⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣉⡭⡚⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣟⣴⣋⣀⠀⠀⠉⠲⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠓⠉⠉⠉⠉⢹⡞⠉⠉⠉⠑⠃⢆⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠘⡦⣀⠀⠈⠐⠤⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡠⠤⣄⣀⣀⣀⠀⠀⠂⣂⡾⠱⡠⠃⣠⠖⠁⠀⠀⠀⢠⠃⠀⠀⢸⡀⠑⠄⠀⠀⠙⡄⠀⠈⡧⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀
⢸⠸⢍⠉⠀⠀⠀⠈⠉⠉⣩⠃⡰⣠⠞⠁⡀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡇⠀⠈⠢⡀⠀⠘⢆⠀⠸⡆⠀⠉⠁⠈⠁⠒⠶⠶⢯⢳⡀
⠸⡢⠄⣉⠐⠒⠂⠒⣒⡉⠼⣰⡵⡉⠤⡔⠀⣈⢁⡴⢱⠀⠀⠀⠀⢸⠠⡀⠀⠀⠀⠀⠀⠈⢆⢃⣗⢢⠤⢀⣀⣀⡀⠤⠐⠩⣺⠁
⠀⣏⠒⠠⠤⠄⠐⠦⣤⡤⠗⠋⣀⣠⠞⠀⣠⠔⠉⠀⢸⠀⡀⠀⢠⠇⠒⠱⣄⠀⠀⠰⡀⠀⠀⠣⡧⢉⣐⠂⠀⠀⠀⠐⠂⡉⡏⠀
⠀⠸⡭⣐⣒⣒⣒⣒⡒⠭⢻⢉⡴⠃⡠⢚⣽⣷⣦⠢⠘⢀⠇⡠⢃⠀⢀⣀⡈⠢⣀⠀⠹⡦⣄⣀⣬⡿⠥⣈⣉⣀⣀⡠⠤⢴⠃⠀
⠀⠀⣇⠈⠉⠉⠉⢀⣂⣭⢞⣡⢴⢾⡃⢸⡈⠿⣤⠇⢠⣟⠔⠁⢠⣾⣿⡿⢏⠻⡏⠑⠦⣝⡢⣿⠲⣀⠉⠓⠒⠲⠶⠦⠋⡏⠀⠀
⠀⠀⣇⡉⠁⠈⢉⣁⡽⢭⣿⣇⠇⢸⠁⠈⠂⠤⠜⢀⠝⠁⠀⠀⠀⢧⠚⠳⡞⢀⠃⠀⠀⡆⢸⠙⣯⣫⠍⠒⠂⠤⠤⠤⠐⡇⠀⠀
⠀⠀⢥⢑⡛⠭⠤⠤⠒⠋⣸⢟⣰⠸⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠜⡇⠀⡸⢀⠆⠀⣹⡘⠫⠕⣒⣒⣂⠰⠖⡇⠀⠀
⠀⠀⠸⠤⠄⠾⢶⢶⡺⢿⡁⠀⢳⢆⢷⣝⡲⡤⢀⡀⠐⠤⠤⠀⠀⠀⠀⢀⣈⣴⢁⡼⠧⠊⠀⠀⠛⢦⡤⢄⣀⣀⣒⣒⣸⠇⠀⠀
⠀⠀⠀⠀⢻⣉⣉⣡⡞⠞⠀⠀⠈⠊⠃⠉⠨⣾⡾⠖⣏⣽⣅⢒⣆⠫⣛⠉⣕⠱⠋⠀⠀⠀⠀⠀⠀⠸⣌⠚⢳⠦⢬⡍⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠳⡜⣦⣀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣎⣀⢘⡇⣉⡣⡠⢞⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢒⡶⠚⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⣠⡔⠁⢀⡟⠘⢠⡇⠚⠃⢻⠃⠉⢥⡀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠓⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡷⡞⢠⢒⠃⠀⡤⡇⠀⠀⠐⣣⠀⢈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⣪⡴⢁⠖⡦⢄⣷⣇⣀⢀⠤⡷⣇⠻⠗⡱⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡠⢁⡰⠁⠀⡇⠀⡇⠀⠇⠐⡌⣦⡌⠊⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡅⣒⡠⠃⠀⢅⣒⣚⢭⣵⠞⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⡜⡧⠀⠪⢼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡠⡇⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀