⠀⠀⠀⠀⠀⠀ ⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾
⠀⠀⠀⠀⠀⡐⢕⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢳
⠀⠀⠀⠀⢰⢕⡇⠀⢀⡞⠙⢆⠀⠀⢀⣀⣀⣠⠶⠛⠉⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢸⢕⡇⠀⣸⠀⠀⠀⠉⠒⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢸⢕⠗⠉⠏⠀⢀⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠃
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠈⠁⠤⣆⠪⠸⠀⠒⠂⠜⠒⠀⠀⣠⠞⢷
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠚⠲⠶⡤⡤⠔⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⡾
⠀⠀⠀⠀⠀⠙⠛⠉⠑⠒⠢⠤⣾⡷⠓⢾⡷⠈⢾⣷⠒⠒⢾⣷⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣚⣥⣤⠀⠀⢀⡷⠔⠒⠒⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣾⣿⠟⠁⡠⠖⣡⣶⣶⣶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡔⣱⣿⠟⠁⡠⠊⣠⣾⣿⡿⠟⠁⠀⢀⠌
⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠉⠀⠘⠛⠛⠁⠀⣀⠤⠚⠁
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠁
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ 
⠀⣰⠁⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ 
⢰⠃⠀⠀⠛⠁⠐⠂⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⢹⠀ 
⠈⢧⣠⣾⣷⣦⣠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⡇
⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠈⢿⣿⣿⣿⣿⣯⡉⠉⠉⠒⠲⢤⡔⠁
⢀⠔⠁⠈⠻⣿⣿⡿⡋⠉⠓⠦⡄⠀⠀⠉⢫⠉⡆
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠈⢢⠤⠤⠜⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢇⠀⡖⠒⠒⠤⣀⠇

.............................⢀⣶⣶⣦⣀⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠙⠿⠋⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣤⠈⠓⣻⠏⠀⠹⣟⠚⠁⣤⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⡇
⣤⠤⠶⠶⠖⠚⠛⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⠶⠶⢤⣤
⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠈⠙⢳⡶⠖⠛⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠛⠲⢶⡞⠋
⠀⠀⠀⣰⠏⠀⠀⠀⢀⣀⣤⠶⣏⠀⠀⠀⠀⠀⠀⠀⢹⡶⣤⣀⡀⠀⠀⠀⠹⣆
⠀⠀⠈⠙⠛⠛⠛⠋⠉⢻⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡟⠉⠙⠛⠛⠛⠋

⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⣸⡏⣻⣦⣤⣤⣤⣤⣀⠀⠀⣀⣤⣤⣤⣤⣴⡟⣹⡇
⠀⠀⣸⡇⠀⣹⡆⠀⠀⡈⡙⣷⡾⡋⡁⠀⠀⣰⣏⠀⣸⡇
⠀⠀⣾⡛⡛⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡛⡛⣷
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋
⠀⠀⠀⡘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡃
⠀⠀⣀⣀⣈⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⡁⣿⣦
⠀⣾⡋⡉⡉⡻⣮⡻⣦⠀⠀⠀⠀⠀⣀⣴⡟⡁⠀⣠⣿⣬⣷
⠀⣻⣄⠀⠀⠀⡈⣻⣌⣻⣦⣀⣀⣴⡟⡁⠀⠀⠀⡉⣱⡟⡛
⠀⠀⡉⡛⡶⡶⡶⡞⡛⣯⣈⡉⡉⡁⠀⠀⠀⠀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡷⣦⣤⣤⣤⣤⡶⡟⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣆⠀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⡿⠀
⠀⡴⡟⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣿⣿⣿⣯⡙⡄
⢸⡃⣇⣀⣄⣤⡄⠀⠀⠀⠀⢀⣔⣿⠏⠁⠀⠀⠘⣿⣼
⠸⡼⣿⣿⡿⠭⣎⡗⣆⡀⠀⣾⣿⠏⠀⠀⠀⠀⠀⣿⡟
⢸⡜⣿⡟⠉⠀⠀⠉⠧⣵⣤⣿⡇⠀⠀⠀⠀⠀⠀⣿⠃
⢸⡇⣿⡇⠀⠀⠀⠀⠀⠠⢹⣿⠀⠀⠀⠀⠀⣀⣾⠃⠀
⠈⠻⣿⡗⡀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣠⡿⠁⠀⠀
⠀⠀⠙⣟⡷⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀
⠀⠀⠀⠀⠉⠉⠓⠬⣅⡱⣂⢄⠀⠀⡞⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢗⣼⣁⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠰⡭⡲⠤⠤⢤⠞⣉⣶⡿⡝⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡲⠃⠀⠀⠀⠸⣀⣻⣀⣹⡅⣹⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣇⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣉⣯⠀⠸⠀⠀⣠⡀⠀⠺⠀⠀⡧⠆⠀⠀⠀⠀⠀⠀
⠀⡗⣄⠀⠀⠀⠀⠀⠜⡣⠤⠤⢄⡉⢁⡠⠤⠤⣼⠣⠀⠀⠀⠀⢀⡰⢳
⠠⡓⠤⠍⠉⠉⠑⠢⡜⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢣⠊⠉⣀⠀⡠⠔⣳
⠀⠹⣖⣂⢈⠉⠃⢀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠋⢈⠇⢐⠾⠁
⠀⠀⠀⠁⠊⠉⠈⠁⠈⢷⢄⠀⠀⠀⠀⠀⢀⡠⠊⠀⠉⠈⠉⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀