⠟⠉⠀⠀⡌⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠒⠄⡀⡐⠡⢢⠀⠀⠔⡼⠤⠊⠁⠀ ⡿⠁
⠏⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠁⡇⠀⠀⠀⠈⠀⢰⣾⠀⠀⢿⡇⠀⠀⠀⠀ ⠃⠀
⠃⠀⠀⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⢋⣀⡠⠤⠒⠒⠒⠒⠢⠿ ⡟⠀⠀⢿
⠇⠀⠀⠀⠀⡎⠀⠀⠀⢸⠀⠀⢀⠔⠁⠀⠀⢀⠄⠊⠉⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿ ⡇⠀⠀⢸
⡏⠀⠀⠀⠀⢠⠁⠀⠀⠀⠘⣆⠔⠁⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⡇⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⡇⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢄⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⢱⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⢀⣤⠞⠁⠀⠀⢣⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠊⠠⠃⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠱⡀⣀⡴⠋⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠠⠮⠥⡲⠁⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⡘⠀⢇⠀⠀⠀⠀⠀⠀⠀⡸⠀⣠⠿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⢠
⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣜⠀⠀⠘⡄⠀⠀⠀⠀⠀⣰⣣⢞⣡⣤⣼⣦⣀⣀⠀⠀⠀⡀⠀⠀⣀⠔⣸
⣷⠀⠀⠀⠀⠀⠀⢠⠈⡣⠔⠂⡡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣊⣈⡓⢦⡀⢣⠀⡆⠀⠀⡰⠋⣵⠟⣉⣀⡈⠙⠻⣷⡦⠤⢤⠼⠯⠉⠁⣰
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⢛⣋⣙⡛⠦⠀⠘⣤⠃⣠⠞⠁⠀⠁⠀⢨ ⣆⠀⠹⣷⠦⢸⠀⠀⢀⣴
⡇⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⡟⠁⠀⢈ ⣄⠀⠀⠋⠈⠀⠀⠀⠀⢸⣶ ⡄⠀⢹⡀⠸⣤⣶
⣧⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠛⠍⠉⠁⣀⡿⠀⠀⣦⣾ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣏⠻⠿⠟⢸⡇⠀⠘⡅⠀⢻
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⡇⠀⠈⣟⠻⢿⡿⠏⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⠞⠀⡀⠀⢰⠀⠈⢿
⡄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡰⠂⡇⠀⠀⠘⣧⠀⠀⠹⣦⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡍⡑⢀⠂⠈⠀⠀⠈
⠇⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢰⠁⠐⢲⠀⠀⠀⢃⠐⠠⠤⠄⡉⡃⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⠔⠰⠁⡌⡌⡸⠀⠀⢀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⠀⢀⢸⡄⠀⠀⠈⠢⣌⣈⡐⡰⠠⠁⢰⠦⠤⡤⠴⠚⠉⠉⠙⠻⢿⣯⣹⠀⠀⠀⠠⠔⡁⠀⠀⢸⣼
⢇⣴⠃⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢣⣴⡿⢳⠀⠀⠀⠑⢖⡁⠐⠁⠀⠀⢸⠘⠜⠁⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⡰⠀⠀⣠⣾
⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣼ ⠁⠀⢧⡀⠀⠀⠀⠈⢑⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠴⣥⠖⢊⠇
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⠸ ⠀⠀⠀⠛⣬⣷⡂⠒⠁⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡤⢾⣧⡤⠎⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⠙⢧⣀⣀⡠⠎⠉⠛⠂⢄⡀⠀⠀⠀⠀⠑⠦⣄⣀⣀⣠⠴⠞⠁⣀⡤⠚⠉⠀⠘⢿ ⣤
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠄⠀⠀⢰⣤⣀⢠⠔⣾⣇⡒⠢⠤⠤⠤⣀⢠⣤⡴⠒⠚⠉⠁⢠⣤⣴⡶⠾
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣬⣶⣤⣸⠿⠛⣉⡱⣟⣸ ⠿⣷⡶⢶⣶⡿⢿⣏ ⣶⣶⣶⣶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢌⣽ ⠟⢁⠔⠉⠀⠀⠈⠙⠻⠶⠿⠷⠾⠿⠟⠛⠁⠉⠙⠻⢿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⢎⣾ ⢏⢠⣮⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙