⠀⡟⢁⠘⢿⡷⣇⣮⣁⣀⢀⠀⠠⠑⢄⠈⠀⠠⡀
⠀⡀⢀⣻⡦⢌⣙⣒⠒⠛⠒⠁⠄⠠⣦⢽⣞⠓⠈⣮⣿⡶⠀⠈⡫⠅⢠⣖⣤⣤⠜⠀⠹⢿⣶⣯⣦⣭⣭⡅⢠⡗⣠⣦⣅⣩⣷⣴⡿⠿⠄
⠀⠈⠀⠉⢉⠉⣉⠉⠆⡀⣮⠹⣀⣶⣿⢺⣍⣙⣒⣪⢞⠁⣶⣄⠻⢷⡬⣭⣥⡄⠠⡤⠴⠶⢶⠓⠷⠶⠶⠦⠫⠶⣜⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢠⠸⡦⣹⠳⣔⣦⢮⠙⠛⠛⣋⣉⣉⠫⢅⡐⣯⣳⣬⡿⡏⣲⡉⡓⠈⡓⣤⡤⠶⣞⢿⠻⣿⠗⠊⢰⢶⣻⡛⣻⡛⢏⠛⠛⠁
⠀⠀⠀⠀⠀⠉⠓⠦⣄⠸⣷⣦⣌⣛⠓⠲⠮⣽⡲⠿⠲⡿⣮⣻⣤⠽⡿⣿⣒⠛⠾⠿⠖⠚⠛⠉⠠⡖⢄⣈⠲⢶⡐⢄⠝⠾⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠖⠉⠉⠁⠀⠀⠀⠉⠉⠁⠉⠈⠀⠀⠀⠀⠀⠁⡉⠙⠷⠖⠒⠒⠲⢶⢻⣯⣹⠯⠭⠓⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

⠀⠀⠀⠀⢰⣿⡲⠶⣄
⠀⠀⠀⠀⠀⢽⣇⠀⠈⢦⣀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⠑⢦⡀⠀⠙⢦⣀
⠀⠀⠀⢀⣾⡿⢿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢸⠇⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠈⠉⠓⠀⠀⠀⢀⡶⠋⠉⠁⠀⠙⢦
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠘⣦⣸⣷⣶⣣⣄⣀⣀⣘⡇
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢻⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⡟⠛⠿⠿⠻⠿⣯⣍⣹⠇
⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠹⣆⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣤⡀⠀⠈⢛⡟
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠈⠑⠦⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⣰⠁⠀⣠⡿⠁
⠀⠀⠀⠀⠀⣠⠃⠀⣰⡟
⠀⠀⠀⢀⡴⠁⠀⢰⣿⣷⣤⣀
⠀⢀⣴⣿⣄⣀⣀⣀⡈⠛⠿⣿⣇
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⠒⠤⣀⠀⠀⠀⠀⠀⣠⠖⠉⠛⠲⢄⠀⠀⠀⠀⠀⣠⠔⠒⠢⢤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠑⠒⠤⠒⠊⠁⠀⠀⠀⠀⠀⠑⠦⠤⠤⠞⠁⠀⠀⠀⠀⠈⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠤⢄⡀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠦⣄⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠒⠤⠤⠤⠒⠉⠀⠀⠀⠀⠈⠳⢄⣀⣀⠴⠃⠀⠀⠀⠀⠉⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡄⣻⣶⣤⣀⣀⡀⠀⠀⠀⣀⣤⠞⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣦⣤⡎⢀⣀⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠇
⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣻⣿⣿⣟⣻⣯⣿⣿⣟⣾⣻⡿⣻⡟⣻⡿⣻⡿⣿⡿⣿⢿⣿⣿⣿⣿⣷⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠏
⢀⣠⡴⠾⠟⠛⣿⣶⡛⠀⠙⠻⣮⣉⣠⣤⣤⣥⣿⡬⢥⣬⣧⣭⣠⣟⣘⠛⠁⠋⠘⠋⠾⠇⠸⠟⠹⡿⢻⣿⣿⣿⡿⣶⣦⣤⣤⣾⣷⣶⡟
⠀⠙⢣⡀⣀⠻⠿⠟⠀⠀⢀⠀⣻⡟⡟⠓⠉⠉⠈⠉⠉⣁⣀⣨⠭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠾⠿⢿⣿⣿⣻⡅
⠙⠻⢦⣥⣞⡃⠀⠀⠀⠀⣴⡀⣿⣓⣳⣤⣤⠖⠈⠉⠉⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠉⠁⠉⠀⠀⠀⠀⠻⣝⠛⢻⡀
⠀⠀⠀⠀⠉⠛⠻⠶⣶⣮⣿⣿⡟⣛⣛⣿⣿⣿⣭⣭⣭⣵⣶⣶⠶⠶⢷⣴⣤⣶⣴⣶⣶⣾⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣿⣯⣭⣭⣭⡭⠽⠿⠿⠿⠟⠛⠛⠛⠻⣿⡻⠏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣷⣦⡀

⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣭⣭⣭⣭⣍⣉⡉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣫⠥⣶⣶⣶⣾⡯⢭⣙⠓⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣶⣟⡛⠉⠉⢙⣛⣻⢯⣗⠦⣙⠷⢄⡈⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢢⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣟⡉⠉⢹⡄⢴⣟⣿⣟⢷⣮⠙⠪⣻⢦⣙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⢰⢲⠇⠈⠀⠁⠈⠀⠀⢀⣴⣶⣶⣦⣄⡀⠀⠀⠈⠛⠋⠀⢠⡇⡸⣿⣾⢡⡆⠹⣵⣄⠈⠳⣮⠑⢦⣉
⠀⠀⠀⠀⠀⠄⠀⡱⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣭⣄⡀⠉⠛⠻⣷⣦⡀⠀⠀⢀⡼⠀⢉⡩⢪⡞⣀⣉⣉⣿⣷⣤⣌⣳⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠿⡤⠈⠹⡄⠀⠀⠀⠈⠛⠶⣦⠞⣡⣔⣩⣾⠿⣻⣿⣿⣥⠤⣄⠉⠛⡝⠻⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡒⠝⢧⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⣾⣷⠾⣛⠿⣫⡵⣻⠟⣫⠽⣿⣿⡌⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣞⠀⢀⡀⠙⢷⣤⣤⠏⠀⣀⣤⡾⠿⠛⣉⠤⢊⠵⢋⠔⡽⠁⢸⠁⣻⣿⣾⠷⢁⡴⢁⠜⡠
⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⡻⣝⠛⠛⠿⢿⣶⣿⡿⠷⠿⠛⢛⣛⣩⠥⠔⢒⣩⠴⢚⢁⡴⢋⡜⠁⣰⡞⢦⣙⢿⣍⣛⣛⣊⣡⣖⣥
⠀⠀⣠⣴⡿⡻⠝⣚⣉⡙⠊⣿⠢⢭⣑⣲⣶⣬⣿⣿⣿⣿⣯⣭⣴⣶⣒⣩⣩⣤⣴⣴⣯⠶⠿⢶⣿⣿⣧⣤⣭⣳⣿⣷⣶⣾⣟⡛⠫
⠰⠟⣱⢋⠊⠔⠉⣁⣍⣉⣴⣿⠴⠚⠉⠉⠥⢖⣛⣩⣙⣛⣿⣿⣯⣭⣭⣭⣄⣤⣤⠤⠶⠶⠖⠲⠤⠤⢄⣀⠀⠉⠉⠙⠛⠛⠿⠿⠷
⢀⢰⠃⠔⠈⠀⠀⣯⣿⠿⠟⡁⠄⣢⠴⠚⢋⣉⣡⣤⣤⣶⣶⠖⠛⠛⠟⠿⠟⣛⣛⣛⡛⠿⠟⠻⠿⢶⣶⣤⡭⢽⣶⣶⣶⣤⣤⣤⣤
⠈⢸⠀⠐⡐⢄⡁⠒⣂⣈⣤⠶⣚⣁⣤⡴⢞⣿⣭⣽⣿⣿⣿⢿⣷⣶⣦⣤⣄⣀⣈⣉⣉⣉⣉⣉⣭⣭⣤⣤⣭⣐⣒⠦⢄⣀⣀⣀⣀
⢈⠸⣇⠀⠉⠦⢍⡉⣉⣥⡴⠿⢛⣩⡵⠾⠛⠉⡉⠁⢀⣀⣠⣴⣶⣶⣿⣿⣿⣷⣤⣤⣤⣴⣞⠫⣅⣶⣶⠦⣌⠙⢧⡈⠍⠐⠛⠟⠟
⠐⠀⢙⣷⣤⣤⠶⠛⠉⢀⣠⡶⠛⠉⠀⢐⣨⣴⣒⠋⠩⠁⢈⠔⠑⠡⣟⡿⡯⠛⢦⣙⠻⢯⣈⠥⠚⢹⡀⣾⣼⡁⠀⢳⡀⠁
⠘⠛⠛⠉⠁⠀⢀⣠⠶⢟⠉⢐⣠⣴⣊⣉⣀⣬⣍⣁⣒⣮⣀⣤⣀⡬⠜⠋⠁⠀⠀⠙⠻⣔⡛⠶⣄⠀⠙⢮⣳⢶⣮⡤⠛⢦⡀
⠈⢀⣀⣀⣤⢖⣋⣁⡤⠴⠚⠋⡉⠩⠄⠀⠒⠐⠒⠒⠒⠬⣭⣍⣉⡛⠛⠶⠦⣤⣀⡀⠀⠀⠉⠙⠛⠻⢦⡀⢌⡙⠛⠻⠷⢶⢿⣷⣶
⠸⠿⠟⠛⠛⠛⠋⢉⣭⣭⣉⣙⠛⠒⠲⠶⠤⠤⠤⠴⠖⠒⠒⠒⠛⠛⢛⣛⠋⠭⠽⠿⠷⠶⣶⣤⣀⡀⠀⠉⠳⣽⣧⣅⡠⠄
⠠⡤⡤⠴⠶⠚⣋⣉⣉⣉⣉⣉⣉⣛⣒⡒⠶⢤⣤⣤⠴⣖⣒⣂⣉⣡⣤⣤⡤⢤⠤⠄⣒⣒⡈⢛⠿⣯⣿⡛⢲⣶⣿⣿⣿⣮⡄⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣀⣀⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠠⡀⠀⠑⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠉⣶⣄⣻⣯⣿⠿⢟⣻⡦⠀⠀⠰⡆⠀⠄⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⠀⢿⣿⣿⣏⠀⢸⣽⣽⠇⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡰⣿⣿⣦⣀⣬⣙⣛⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⣻⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⠟⠛⠋⣀⣤⠞⠋⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⣤⠤⠴⢶⣯⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣿⣿⣿⣷⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⣿⣿⣿⣿⣿⡟⣻⠷⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣿⣿⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢁⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠙⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⡌⠀⠹⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠐⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣆⣶⣶⣶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣧⠺⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣾⣷⠀⣠⠆⢄⣀⣠⣾⠻⣷⠀⠀⠀⠀⠀⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢹⣶⣼⣿⡛⣾⣿⣄⠈⢿⣿⣿⡇⣿⣶⣦⣀⠀⠀⢀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣀⡄⣀⣀⣾⣿⡛⠉⠳⡌⠿⠃⢀⣻⣿⣿⣿⣼⣿⣇⣿⣧⡔⠫⠀⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠻⠆⠀⠀⠠⡘⡄⠀⠈⡏⢹⡗⠛⡿⢿⣿⣿⣿⣧⣤⣰⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠘⠛⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃⠈⠁⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡘⣸⠀⣿⢠⣿⣿⣦⣄⠄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⢀⣴⣒⣠⣶⡿⠟⠻⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⣸⣧⣿⣿⣿⣿⣿⡀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠛⠋⠋⠛⠛⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡟⠠⢱⣿⣿⣿⣿⣿⣿⣿⣦⡞⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠈⢀⠀⠀⣴⠃⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠈⠀⠀⢿⡟⢏⣿⣿⣿⣍⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠠⠿⠖⠚⠛⠛⠛⠛⠻⣿⡶⠶⢿⣥⣤⠀⠀⣀⣠⣤⠀⠀⠀⢚⣿⡿⠃⠀⠀⠀⠀⢀⡀⠀⣠⠔⠀⣰⡿⠻⣿⣿⠟
⠀⠀⠀⠠⠔⠒⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⣀⣀⣒⣀⡀⠀⠐⢶⣬⠁⠀⠀⠉⢹⣤⣶⠉⠉⠉⢴⣦⠖⠁⢀⠔⠛⠻⠟⢛⠶⡟⠋⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠤⢤⣀⡀⠉⠉⠉⠉⠀⠀⠀⠀⢀⣉⡿⠛⠀⠀⠉⠥⢀⣀⣠⡶⠤⢀⣾⠗⣀⡤⢀⠀⠠⣾⣿⣴⣶⡟⠁
⠀⠀⠀⠀⠀⢠⣤⡾⠋⠁⠀⠠⣄⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠀⠀⠈⠁⢀⣬⣭⠤⣤⣤⣤⣭⣤⣤⣶⣯⣵⣿⣿⣿⣿⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⣿⣅⡀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠒⠒⠒⠶⠤⢴⣿⠠⠤⣄⣻⠀⠀⠈⠁⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣄⢀⣸⣄⣤⣤⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠰⢶⣶⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠄⠁⠀⠛⣒⣲⣦⣤⣬⣿⣛⣿⣿⣽⣿⠿⣿⣿⣿⣿⣿⡿⣛⣉⣭⣤⣶⣿⣿⣾⣿⢶⡄⠀⠀⠥⠤⠤⠭⠄
⠀⠀⣠⣏⣉⡉⢙⢻⣯⣵⣮⣭⣿⣿⣿⡿⠯⠼⣿⣟⣁⣍⣿⣿⣿⣿⣿⣿⣯⠿⣿⣿⣿⣯⣭⣥⣤⠀⠐⠂
⠈⠉⣉⡙⠛⠛⠛⠛⠿⣉⣉⣁⣚⡉⠛⢿⣿⣟⠋⢽⣿⣿⡿⠛⠒⠒⠉⠉⠭⠯⠭⠿⢿⣿⡇
⠀⠀⠈⠉⠉⠉⠀⠐⠲⠦⢭⣉⣉⡀⠀⠈⠉⠉⠥⠬⠽⣿⠧⠀⠈⠙⠛⠚⢛⣋⣉⡭⠭⠉⠁⠀⠚⠛⠛⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠀⠀⠛⠃⠀⠀⠉⠉⠒⠒⠀⠀⠀⠈⠉⠙⠓⠚⠛⠋⠁

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣠⣤⣤⠤⠤⠤⣤⠤⣤⣀⡀⣀⣤⣰⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣍⠻⣗⡒⠰⣟⡳⢉⣽⣟⢿⣿⡿⣶⣭⣟⠯⣫⡿⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢸⠐⣽⡧⠹⡿⠑⠺⡻⡿⠻⠍⡣⢛⢿⣿⡿⣿⣿⣮⣔⢩⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣏⣶⣘⣿⡀⠇⢠⢀⡇⠀⠀⠐⠀⢸⣆⡠⢃⣿⣿⣿⣿⣷⣻⣽⣿⡀
⠀⠀⠀⠀⠀⠀⣴⢛⣭⣍⣉⡉⠘⠒⠋⢙⣷⠦⠤⠤⢔⣘⣠⠔⣨⠀⢛⣹⣿⣿⣿⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠦⣦⡐⠀⠀⠉⠉⣛⣯⣤⣤⣄⣤⣾⣉⣁⠚⣠⣿⣿⣾⣽⣿⡿⣿⡾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣴⡖⠮⢿⣿⡿⢿⡛⠷⠊⠁⠀⠙⢿⣿⣿⡿⢛⣭⣬⣿⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣴⣤⣄⣀⡀⠀⠈⠁⠀⠙⢛⣫⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠀⠙⣿⣯⡹⣿⠀⠀⠀⠀⠐⣿⢿⢿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠓⠦⢼⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⡄⣤⣄⡀⢰⣾⢷⡏⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣀⣀⣀⣀⣀⡼⠃⣽⡿⣷⣝⣯⣿⡾⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⣿⣿⠀⠀⢹⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡯⢿⣿⣤⡐⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣽⢿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣡⢿⡿⠁⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣆⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⠿⣿⡿⠿⠿⢯⣭⣿⣿⣾⣿⣮⣜⡿⣆⠀⢉⣦⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣒⠚⠓⠈⢀⣀⣀⡼⢥⣿⣿⠼⠋⠛⠻⢿⣼⡄⠀⢀⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢠⣾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠒⠒⠢⣤⣤⠰⢿⣿⡦⠌⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣤⣤⣤⡾⠙⠏⢀⣼⠅⠀⠀⠒⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣀⡔⢿⣿⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠐⢂⡄⠉⠉⠉⠁⠐⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣥⣄⣀⠀⠀⠺⣿⢶⣿⣿⠄⣠⣶⣶⠀⠀⠉⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⣿⣿⣿⣿⣧⠀⢀⣠⣀⡠⢋⣾⣿⣿⡿⣣⣼⣿⠟⢠⣄⣤⣬⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠀⣼⠟⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠉⠉⠋⣾⣿⣿⣿⠙⠿⠿⠜⠛⠛⢂⠤⣜⡂⠤
⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⢃⣼⡟⡌⠁⠋⢻⣿⣿⣿⠏⢰⠰⣴⡀⠀⠰⠀⠁⢀⠴⠒⠒⠒⠒⠀⠀⠀⢴⣿⣿⣶⡶⠖⠒⢷
⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⣷⣾⠛⢡⠀⠀⠀⠸⣻⣿⠃⢀⡟⣧⣿⣧⡀⠀⠀⠠⠃⠀⠀⡀⠊⠐⠀⣠⣶⣿⣿⣿⣿⠿⣆
⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⡏⠀⢠⠀⠀⡀⡀⠈⠃⢰⣼⡇⠸⣿⣿⣷⢀⠀⠀⠀⡠⠊⠉⠀⢢⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰
⠀⢀⡴⢋⠝⣫⣿⣿⣿⣿⣿⠇⠀⢸⡀⠀⠱⡐⣄⠀⢸⣿⣿⣄⠈⠛⠿⣿⣦⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⡏
⣰⠋⠀⠀⠊⣡⣿⣿⣿⣿⡵⠂⢀⣾⡇⠐⢄⠘⠮⡳⢎⢿⣿⣿⣷⣦⣄⣀⠈⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡃⡜⠀⡞
⢻⣀⠀⠀⠀⠺⣛⣭⠞⢁⣠⣶⡿⠃⠘⡄⠈⠓⢤⣘⣆⠳⢍⡻⠿⠿⠿⢿⣿⡦⠀⠀⠀⡈⠉⠒⠄⡈⠙⠻⠿⣿⠞⠀⡸
⠀⠈⠙⣶⡾⠟⠋⠀⠀⣿⡟⠉⠀⠀⠀⠈⠦⡐⢤⣈⠉⢅⣀⠈⠉⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⣉⡒⠇
⠀⠀⢸⡇⠀⢀⣴⣾⣷⠋⣽⣗⡀⡀⢀⣠⣤⣌⡒⠤⣉⠉⠩⠕⠲⣄⡀⠀⠀⠀⠉⠒⠦⠤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠉⣢⠁
⠀⠀⠘⣇⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠭⠀⠀⠐⠊⠁
⠀⡴⠋⠁⠩⠾⠟⣻⣿⣎⣝⣛⣷⣆⣀⣈⣉⠉⠛⣿⣿⣿⣿⣿⠀⣶⣤⣄⣀⣤⡤⠤⠄⠒⠈⠁
⠾⠒⠒⢶⡠⡄⣍⠹⣿⠟⢿⣿⣿⣿⣫⡞⠁⠀⢸⣿⣿⣿⣿⡏⢸⣿⡟⢿⡿⠙⠀⢀⠁
⠀⠀⠀⠀⠳⡱⣌⢷⡅⠀⠸⢟⢭⣻⡿⣷⣄⠀⠀⠈⠙⠿⠟⢀⣿⣿⣿⢸⣷⡦⢔⡀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⣠⣤⠄
⠀⠀⠀⠀⠀⠙⢾⡶⠇⡠⠶⣶⣦⣬⣉⡛⠻⢷⡀⣤⣀⠀⠠⣿⣿⣿⡟⣼⣿⣷⢰⣍⣾⣿⣿⣿⣿⣿⣿⠧⣀⡴⣨⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣛⣶⣮⠉⠛⠛⠛⠚⢻⣦⣝⢷⣤⡀⠈⠉⠰⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡇⢰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⣶⣄⣀⠈⠁⠀⠹⠟⠙⠿⢿⣿⣿⣿⢧⣓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠙⠋⠁⣠⠞⠉⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⣠⣴⣿⣿⣿⠛⡗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠹⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣻⣿⣷⣿⡏⠒⠄⢹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣝⢷⡝⢟⢮⡋⠓⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠠⣀⠙⠦⡀⢨⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢔⡀⠑⢄⣸⠿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠅⠈⠀⠁

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠠⠴⠛⡻⠛⠉⠙⠻⢿⣿⣷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⣿⡿⠟⠋⠉⠛⢿⠛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣿⣦⣴⣤⣄⣀⡀⠀⣾⣿⣿⣿⣿⣷⠀⠀⣀⣠⣤⣴⣤⣾⣿⣿⡿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣘⢺⡶⢦⣝⣿⣿⣿⣿⣯⣿⣿⣯⣯⣿⡛⠛⣋⡤⢶⣗⢓⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢒⣒⡒⠒⠿⠯⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣽⣿⣶⣿⣿⣿⡿⠭⠿⠓⢒⣒⣒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⢛⡉⠉⠉⠉⠽⠧⠿⠿⠛⠛⠛⠛⠻⠿⠼⠿⠍⠉⠉⢉⡛⠛⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠛⠒⠪⢥⣂⢄⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢿⠀⣿⠿⠶⢮⣑⠮⣒⢄⡀⠀⠀⠀⠀⠀⢀⣤⠶⠒⣒⣒⡒⠤⢄⣀
⢉⣉⣉⣉⡓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⢸⡆⢿⡀⣴⣶⣬⣙⠮⣓⢭⡲⠤⣤⣤⡴⠟⢁⣴⡿⠋⢉⣉⣉⣓⠲⢭⣓⡲⠤⣤⣀⣀⣀⣀⣀
⠛⠋⠉⠉⠙⠛⢦⣑⢄⠀⠀⠀⠀⠀⣼⠃⣠⣾⠇⢸⡇⢹⣿⠟⠛⠷⣮⡓⢬⣓⠶⢤⣤⣶⠿⠟⠀⣰⡿⠋⣩⣭⣙⡓⠦⣍⡓⠶⢤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⠷⢦⣌⠳⣕⢤⡀⠀⣰⠇⣸⠏⢁⣠⣾⡇⢸⣿⠀⢠⣶⣤⣙⠳⣬⣛⠶⣤⣤⣤⣤⣾⡿⠃⣸⣿⠛⠛⠛⠷⣦⣍⡓⠶⣤⣤⣤⣤
⣶⣶⣶⣶⣴⣶⣦⣬⡓⢮⡳⢬⣙⣉⣰⡟⢠⡿⠋⣁⣤⣾⡿⠀⣼⣿⡟⠛⠿⣦⣝⠻⢶⣤⣬⣥⣤⣤⣾⣿⠃⣠⣾⣶⣶⣤⣉⠻⢷⣦⣬⣭⣭
⣤⣤⣀⣉⣉⣉⣉⣉⡙⠳⣭⡳⢬⣉⡋⢀⣾⠃⣾⡿⠋⢉⣀⣴⣿⡟⢀⣴⣶⣦⣙⠻⢶⣤⣍⣉⣉⣉⣉⣀⣴⣿⠟⠋⠉⠛⠿⢷⣦⣤⣉⣉⣉
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⣭⡓⢮⣝⣛⣃⣼⡿⠀⣾⣿⠿⠛⠋⣠⣾⣿⡿⠿⠿⢿⣦⣍⣙⣛⣛⣛⠛⠛⠛⢉⣠⣶⣿⣷⣶⣤⣌⣙⠛⠛⠛
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣦⣭⡓⢮⣝⣛⠛⢁⣼⡿⢁⣴⣾⣿⠿⠟⠋⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠛⠛⠻⠿⠿⠿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣙⠳⢮⣭⣛⡛⠛⣁⣾⡟⠉⣀⣤⣤⣴⣶⣾⣿⣿⣿⣷⣦⣤⣴⣶⣶⣶⣶⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣤
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠶⣦⣍⣙⠛⠛⢋⣠⣾⠟⠛⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠻⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡄⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡻⣿⣿⣿⣿⣿⣷⣦⡻⣿⣿⣿⣿⡿⠿⠛⠋⢹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡿⣿⣿⣿⡄⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠛⠿⠟⠻⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⡀
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠈⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⠈⠛⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣶⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⢺⣿⣿⣿⣿⣿⣿⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠉⠻⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡎⢠⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠀⠀⠀⠀⢀⠀⠀⠐⠀⣀⠤⠀⠀⢀⠀⠀⠀⠘⠄⠀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠉⠠⠀⠘⠓⠁⠀⠀⡐⠂⠾⡐⢄⡀⠀⢠⡘⠀⠄⢼⣷⡤⠅⢷
⠀⠀⠀⠀⠀⠠⠄⢰⡀⠀⠂⠠⠀⠀⠀⠀⣰⡿⣣⣾⣧⣁⣈⠀⣇⠉⠀⠀⠀⡀⠱⡄⠈
⠀⠀⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⠀⠈⠆⠠⠄
⠀⠀⢳⡀⠀⠈⠛⠿⠿⠷⠾⠲⠶⠶⠶⢶⣶⣒⣛⣛⣛⣛⣛⣉⠉⣿⠀⡸⠃⠀⠀⠀⠀⠂
⠙⠛⣉⣉⣐⣛⣛⣛⣋⣁⠀⠀⠈⠛⠿⠯⠭⢥⣤⠀⠀⠀⠀⠀⠀⢹⡗⠰⠀⠀⠀⢱⠀⠀⠁⠀⠀⣠⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣦⣬⣭⠉⠁⠀⡀⢠⠀⠀⠀⠬⣤⣴⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⡉⠀⡀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠀⣿⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⢰⡀⠀⠀⠛⠁⠀⠀⢰⡀⠐⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼⠁⠠⠄⠀⠀⠀⠀⠀⠀⠁⠐⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡓⠀⠀⠀⠄⠈⠛⠉⠓⠄⠀⠠⠀⠀⠐⠊⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠽⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣀⣀⣤⣤⣶⣦⣀⣀⣀⣓⣠⣤⣤⣤⡀⠀⠀⠶⠿⠿⠛⠛⠉⣉⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠉⠉⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⢟⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣫⣍⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣦⣀
⠀⠀⠀⠴⠷⠶⠾⠿⠿⠷⠟⠟⠿⠾⠷⠶⠦⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⠆
⠀⠀⠀⠀⠀⠀⢀⣤⣦⣴⣿⣿⣶⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⢛⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠛⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣾⣷⡏⠀⠘⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠷⢶⣶⣾⣦⡀⠀⠀⣴⣿⣿⣿⣿⠿⢿⡿⠶⠤⠤⠄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⡀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣻⡃⠉⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢟⠛⢷⠀⠀⠀⠀⢠⣶⣄⡼⠛⠿⠀⠀⡿⠋
⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣷⡤⣤⣄⣰⣦⣀⡀⠀⠀⢀⣠⣾⣿⣿⣿⣻⣿⣿⣄⣀⡀⡀⡀⠀⠀⠻⠇⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠋⣿⣿⣶⣬⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣿⣭⣭⣭⣽⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠲⠶⢾⣿⣟⠻⠿⢿⣿⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣠⣾⠿⠿⠛⠿⠿⣿⣀⠁⠀⠀⠀⢠⣶⣶⡆⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣿⠟⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⣀⣤⣿⣿⣿⣧⠘⢆⠀⠀⠀⡄⠀⠀⠀⠀⢀⡴⠟⢛⣻⣷⣄⣀⣠⣴⣞⣀⣀⣀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠁⠀⠀⠈⠉⠁⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠔⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣤⣶⣷⡆⠀⠀⠀⠀⠀⠈⢀⣾⣿⠇⠀⢀⣴⡟⣛⠁⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⢀⣤⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠘⢿⠁⣠⣶⣶⣿⣟⣿⡶⠂
⠀⠀⠀⠀⣠⣾⣿⣽⣿⣿⢿⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣵⣾⣿⣿⣿⣿⣼⣿⢦⣴⣾⣿⡛⠀⠀⠀⠀⠐⢿⣿⣿⣮⠟⠋
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁⠐⠓⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠈⠉
⡾⣶⣷⢶⢶⡷⣶⠶⢶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣿⣶⣶⣶⣿⣿⣷⣶⣶⣾⣿⣾⣷⣶⣷⣾⣷⣾⣶⣶⣶⢾⣷⢶⣶⣶⣶⠶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣲⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⣟⣵⣋⣁⣀⡷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⢬⣙⠲⢤⣈⡩⠤⠶⠒⠒⠒⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⣹⢂⡇⣀⣀⣠⠤⢤⡄⡖⠒⢮⣳⡄⠀⠀⠀⠀⠀⣿⠤⠶⣈⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠾⣍⣓⠦⣤⠇⣼⢰⠁⢸⣿⠀⠀⢷⠹⣄⣤⠷⠙⢦⠀⠀⠀⠀⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢲⣟⣉⣀⣀⣀⣤⡬⠽⠶⣤⣇⡘⠒⠚⠉⣉⣉⣉⣠⣤⠤⠤⠤⠘⠳⣄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⣹⣋⠔⠊⠁⣸⠉⠉⡏⠀⠀⢱⡀⠀⠘⢦⢻⡉⠉⣉⣉⠉⣀⣀⠀⢠⠤⡀⢰⠒⡌⠳⣤⢼⣧⣤⡀
⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠻⣄⡀⠀⠀⠇⠀⠀⢃⠀⠀⢀⣇⣀⡠⠜⠊⢧⣀⣓⣚⠀⠓⠚⠀⠘⠒⠁⢈⣉⣀⣀⣬⠧⠔⠋⢻⡄
⠀⠀⢠⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣻⡿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⡉⣉⣭⣍⢩⠵⢦⠀⠀⠀⠀⢀⡹⣤⣀
⠀⠀⠈⠙⢿⣟⡛⠛⠛⠛⠛⠛⠋⠉⣩⣭⠤⠴⠖⠒⣦⠀⣀⣀⣀⢀⣤⣤⡄⣴⠶⠖⠒⠛⠛⡇⣏⣉⡇⢧⣤⠼⠘⠒⡚⡁⠀⣠⣤⣼⣷⠟⣸
⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀⣀⠀⠀⠀⠙⠲⣄⠀⠀⢘⡆⢳⣀⣸⡏⣧⡤⠇⠸⠶⠒⠒⠛⠋⠁⠈⠁⠀⢀⣰⣲⣿⣾⡶⠛⣟⢉⡤⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠉⠙⠛⠿⢶⣤⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣠⣶⡶⠶⢶⢿⣿⣿⠿⠧⠨⠥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡃⠀⠀⠀⠀⠀⠉⠓⠶⣦⣴⣿⠶⠶⠶⠶⠶⣿⡟⢿⣭⣽⣿⣾⡷⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⠶⠞⠛⠿⠟⠂⠸⠦⠔⠶⠖⠲⠿⠝⠛⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠤⠒⠒⣒⠤⠀⠀⠀⡠⢴⢒⡦⡄⠀⠀⣀⠤⢶⣤⡀⠀⠀⠀⡠⢤⡤⠄⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⡄⠀⠀⠀⠰⡁⠀⠀⣠⣎⠀⢸⡋⠀⠀⣠⠞⢁⢠⠋⠀⠀⢀⠠⠊⠀⡏⠀⠀⠀⠀⡤⠊⣿⣟⠁
⠀⠀⠀⠀⠀⡀⠄⣀⡉⢙⠉⣼⡇⣜⢘⡗⢲⠊⣱⣮⣿⠨⣷⠖⡆⡹⢀⠀⡀⢉⠒⡒⠒⠉⠨⢠⡁⣏⡲⠶⣖⠃
⠀⠀⢐⡇⠀⠀⡀⠀⠄⠀⠐⢸⠏⠁⡎⡧⠃⢐⢸⡿⠋⡄⢸⡦⠃⢠⢩⠀⠇⠀⡀⢟⠄⠁⢰⠋⡡⠋⢠⢺⣇⡇
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄⠀⠀⠄⣠⠁⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠄⠠⠐⠰⠀⠁⠁⠢⠘⠁⠀⠪⣼⠀⠀⠀⠀⠔⠃⠘⠰⠀⠁⠊⠅⠀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠳⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⢱⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⡀
⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠁
⠀⠀⠀⠀⣿⠃⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⢀⣄⠀⢁⣤⣄⡀⠀⣤⡀⢠⣄⠀⣤⡀⢠⣄⠈⢩⡍⠁⢀⣤⣀⡀
⠀⠀⠀⢰⡟⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠋⠀⣿⠀⣿⠀⠘⠇⠀⣿⠀⢸⡇⠀⣿⠁⠸⣿⡄⢸⡅⢠⡟⠀⠘⠇
⠀⠀⠀⠸⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣴⠀⠀⣿⠀⢿⣦⣀⠀⠀⣿⣀⣸⡇⠀⣿⠀⢀⡻⣇⢸⠇⣾⡷⣆⣀⣀
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠛⠀⠀⣿⠀⠈⠙⢻⣷⠘⣿⠉⢹⡇⠀⣿⠀⠰⡆⢻⣼⡅⢿⡇⠀⢸⡏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣆⠀⠀⣿⠀⣿⠀⢸⡇⠀⣿⠀⢰⡇⠘⣿⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣃⡀⠀⢐⣟⣀⠛⣳⣖⠁⢀⣿⣆⢸⣷⡀⣿⣇⣸⣧⡀⢹⡀⠀⠙⣳⣞⢿
⣿⣿⡿⠿⣿⡿⠿⠿⡿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⢦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣄⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣟⣷⣼⣿⣿⣿⡿⢟⣯⣽⡟⠟⡴⢋⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⢷⣶⣿⣿⣿⣿⡿⠋⠑⢋⡽⢛⡅⣠⢿⠟⡉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠻⠿⣿⡘⣿⡇⡄⠀⠀⠀⢉⡞⠟⢸⣴⣷⣦⣿⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⠀⣘⣶⣶⣝⠻⡧⢳⣄⣀⢀⣼⣤⡄⣨⡭⠭⣂⣀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠽⣿⣿⠀⢷⣆⠛⠛⠛⢛⡭⠀⢰⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣷⣤⠙⠿⠶⣟⣫⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠩⢭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⣠⠴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣣⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⡏⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢿⣿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⠈⢻⣷⣄⠀⠀⠰⠿⣧⣀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡇⠀⠀⠀⢿⣿⣷⣦⡀⠀⠀⠉⢿⣿⡟⠋⣉⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇⠀⣦⡄⠈⠿⠟⠙⠻⣷⣤⣤⣾⣟⠳⣌⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⢻⡝⢳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠈⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠐⡋⠐⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⠖⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⣈⣀⡰⢁⡎⠀⣀⠀⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡞⠛⠙⠽⡯⠙⠙⣿⣿⠿⢷⣤⣀⡠⠀⠀⠀⠠⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣙⣾⢄⠀⠀⠠⠁⠚⡉⠨⢢⡙⣐⠒⢹⠕⠶⣤⠴⠀⠀⠀⣠⢏⡔⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠐⠒⠀⢀⣴⡿⣙⣍⣵⠋⢠⡔⠄⢢⠀⠀⠀⠀⠝⠀⠀⠀⠱⠌⠊⠀⢤⣀⣴⣷⡿⢀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⣤⡤⠀⢀⣴⣯⣿⣟⠛⠿⠷⠤⠟⠛⠦⠀⠀⣄⢀⠤⠀⢧⢪⠔⠁⠀⠀⠀⠸⢏⢻⣿⣿⡀⠀⠀⠀⠀⡠⠖
⢀⠏⠀⢔⡕⣊⠒⣍⠿⠀⢀⡶⠀⠀⠈⠀⠠⠄⠋⠅⠰⠈⠊⠼⠇⡠⠀⠀⠠⠠⣀⣾⣿⡋⠁⠀⠀⠀⢸
⡋⢣⠀⠸⡘⠿⢀⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠨⠡⠁⠡⢠⢁⣠⣀⡶⠖⠒⣶⣾⣿⣯⡁⠀⠀⠀⠀⠈⢣
⠑⠈⠓⠀⢈⢙⡉⠄⠀⠀⠀⠀⢀⠘⡠⡀⠂⢀⡤⠰⣢⣌⣋⣰⣽⠏⠱⠈⠀⠸⣿⣿⠎⠓⠄⠀⠀⠀⠀⠐⢆
⠀⠀⠲⢄⠀⢠⠀⡀⠀⠠⠠⠐⢁⣼⡇⡀⠠⠀⡰⠀⣶⣿⣿⣿⡟⠀⠀⠀⠒⠒⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠉⠒⠄⣀⣀⣤⣖⣄⢺⣿⣧⣈⢀⣀⣠⡾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣸⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠳⡿⣿⣿⣿⣷⣻⣿⣿⡿⠟⠀⠀⠀⡐⠀⢠⠇⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠙⢿⣛⠛⠛⠛⠿⠛⠦⡀⠠⠀⠈⠀⠀⢸⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠡⠀⠀⠀⠁⠙⠲⠤⡀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⠀⠀⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⠏⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⢿⣿⣷⣤⡀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⣀⣀⠀⠈⠙⠿⣆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣴⣿⣿⣿⣿⣦⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠟⠁⠀⠀⠀⠈⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠠⣀⠀⠀⠀⠀⠠⠾⠛⣛⣩⣥⣶⣶⠶⠷⠶⠶⢦⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⣁⣠⡤⠶⠚⠋⠉⣉⣉⣉⣉⣙⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣬⣉⣉⣉⣁⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣶⣶⣾⣷⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⢋⡄⠀⠀⠀⠀⢲⡴⠋⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⢃⠀⠿⢿⣿⣿⣦⡾⠁⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⡥⢾⠀⢠⣶⡇
⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠈⠳⠀⠘⠟⠁⣿⠇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠙⠻⢿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣷
⠀⠀⠀⠀⣰⠿⠁⠀⠈⠉⠀⠀⠀⠀⠈⠈⠓⢀⡀⠤⠤⠄⠻⠀⠀⠀⠸⠹⡤⠀⠀⡐⠀⠔⠈⡇⠀⠀⠀⠀⠀⠲⠈⠀⢀⣀⡀⢻⡆
⠀⠀⠀⢠⠏⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢰⡆⢛⠶⠄⠀⠀⠀⠀⢀⠑⠀⠀⣶⣄⠀⠁⡠⠂⠀⠀⠀⠀⠀⠀⠠⣍⠡⣦⡁⣀
⠀⠀⠂⠈⢢⡈⠛⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠰⠋⣠⡎⠀⠀⠀⠘⢿⡀⡠⠖⣁⡠⣴⠊⠀⠀⠀⠀⠀⠀⠙⢶⣾⣿⣶⣶⠟
⠀⠀⠐⠗⠤⣅⣀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣯⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⠝⢋⡹⠿⣦⡀⠀⠀⠀⠀⠀⣠⡶⡿⢛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡁⡰⢁⠔⣁⠔⢊⡭⠟⢶⣦⠀⢠⡾⢫⠊⢀⠼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠾⠿⠿⠷⠷⢧⣾⣡⣞⡡⠖⣻⡟⠁⢠⡟⣰⠃⢠⠏⢈⠝⣻⣷⠆
⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠐⠲⢤⡀⠀⠉⠙⠒⠭⣛⢷⣯⣽⠃⢀⡿⣰⠇⣠⠏⢠⠏⢈⡾⠃
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠑⢌⠳⣄⣸⡷⢋⡴⢋⣴⠏⢠⡟⠁
⠀⠀⢀⣴⡏⠀⠀⠀⢰⣿⣳⠀⢠⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠀⠈⠻⠿⠿⢞⣋⠵⢢⡟
⠀⠀⠸⣏⠳⠆⠀⠀⠈⠛⠋⠀⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣒⠂⢸⠃
⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⡼⠀⠀⣸⣧⣀⠀⠀⠀⠀⠀⣠⠶⢶⣦⣍⠲⢤⡀⠸⣇
⠀⠀⠀⠀⠀⠈⠛⢶⣤⣤⠄⠈⠀⣀⡼⢿⣗⢭⡳⣆⢀⣠⡾⣟⢦⣄⠹⣿⣝⢦⣍⠢⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠿⢯⣤⣤⣽⣿⠾⣿⣿⡧⡙⢮⣱⣿⠇⠹⣟⢧⡈⢷⡀⠈⡻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣟⢦⡑⢌⠪⣳⡾⠋⠉⠀⠀⠀⢻⡆⠻⡄⠹⣄⠪⣑⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣝⣧⡙⢦⡑⢽⣧⠀⠀⠀⠀⠀⠀⢻⣄⠹⡄⠘⢦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣺⣿⣦⣝⢎⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⢦⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⢯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⠁⠽⡜⠙⢛⠒⠤⣄⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠓⢤⣀⠀⠠⠔⠐⠚⠛⠋⠉⠉⠉⠋⠙⠻⠶⣤⡀
⠀⠀⠀⠀⠀⣠⡴⠉⠀⠄⠀⠒⠂⢀⣀⣀⣤⣤⣤⣤⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡠⠀⠠
⠀⠀⠀⠀⠈⠙⠛⠛⣷⣂⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠰⠞⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠓⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠐⠂⠈⢥⢈⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⣶⣶⣶⣶⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠁⠉⠉⠀⠀⠀⠀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⠟⠋
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⣀⣠⣠⣤⣽⣭⣭⣿⣿⣿⠟⠁
⠀⠙⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⢠⢲⣄⠔⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⣨⣿⣡⣦⣴⡮⣉⣈⡀
⠀⠀⠀⠀⠀⠀⢀⣰⢶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣅⠈⠁⠂
⠀⠀⠀⢀⡤⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣋⡤⠤⠄
⠀⠀⠰⠞⠛⠻⣷⡍⠱⣤⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣖⣀⣀⠁
⢐⣁⣀⣀⢦⡀⣝⢦⣄⢪⣭⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠁⡽⠿⣿⣽⠷⠄
⠾⠛⠛⠿⢿⣿⣾⣿⣿⣿⣿⣭⣷⣴⡀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣹⢿⡃⠠
⠀⠲⢤⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡹⣿⣿⣿⣿⢆⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀
⠀⢠⡀⣌⣻⢟⠚⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡄
⠀⠈⢿⣿⣿⣷⣷⣦⣦⣵⣴⣦⣄⡹⠿⣿⣿⣿⣿⡿⣿⣿⣿⣦⡑⠲⢶⣾⣷⣴⣾⣷⣦⣴⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣇⡀⣄⢔⢮⣉⡉⠻⣿⣮⣝⡿⣿⣿⣷⣦⣬⣭⣭⣿⣿⣿⣯⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣉⣉⡭⠭⠭⠉⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣈⣉⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡇⢻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠈⡏⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡇⠀⢹⠈⢟⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇⠀⢸⡄⠸⡜⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡇⠀⠘⡇⠀⢧⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇⠀⢀⡇⠀⢸⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⡇⠀⢸⠇⠀⢸⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡇⠀⣸⠀⠀⢸⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⡇⢀⡇⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣾⡇⡼⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣀⡀⠀⢀⣿⣿⡥⠤⣤⣀⡀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⣿⡶⠿⠿⠛⠛⠟⠛⠉⢉⣉⣉⣽⣿⣿⡿⠟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣒⣩⣭⣤⣤⣤⣶⣶⣶⡾⠿⠿⠿⠟⠛⠋⠉⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠉⣉⣉⣉⣉⣁⣠⣤⠤⠤⠤⠖⠒⠒⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⣀⠁⠑⡌⠦⠀⣤⣀⠉⠀⢀⡷⣤⡀⠀⢕⣠⣀⣛⣀⣄⡊⠀⠀⠰⣿⡍⢿⡀⠀⠀⠈
⠀⠀⠁⠀⠐⠀⠀⠀⠈⠁⠀⠀⠛⠛⠋⠁⠀⠀⠀⢀⣄⠀⠀⠀⣀⣠⣄⠘⢷⠈⣿⠀⠠⠴⠤⠴⠄
⠀⠀⠀⠀⣠⡟⠛⢦⠀⠈⠉⢉⣳⣦⣶⠀⠀⠀⢀⣸⣇⣈⡂⠈⠁⠶⢿⣦⣀⣀⠈⠀⢀⡀⠀⠀⡠
⠀⠀⠰⣾⣿⣿⠃⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠉⠉⢉⠉⠁⠀⠀⡀⠀⠈⠉⢉⠀⠊⠛⠶⠖⠚⠁⠁
⠀⠀⠀⠀⢈⡄⣠⠄⠀⠀⠀⠰⠤⣄⣠⣄⣤⠤⠆⠀⠀⠉⢟⣿⣾⣿⣿⣗⠏⠁⠀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⢀⣼⡿⢋⣵⠕⠀⠀⠀⠈⠉⠉⠉⠉⠙⢉⣁⡀⠀⡤⠤⢤⣀⣶⣀⡤⠤⡤⠀⠀⢀⣄⠈⠙⠦
⠀⠀⠉⠉⠚⠋⠁⠀⠀⢠⣾⣿⣦⠀⢀⠀⣤⣟⣵⠍⠃⠀⠐⠘⠛⠛⠛⠃⠀⠀⢠⣶⣮⣩⣶⣦
⠀⠀⠑⢦⣀⣀⡤⠊⠀⣼⣁⣦⣹⡄⣀⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⣤⢿⡿⣤⠀⠀⠀⠀⠀⠀⠀⠙⣿⢻⠟⠀⠀⠀⠀⠀⣠⣀⡀⠈⠀⢠⣤⠀⢀⣼⣿⣥⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠔⠀⠀⠦⠀⣠⣛⣌⡂⠀⠀⣠⣆⣼⣷⠤⠤⠀⠀⢾⣿⣆⠀⠀⠉⠙⠛⠛
⠀⠀⠶⠀⠀⠛⠀⠀⠁⠀⠋⠀⠀⢀⣉⡉⠉⠀⠠⢄⡉⠉⠉⢀⡠⠄⠀⠀⠀⠉⠛⠿⠶⠶⠶⠦⠤⠄
⠀⠀⠀⠀⢀⣤⣾⠅⠀⠀⠀⢀⣴⣟⣉⠉⠓⠀⠀⢀⣙⣿⣿⡉⠀⠀⠙⠑⠶⣤⣀⡤⣄⣠⡴⠖⠙⠁
⠀⠀⠀⠈⠋⠙⠃⠀⠀⠀⠀⠋⠙⠛⠋⠀⠀⠀⠀⠘⠋⠛⠋⠁⠀⠀⠀⠀⠈⠚⠛⠛⠛⠛⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⢼⣤⣤⣮⣤⠾⠤⠴⠒⠐⠒⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠿⠇⠀⠀⠉⠉⠉⠈⠁⠀⠀⣤⣴⣶⠶⠟⠛⠉⠑⠦⠄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⣉⣉⣷⣶⣒⣂⣀⣤⣀⣀⣤⣄⠄⠠⣤⣤⣤⣤⣤⣤⣤⡄⣤⣤⣤⣄⡀⢐⠲⠶⢶⣶⡶⣶⣶⣶⡶⢶⠖⠁
⠀⠀⠀⠀⠀⣠⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⢛⣓⡛⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣠⠞⣛⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠞⠋
⠀⠀⠀⠀⠻⡏⢹⣯⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣛⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⣿⣼⣿⣻⣟⣩⣿⣾⣀⢴⡿⣿⠯⢀⣩⡐⢺⠦⣿⠙⣽⣾⢻⣟⣹⡯⣿⢻⠤⠦⢀⣶⣂⠤⣤⣤⣄⠀⠃⣶⣴⡄
⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠉⠉⠀⠀⣩⣿⣿⡿⠻⠙⢷⣄⡙⠀⣇⣼⡞⣯⣿⣷⣿⣨⣧⡏⠈⠁⠝⡘⣯⡿⢹⠋⢰⢞⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⢋⣠⣤⣦⣿⣿⣿⣀⠈⠭⠵⠯⠌⠸⠟⠟⠇⢤⡤⠙⣿⣿⠇⠀⣴⣗⠼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⠀⢸⡧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣯⣿⣻⣿⣿⢟⣻⣿⣿⣷⣯⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⡇
⠀⠀⠀⠀⢀⡀⣴⢿⣿⣿⣿⣿⣿⣿⡛⠩⡽⠎⠈⠓⠊⠁⠉⠙⢼⡽⠃⢘⣿⡯⣵⠉⢻⣿⣷⣄⡀⠀⠀⠀⠀⠉⠛⣻⡷⠇
⠀⠀⢰⡾⣏⡿⢋⣿⣿⡟⣿⣿⣿⠁⠂⠀⠀⢀⣀⠀⠀⠀⠀⢠⡶⠁⠀⠈⠉⠁⠀⠀⠈⠴⠬⠻⣧⡀⠀⠀⠘⠳⠾⠙⠇
⠀⢠⢤⣷⡽⣤⣿⣿⣿⣴⣿⡿⠉⠀⠀⠀⣀⠜⢿⣦⠙⢷⣤⣸⣿⠳⠤⠀⠀⠀⣀⡔⠀⣀⣤⠴⠒⣬⣶
⠀⢹⡄⢿⣷⣿⣿⣿⣿⡿⣿⡇⠀⠀⠘⠋⣁⡈⠀⠙⠃⠘⠻⠿⠌⠳⣄⠈⠶⠬⠄⡁⠈⠙⢁⣴⢋⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⣿⣷⠙⣿⣻⣿⣿⣿⣿⣷⣤⠶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣽⣿⣦⣤⣤⣬⣷⣤⣥⣈⣙⣳⢦⡆⠀⠀⠀⣿⣿⠋
⠀⢀⣿⣿⠀⠛⢿⣿⠻⣿⣿⣾⣧⢀⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣿⠿⣻⣯⣥⣼⡿⣿⣦⢈⠉⢭⡿⠎⠀⠀⠀⠀⠈⠉
⠀⠈⣽⣿⣧⢀⣠⠙⣷⡌⠛⠚⢿⣿⣿⡇⣾⣿⣿⠷⠾⣫⣾⣿⣿⣿⣿⠿⠋⢉⣿⣿⠇⠀⠀⠀⠄
⠀⠀⠸⣻⣿⣦⡈⢁⣙⠻⣦⣀⠈⠉⢻⡇⢸⣿⣯⡿⠟⣵⣿⡿⢃⣴⣶⣶⠏⢉⠛⠉
⠀⠀⠀⠹⣿⠿⠿⢦⣝⣄⠀⠉⠳⣀⣠⣇⢸⣿⠏⢀⣠⣷⣻⠿⠋⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠸⠟⠙⠋⢂⠰⡶⠾⣿⡧⢿⡇⠀⣰⣶⣦⣤⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠵⣮⠓⠉⠁⢾⡇⠀⠀⠀⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡄⠀⠀⠀⠀⠀⢀⠁⣠⡔⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⢿⡀⠀⠀⠀⣀⣴⠾⠙⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠈⢳⣤⣴⠾⠛⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⣿⣶⣿⣿⠟⣫⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋
⠀⠀⠈⠻⢆⣿⡄⠀⠀⠀⠀⣆⠀⠀⠀⠀⣿⣿⠉⠙⠻⣿⡿⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠉⠙⠙⠲⠦⠴⠁⡆⠀⠀⠀⣿⡏⠀⠀⢠⡿⠀⠀⠙⢷⣤⣀⢀⣠⣤⣶⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠈⢻⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠈⣷⣄⡀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⢰⡿⠁⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡇⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡉⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠄⠀⠀⠀⣶⠟⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠟⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠋⠀⠀⠀⢀⣀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣤⣤⣤⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢀⣀⡀⣀⠤⠴⠞⠋⢉⣧⣄⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⢳⣄⠘⠄
⠀⠀⠀⠀⠀⠀⠐⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠶⢶⣖⣒⣚⣒⣲⣦⠼⠧⣀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢢⣻⡤⠴⠒⠒⢒⣒⣛⣛⣛⣯⣭⡭⠭⠭⠶⠶⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠳⢦⣄⠙⠢⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣹⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢸⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠸⠁⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⢀⡼⢃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⠀⠀⣠⣾⡿⠋⠁⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢠⡞⢀⡼⠋⠁⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⡟⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡼⡿⠁⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⡼⠁⠘⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⡼⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⡼⠁⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⡾⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⣡⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠁⠀⠀⠛⠉⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⡀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⢀⣴⠟⣁⣠⠀⠀⠀⠀⠀⣸⣷⠏⠀⠀⠀⠀⠀⠀⠸⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⢀⣴⣿⣿⣿⣯⣥⡤⠶⠶⢻⣿⣯⣤⣤⣄⣀⣀⣀⣀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃
⠀⠀⠴⠿⠟⢋⣉⣉⣀⣀⣀⣀⣴⣋⣀⣀⣭⣭⡭⣭⠭⠤⡌⣿⠗⠒⠠⠤⠤⠀⠀⢀⣀⣀⣠⣀⣠⣤⣤⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⡻⡟⠻⠿⣯⣭⣀⣀⠘⠂⠸⢧⣌⣙⣀⣀⣀⠀⠀⠀⠀⠤⢼⠆⠈⠉⣯⠉⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢰⡶⠛⠛⠛⠿⣿⣿⡷⠶⠶⢤⣤⣬⣭⣭⣭⣭⣭⣥⡴⠶⠖⠋⢁⣠⡴⠁⡀⠴⠒⣒⣩⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣾⠁⠀⠀⠀⠙⢿⣷⣄⡀⠀⠚⠉⠉⠙⢻⣿⣿⣿⣿⠿⠿⠛⠉⣀⣠⣴⠾⠛⠉⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠤⠀⠀⠀⠀⠙⠻⣿⣛⡒⠚⠀⢀⣠⡿⠈⠛⠻⠿⠿⠿⠟⠋⠉

⠼⣅⠃⠐⢄
⢫⡀⠀⠤⠎⠦⠀⢢
⠀⠙⠦⣄⣀⡀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠠
⠀⠀⠀⠀⠉⠹⣆⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣇⡤⠒⠀⠀⠀⠀⢀⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠈⠓⢄⡀⠀⣹⣦⣤⣀⢀⣤⣶⠟⢈⡄⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠶⣄⠀⠀⠀⠀⠑⢦⡘⣿⡉⠉⠉⠉⠀⠀⠘⣷⡀⢀⡴⠃⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⢷⣄⠀⠀⠀⠀⠉⠸⣿⣦⠐⠀⠀⠀⢀⣿⣷⡈⠷⣄⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠳⢄⡀⠀⠀⠀⣿⣿⣦⣀⣀⣠⣾⣿⣿⣿⣇⠈⠓⢄⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢯⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⢦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠋⢻⡀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⢧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⢸⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣇⣰⣦⣿⣷⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⣶⣿⣾⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⠹⣿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⢻⣿⢿⡯⠟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣧⡘⠠⢻⡋⢀⣠⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠺⠟⢀⡼⢻⣃⣴⣆⢀⣤⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⢿⣿⣿⡀⢸⣿⣿⣿⡋⠀⠀⠀⠀⠀⢀⢴⣾⡿⠟⠛⠿⣿⣿⣶⣴⣿⣤⣿⡿⢻⣿⠟⣹⣟⢀⠻
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⡀⠀⠀⠙⣿⣇⡟⢹⡟⠛⠻⣾⣿⣷⡄⠀⠀⣠⡄⣘⣁⣹⣄⡈⠹⣷⡦⢭⣭⣽⠥⣤⠁⠏⢁⣨⢈⡁
⠀⠀⠀⠀⣀⡼⣿⡦⠀⠘⣻⢗⣶⣷⣄⢸⣿⣧⣾⣷⣷⣦⡀⠟⢿⡿⠀⠀⠤⠴⠿⠏⠛⠿⠟⠷⣿⣏⣛⣛⣩⣤⣨⣤⡾⠛⡟⣿⣿⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠻⠊⠉⠉⢻⠿⠿⣿⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠋⠉⠉⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣠⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠒⢿⣿⣿⡟⠋⠻⠟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣀⣄⣠⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠈⢻⣿⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⢿⣿⢿⣿⢿⣍⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠙⢀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⣿⠀⠙⣼⣿⣿⣾⡿⠛⠋⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧⣶⣄⢢⢈⡄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠛⠻⠷⣿⣶⡿⢸⠻⣿⢿⣷⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠣⡹⢫⢿⡿⢠⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣰⣤⣤⣄⣉⠿⣾⣾⡏⣾⡁⣸⡇⣤⣌⠛⠳⠀⠀⠒⢀⣀⡀⠀⠄⠀⠐⠒⠚⠋⠀⠀⠀⠀⡼⡁⠈⠀⢻⡏
⠀⠀⠀⠀⠀⠲⠖⠋⠙⠁⠉⠐⠩⠟⠋⠩⣾⠭⠯⠷⠛⠉⠰⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡠⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠱⠄⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⢦⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠂⢾⡷⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣿⡇⠙⠆⢆
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠸⢻⡏⠀⡇⠸⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠁⡌⡇⠀⢧⠀⢩⣄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢸⠇⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⢘⡀⠀⡈⢿⣆
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣇⠀⠦⠈⠟
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⡑⢀
⠀⠀⠀⠀⣸⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠷⢀⠀⠀⠀⠀⢀⡹⢦⣶⡀
⠀⠀⠀⢀⣿⣿⣦⠂⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠲⠶⣽⣾⣿⣿⣦⡀
⠀⠀⠀⠈⠛⠛⠷⠾⠷⣤⣤⣤⣀⣀⣸⣻⣰⣀⣀⣠⠀⡀⠀⠀⠈⢂⠀⠀⠀⠀⠈⠉⠙⠛⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣄⣼⣭⣭⣿⣿⣡⣶⠰⣧⣧⣤⠧⣀⣸⣦⣤⣴⠶⠒⠒⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣴⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠙⠹⠟⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⠓⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠿⠌⠁⠀⠀⣠⣤⣶⣽⣿⠷⣆⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠛⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡻⠇⣀⣀⣤⣼⣿⣟⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⢻⠋⣠⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠭⣠⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⡿⠛⠻⡿⣇⠛⠸⣽⢿⡟⢁⣡⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡼⠛⠉⠹⠁⠀⠀⠀⠈⠓⠓⠛⢉⠞⢠⣿⣿⣿⣿⣿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠴⢟⣋⣉⠉⠉⠉⠉⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⢃⡴⠊⢉⣤⠄⠉⣰⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⡟⢧⠀⠀⠀⢀⡀⠈⠒⠀⠀⠀⠐⠈⠀⠀⠉⣀⣤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣎⠓⢦⣰⣆⡙⠳⠦⠔⠀⠀⠀⢀⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⣤⣶⣿⠿⣛⠓⠂⢉⣿⣿⠟⠛⠶⢦⣭⣉⣉⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⣾⣿⣿⣮⣶⣭⣾⠏⠀⠀⠀⢀⣠⣴⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⢀⣠⣤⠶⢾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢿⣽⠀⠀⢉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⡀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣀⣀⣊⢻⣧⣦⣸⣾⡇
⠀⠀⠀⡠⠂⠀⠀⢰⣿⠏⠉⡉⠑⠒⣨⣿⣿⣷⣄⠀⠀⠀⠀⠀⡿⠁⢐⣢⣾⣿⣿⣿⣿⣿⣿⠃⠈⠻⣿⡿⠏⠙⣛⡡⡄⠁⢄⠀⠀⡀
⠀⠀⢸⡇⠀⡆⢧⣷⡉⠻⣟⣀⠀⠠⢄⣄⡈⠻⣿⣷⣄⡀⠀⠀⠛⣿⣿⣿⣿⡯⠥⢴⣶⣿⣧⣤⡤⠾⢷⠿⠛⠉⠀⣠⢡⠆⡜⣀⡼⠛
⠀⠀⠀⠻⡠⣟⠿⣿⡻⢷⣾⣿⣟⠲⡶⢭⣉⣉⠉⣙⣿⣿⣿⣦⣾⣿⣿⣿⣿⢷⣿⣿⡟⢛⣿⣶⡶⠿⠛⠭⡠⠴⢚⣥⢟⡼⠣⠋
⠀⠀⠀⠀⠘⠪⢻⣾⣿⣿⣿⣿⣿⣷⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⢛⣫⡥⣶⣦⣤⣤⣶⣾⡻⣵⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠀⠹⠿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⡿⠟⢯⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠿⠿⣶⣾⣿⣿⣷⡶⠟⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⢦⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠼⠿⠟⠙⠛⠁⠀⠺⢽⣷⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣠⡴⢤⡀⠀⠀⣉⠛⠶⣤⣀⠈⠳⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣠⣾⣭⣷⣿⣿⣿⣶⣄⠙⢦⡈⠻⣷⡢⡀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⣀⣬⡿⠋⠁⠀⠀⠀⠙⣿⣿⣷⣤⣹⣌⢮⣿⡹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠉⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡜⣿⣇⣿⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠇⣿⣯⣿⠇⢸⢇⠄
⠀⠀⣀⡤⠶⠶⠿⠷⢿⣿⣷⣦⣄⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣋⣵⣿⣿⣿⣿⣿⠟⢠⡿⣽⠟⢠⢏⠞⣴⣄⡀⢀⠔
⠀⠈⠁⣀⡤⠶⠞⠛⠻⠿⠿⢿⣿⣿⣶⣄⡈⠉⠙⠒⠶⠶⠾⠛⣛⣩⣭⣶⣿⣿⢿⣻⣿⣿⠿⢋⣴⠟⡽⢋⡴⠫⣫⣾⣿⠟⡡⢋⠔
⠀⠀⠈⠀⠠⠴⢒⣛⣛⣛⣓⣶⠦⣬⣙⠛⠿⣶⣄⡀⠠⣭⣍⣉⣉⣉⡉⠩⠵⣶⣛⣛⣭⡴⠾⠋⠁⠀⠀⣀⣤⣾⡿⢛⣥⡮⣖⡵⠋
⠀⠀⠀⠀⠀⠉⠉⠩⠭⠭⠭⢭⣿⣟⣿⠷⣦⣌⡙⠻⢷⣦⣌⣙⠻⢿⣿⣶⣄⡉⠉⠁⠀⠀⠤⠴⠒⡚⣛⣋⣭⠴⢞⣋⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠻⠿⠿⣿⣿⣿⣷⣮⣭⣅⣀⡈⠙⠻⠿⣶⣮⣭⣛⡻⠷⠶⣤⣤⣤⣤⣤⣤⣤⠤⠶⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠏⠀⠀⡆⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣿⠏⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⣿⡏⠀⠀⠀⠰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢸⣿⠁⠀⠀⠀⠇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣼⡟⠀⠀⠀⢸⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠀⣿⡇⠀⠀⠀⡞⠀⠀⠋⣿⢿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠠⣿⣧⠀⠀⠀⠇⠀⠘⠀⣿⠸⣧
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣀⣽⣿⡀⠀⢸⠀⠀⠃⠖⣿⡇⢿⣆
⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠈⢽⣿⣇⠀⡇⠀⢠⠀⠰⢿⣇⢸⣿⡀
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⣸⣿⣿⣶⠁⠀⠘⠀⢠⣿⣇⠀⢾⣧
⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⢀⠈⠸⣿⣿⡄⠀⠇⠀⠀⢹⣿⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣟⠘⠌⠈⠀⠀⠘⣿⣷⣰⠀⠀⠀⢠⣿⡅⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⠀⣄⠘⣿⣿⡀⠀⢀⣼⣿⣀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⠀⠀⠙⠿⣃⣍⣿⣷⠀⠘⠻⣿⣏⠀⠀⠸⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠄⠀⠀⠀⢀⣉⣹⣿⣧⡀⠀⣿⣿⣷⣀⡀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠀⠀⠀⢪⣿⣿⣿⣿⠳⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣠⡀⣀⣀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣾⣿⡿⢟⠋⢀⠀⠀⢸⠉⠀⠉⣁⣶⣶⣦⡀⢀⣼⣿⡋⠀⣉⣀⣀⣘⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⣿⣿⣿⢿⣿⠿⢿⣤⣤⣭⢉⣿⣿⠿⠿⠿⢿⡿⣿⣿⣿⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣮⣥⣶⣤⣥⣤⣼⣏⣉⣉⣟⣉⣛⠛⠿⠛⡛⠹⠟⡛⡻⠋⠉⠍⣈⠛⣿⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠟⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⢋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣿⡟⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⡀⠀⠀⣀⠘⠻⢛⠛⠋⠉⠉⠉⠉⠁⠐⣒⡄⠀⢄⣀⡀
⠀⠀⠀⠀⠸⣷⡴⠾⠳⠦⠾⠛⠉⠉⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠀⠑⠿⢿⡯⠝⣚⣩⢠⠄
⠀⠀⠀⢀⡀⢽⡇⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠀⠃⣀⣉⡴⢀⣤
⠀⠀⠀⠸⠟⠛⠋⠀⠀⣠⣌⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠠⢐⠁⠀⠈
⠀⠀⠀⠀⠀⠐⢠⠤⢿⠀⢦⠀⠀⠀⠠⣲⡦⠤⠄⠀⠀⠀⠀⣰⡠⠟⠓⠁⣰⠄⡿⠤⡄⠂
⠀⠀⠀⠀⡠⠒⠁⠀⠸⠖⠉⠁⠀⠀⠲⠀⢀⡀⠀⠀⠀⢀⡀⠀⠔⠂⠀⠈⠉⠲⠇⠀⠈⠐⠄⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄⡀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⣈⣳⡀
⠀⠀⢀⣀⠀⠀⢰⠃⠀⡠⠔⡺⠍⠉⠈⢯⣳⠀⢀⠀⠀⠠⠾⠃⠀⢀⣤⡄
⠀⠀⠈⠁⠉⠀⡇⡠⢊⡀⠀⠁⡞⠷⠀⠈⣿⠰⠟⣁⡠⠴⠒⠒⢦⠈⠁⠀⠀⢀⣤
⠀⠀⠀⣠⣀⠀⢹⡕⢁⢤⡄⠀⠀⢠⡶⠀⣿⠔⠊⠁⠀⢀⣤⠀⠀⢣⡀⠀⠀⠛⠁
⠀⠀⠀⠈⠉⠁⠀⠻⡄⠀⠘⠂⣀⠀⠀⢀⠇⠀⠀⠀⡠⠊⢀⣱⢤⡤⡧⣀⣐⣦⡀⠐⠊⠉⠉⠉⠑⠂
⠀⠀⠀⢀⡤⣄⣀⣀⠼⣦⣤⣀⣙⣅⡴⠛⠓⠚⠣⠴⢽⠦⣜⣡⣀⡫⢧⣄⣁⣼⡁⠒⠓⠒⠒⠊⠑
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⣄⢄⡠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠀⠉⠀⠀⠴⠤⠤⠤⠤⠤⠤⠦⠄
⠀⠀⠀⠀⠀⠑⠒⠉⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣀⡤⠤⠤⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠉⠒⠒⠓⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠂⠀⠰⠆⢠⣩⣅⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠄⣀⣀⠀⠁⠀⠀⠀⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣿⠋⢀⣴⡄⠠⣀⡀⣀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣿⠏⠒⠛⠉⠀⠀⠀⠀⣉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣠⣾⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢿⡄⠀⠀⠐⣦⣿⣧⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⠻⣦⡀⠀⠀⠈⠛⠋⠓⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠹⣿⣿⠀⠀⠀⢀⣠⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⡀⠀⠉⠁⠀⠀⠀⠈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠁⠙⠷⣦⣄⣀⡀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡈⠙⠛⠛⠋⠉⢉⡛⠛⠛⠛⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡱⢶⣶⣾⣷⠎⣱⣿⣶⣷⣆⣉⣉⠙⠉⠉⠢⠄⠀⠀⠤⠤⠰⠒⢐⠒⠲⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠰⠁⣟⣛⣛⡃⠀⠉⢩⣉⣡⣠⣤⣦⣤⣴⠥⠤⠤⠤⠤⠥⢤⣌⣓⣒⣠⣬⠷⠆
⠀⣀⣤⣄⠠⠴⠎⠁⠀⠚⠛⠒⠛⠉⠉⠉⠉⠉⠁⣠⣀⣤⣀⣤⣉⠉⠉⠉⠉⠉⠉⠉⠉
⠚⠁⠀⠈⠓⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠻⠚⠶⠶⢤⡶⡶⠶⠛⠛⢷⣤⢤⣄⡀