⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢔⡚⢀⣇⠤⠒⠚⠙⠛⠦⣄⡀⠀⠀⠀⠀⠉⠉⠓⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡜⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢀⣠⠤⠤⠤⢽⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣈⣳⣠⢞⠁⡠⠦⠤⠢⣀⣀⡇⢀⡠⣒⠶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡞ ⢸⠀⠀⠀⠀⠀ ⠀⣀⡴⠚⠉⢉⡀⠀⣠⢄⣠⣜⠀⣀⠀⣠⠞⠱⠒⢡⡷⠋⠀⠀⣘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡼⠀ ⢸⡄⠀⠀⠀ ⢀⡼⠃⠀⡸⠤⠜⠀⠛⠀⣜⡻⠤⠿⠤⣟⢣⢤⡧⣄⠟⠀⠀⠀⠀⠀⣧⣤⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠃⠀ ⠈⣇⠀⠀⣰⠋⠀⡗⢆⠱⡄⠀⠀⠀⠀⣏⠀⠀⠀ ⠀ ⠀⢈⣱⠏⠻⡤⠰⠀⠀⠀⠀⠸⣏⠉⢉⣇⠀⠀⠀⠀⠀⠀⠀⠀
⡞⠀⠀ ⠀⢹⡄⢠⠇⢰⠉⠀⠈⢦⠙⣄⠀⣠⡶⢿⣆⠀⠀ ⠀⠈⠉⠘⣧⣤⢇⡀⠀⠀⠀⠀⣀⠼ ⠀⡞⢈⠉⠳⢦⡀⠀⠀⠀⠀
⡇ ⠀⠀⠀⠀⠹⣾⢠⡜⠂⠀ ⠀⠀⢣⡘⢾⠭⠓⠉⢸⠀⠀⠀⠀⣀⢼⠝⡀⠑⠫⠭⢎⣻⠭⢿⡉ ⢰⡁⠂⠌⠠⢀⠉⠲⡄⠀⠀
⡅⠀⠀⢀⡔⠋⢁⡜⠹⡄⠀⠀⢀⡞⠳⡈⢳⣄⡀⠘⡧⢤⠴⣎⠝⡈⠐⠠⢁⠂⠡⢀⠈⡉⠣⠬⣏⠠⡁⠘⡀⠂⠌⠠⠙⣆⠀
⢹⠀⢠⠏⠀⡸⠀⠀⠀⠙⢦⢀⡞⢁⠂⠹⣄⠻⡵⣄⢈⡽⣩⠅⣐⣠⡥⠲⠦⠙⠚⠓⠓⠲⠶⢤⣘⢷⣌⠐⠠⠁⠌⠠⢁⠸⡄
⠈⡇⢼⠀⡀⢀⣠⠴⢰⠒⠺⡿⢀⠂⠌⠠⠘⣦⠙⣎⡿⢔⡷⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⣦⡈⢳⡙⢷⣌⠐⡈⢁⠂⢄⡇
⠀⠹⣦⠈⡖⠉⠄⠒⠈⠈⢹⠇⠠⢈⠄⡁⢂⠈⢷⡈⢷⠎ ⠀⣴⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠿⠃⠀⡇⣴⠋⠙⠒⠶⠾⠛⠀
⠀⠀⠹⠄⠈⠁⠀⠀⠀⠀⢸⠠⢁⠂⡐⠠⢁⢂⣼⢳⡄ ⢣ ⠸⣿⡟⠀⠀⠀⠀⠘⠤⠂⠀⠀⠀⠀ ⠀⣰⡵⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠂⠄⣁⣢⠾⣥⡸⣟⣆ ⠱⡀⠀⠀ ⠀⠀⠀⠓⠒⠈⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠟⠞⠊⠁⠀⠀⠉⠛⢻⠒⠉⠲⡤⠤⠤⣤⠖⠒⣖⠛⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀ ⢰⠙⠦⣠⡴⣷⠦⠴⢿⠲⡄⠙⢿⢣⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠉⠀⠈⢱⠊⠑⠒⠉⢣⠈⢳⣤⡞⢠⡇⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⢰⠃⠀ ⠀⠀ ⠀⠈⠳⢤⣤⠤⠞⠀⢰⠓⠦⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠲⠤⢯⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀ ⠀⣀⣀⣀⣸⡦⠴⢾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡏⠉⠉ ⠉ ⠉⠁⠀⠰⣯⡄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢧⣄⣀⣀⣀⣀⣀⣀⣠⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀