⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢷⣀⢀⣆⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢣⡞⣡⡴⠖⠒⢶⣄⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡉⣿⠀⡏⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⢻⡄⣷⠀⠀⠀⢀⡀⡿⠆⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠶⠮⠻⣜⢧⡀⠀⡿⠟⠁⠀⠀⠀⠀⣠⣾⢵⣇⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢯⡳⣄⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠈⢳⠛⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣷⣄⠀⠀⠀⣼⠁⠀⢠⠄⠀⢈⣟⡁⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⣩⣭⣝⣒⠮⣝⣧⣄⠀⣯⠀⠀⠹⠧⢴⡿⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣎⣼⡋⠉⠈⠉⠙⠛⠶⣽⡻⣷⣿⡀⠀⠀⠀⢈⣁⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡗⣂⠀⠀⣀⣇⠀⠀⠀⠀⠈⠉⠙⠿⣆⠀⢠⡏⢁⢈⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠭⠯⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⡈⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠶⣄⠀⠀⢿⣆⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠠⠀⡿⠀⠀⡸⣿⠰⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠉⠉⠁⠀⡰⠃⣿⠀⠓⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠀⢰⢻⢀⣏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠁⠈⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣾⢰⡍⠀
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣼⢇⠷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⡘⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠙⠿⢷⣶⣤⣤⡴⠶⣫⣿⠟⡬⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣇⠛⠂⠀⠀⠀⠀
⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⢋⣽⡿⡫⠶⠉⠀⠀⠀⠀⠀⠀
⠀⠃⠤⢀⡀⣀⡀⣠⡄⠠⣶⡆⣀⡤⠖⣫⣾⣿⠻⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠉⠁⠙⠁⣠⡴⠚⣁⣴⣿⠟⣥⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⣠⣾⠿⣫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠋⠀⣠⣾⠟⢡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠟⠀⣠⡾⠋⠀⠀⡿⡆⠀⢀⡶⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⠃⠀⣴⠟⠀⠀⠀⢰⡇⡇⠀⠘⣇⣀⡔⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⠃⠀⣼⠃⠀⠀⠀⠀⢸⡇⠘⢦⣀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡏⠀⢰⠃⠀⠀⡰⠀⠀⠸⣷⡀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣤⠚⠉⠙⢦⡀⠀
⢸⠇⠀⢸⠀⢀⠆⡇⠀⠀⠀⢣⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣷⡄⠀⠀⠹⡄
⢸⡆⠀⢸⠀⣼⠁⣷⠀⠀⠀⠈⢧⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠶⠆⠹⣷⣄⠀⠀⠈⠻⣖⢤⣀⡀⠀⠀⢀⣠⣴⡿⠀⠿⠆⣰⠇
⠀⢸⠀⠀⠀⢶⡆⠀⠀⠉⣁⠀⠀⠀⠈⠳⣄⡉⢙⢛⢛⡏⣥⠘⢗⣠⠞⠁⠀
⠀⠀⠃⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⣀⡀⠈⢦⠉⠓⠶⠶⠶⠒⠚⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡞⢉⡉⠙⣦⠈⢷⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠱⠴⠞⢀⡿⠂⢸⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠴⠞⠁⠀⣼⡇⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢡⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀