⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢼⠦⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⢜⠄⠀⠀⠀
⠀⠀⠈⠀⠀⢀⡎⡀⢰⠀⢠⠀⠠⠀⢀⠀⢡⠀⢢⠀⠐⡄⠀⠈⠀⠀⠀⠀
⠀⠀⠀⠂⠀⢸⠀⠁⠀⠀⢇⠀⠀⠀⢸⠀⢸⠀⢸⠀⡇⠁⠀⠀⢠⣧⠀⠀
⢀⠀⠂⠀⠀⠈⠣⠷⣘⣦⣘⣄⣰⣀⣜⣠⣎⣤⣂⡴⠕⠃⠀⠀⠀⠇⠀⠀
⢺⠖⠀⠀⡀⠀⠀⠀⠸⢸⠀⡇⠃⢷⢸⠀⠀⡇⢠⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠐⡷⠂⠀⢠⠃⠸⠀⡇⢰⠟⡼⠀⠀⢡⠈⣄⠀⠀⠀⠤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠋⢠⡇⠀⠇⣸⠀⣷⡀⡆⠸⣆⠈⢆⠀⠀⠀⠀⠀⣤⡀
⠀⢀⡀⠀⠈⣠⢃⠴⡹⠁⡸⢰⡏⣇⠻⡇⢳⠀⢣⠣⡜⢆⠀⠀⠀⠀⠈⠀
⠀⠈⣀⡤⡔⠋⠁⢠⠃⡰⠁⡸⡇⣹⢀⣷⠀⢣⡀⣆⠀⠙⢢⠤⣈⠀⠀⠂
⡔⠋⢀⡎⠀⠀⠀⣏⠞⠁⡰⡹⢣⠃⢾⢡⢣⠀⠑⢼⠀⠀⠀⢣⠀⠑⢆⠀
⠀⠀⢸⠀⠀⢀⠔⡇⠀⠰⠁⠇⠘⠀⢸⠈⡆⢣⠀⠈⠱⡄⠀⠈⡇⠀⠈⠀
⠀⠀⠘⠄⢠⠃⢰⠀⡰⠃⠀⣠⠇⠀⠈⢆⡇⠈⢣⠀⡇⠘⡄⠸⠁⠀⠀⠀
⠀⠠⠀⠀⢸⠀⠈⢠⠃⠀⢂⢇⠀⠀⠀⢸⡄⠂⠈⣆⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠄⠈⢆⠀⡎⠀⠀⡞⢸⡄⠀⠀⡇⠸⠀⠀⢸⠀⡰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡀⠀⠀⢳⠀⠀⣇⠀⡀⠀⢀⠀⢠⠀⠀⡼⠀⠀⠸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠋⠀⠀⠀⠣⠀⠘⡄⠁⠀⠀⢀⠎⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⢃⠀⠈⡇⠀⠀⣠⡤⠤⡀⠀
⠀⠈⠺⠭⠝⠀⠀⢰⡇⡇⠀⢹⠀
⠀⠶⠀⣀⣀⣀⣀⠀⠳⠭⠴⠃⠀
⠀⢠⣾⠾⢧⢽⣳⡥⡀⠀⢀⡀⠀
⠀⣿⡇⡄⠀⠀⡇⡿⡅⠀⠈⠁⠀
⠀⢸⣇⠑⠀⢠⢣⡿⢀⣤⡒⠤⡄
⠀⠀⠛⠻⠿⠷⠛⠁⢸⠇⠀⡇⡇
⠀⠀⠀⠀⠀⣠⠶⡄⠈⠣⠬⠗⠁
⠀⠀⠀⠀⠀⠿⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡟⣁⠀⠀⠻⠆⠀⠀⠀⠈⠛⠈⠻⣄⠀
⠀⠀⠀⠀⠀⠀⡟⠸⢭⠵⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠸⡇
⠀⠀⠀⠀⠀⠐⣟⣦⣀⡀⠀⢖⡶⠀⠀⣶⣶⠆⢀⡀⣄⡿
⠀⠀⠀⠀⠀⠀⠀⢹⣯⣹⡷⠶⣤⣀⡀⠀⠀⠀⠀⠁⣹⠇
⠀⠀⠀⠀⠀⣀⣤⢾⠎⡸⢹⣲⢻⣈⣩⣏⠛⢳⣖⣛⡟⠀
⠀⢀⣴⠞⠋⢉⡴⠋⣠⣧⢯⠇⢰⠃⢹⠈⢹⠁⠈⠉⠀⠀
⢀⡞⢁⣠⡴⣋⣠⠞⣽⠋⢸⠀⠘⣇⠘⡄⠘⣆⠀⠀⠀⠀
⠸⣴⠟⠁⢀⡟⠁⠀⡏⠀⢸⡄⠀⢹⡄⢳⡄⠙⣦⡀⠀⠀
⢸⡏⠀⠀⢸⡇⠀⠀⣿⡀⠀⢷⡀⠀⢻⡄⢻⡄⠈⢳⣄⠀
⢸⡇⠀⠀⠘⣧⠀⠀⠘⣧⠀⠘⣧⠀⠈⣿⡀⢻⡄⠀⢻⣆
⠸⡇⠀⠀⠀⠹⣧⠀⠀⠈⢧⠀⢿⡄⠀⢸⡇⠀⣷⠀⠀⣿
⠀⠷⠀⠀⠀⠀⠙⣷⡀⠀⠀⠑⢸⣇⢀⡾⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⣿⠈⠀⠀⠀⢸⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢸⡏⠀⠀⠀⢀⡿⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣠⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀