⣠⠴⠒⢛⣋⣉⣉⣉⣉⣛⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠴⢚⡭⠖⠚⠉⠉⠁⠀⠀⠀⠀⠉⠉⠓⠲⢭⡓⢦⡀⠀⠀⠀
⠀⠀⠀⠀⣠⢞⡥⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡝⢦⠀⠀
⠀⠀⠀⣰⣫⠞⡤⡀⠀⢀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣎⢧⠀
⠀⠀⢰⣷⠇⠈⠛⣵⠄⠀⢁⡆⠀⢠⠇⠸⢼⡀⠾⠻⠢⡄⠀⠀⠀⠀⠀⠘⡾⡆
⠀⠀⡏⡼⠀⠀⣼⠏⠀⢠⣾⠀⢀⡞⣳⡀⠈⣧⠀⠀⠀⢹⡄⢀⡶⣛⣓⣦⢹⣷
⠀⢸⠁⡇⠀⣸⠁⠀⣠⢯⡇⢀⣾⣀⠀⢳⡄⢻⡄⠀⠀⠈⣿⣸⣸⠁⠀⢸⠈⢹
⠀⢸⠀⡇⢠⠇⢀⡜⢁⣟⡴⠋⠀⠉⠉⠓⠻⡜⡇⠀⢀⣖⡿⠿⠋⠀⠀⠋⠉⢻
⠀⢿⠀⣇⢸⡞⠁⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣟⠁⠀⠀⡟⢦⠀⠀⣸
⠀⢸⠀⠹⡾⡯⠿⠦⡄⠀⠀⠀⢀⣤⣦⣄⡀⠀⣧⠀⠀⠈⡷⠆⠀⣇⠸⡆⢾⡷
⠀⢸⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⣿⠀⠀⠸⣇⠀⢀⣿⠀⠹⣾⠃
⠀⢸⠀⠀⡇⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⠉⢸⠀⠀⢙⠀
⠀⠈⡇⠀⢧⢻⡀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⢸⠉⢸⠀⠈⡇⠀⠀⢧
⠀⠀⢹⠀⢸⠈⢷⣄⠀⠈⠃⠘⠉⠁⠀⠀⠀⣠⣿⠀⠀⡏⠀⠘⡀⠀⢿⠀⠀⠈
⠀⠀⠀⢇⠀⢇⠀⠙⠳⣤⡀⠀⢀⣠⡤⢖⣋⡥⡇⠀⣸⠀⠀⠀⣇⠀⢹⡇⠀⠀
⠀⠀⠀⠈⢇⠘⣄⠀⠀⠀⠉⢩⢿⣷⣿⡉⠀⢸⠇⢸⠟⢳⠤⠤⠼⣄⡘⣿⡀⠀
⠀⠀⠀⠀⠈⣧⡙⣴⠋⠉⠉⣻⣾⣇⣿⣧⠀⣼⣰⠃⣰⠋⢀⡤⠖⠂⠈⢳⣧⠀
⠀⠀⠀⢠⡞⣫⠽⢿⣇⡴⡏⢻⣿⣿⣟⣟⣿⡷⠃⣰⠃⡴⠋⠀⠀⠀⠀⠀⣿⢧
⠀⠀⠀⢸⡇⠐⠚⠡⣿⢧⠁⠀⠛⢻⠄⡏⠞⠀⢰⢇⡞⠁⠀⠀⢀⠤⡀⠀⣿⠘
⠀⠀⠀⣸⡇⠀⠀⢸⡏⠈⠀⠀⠀⢸⣶⠛⢦⠴⣻⡞⣀⣀⣰⠮⠶⠚⠁⠀⣿⡄
⠀⢀⡏⡿⢧⡀⠀⠀⣧⠀⠀⢀⣠⠞⣿⣤⠞⢰⠋⠉⠁⠀⠀⠀⢀⣤⠀⢸⡏⢧
⠀⢸⠁⠙⢦⣙⠦⠼⣿⡖⠚⣉⣠⠖⠁⠸⡄⡿⠀⠀⠀⠀⠠⠚⠉⠀⠀⡞⡇⢸
⠀⡟⠀⠀⠀⠎⡍⠉⢹⢿⡏⠁⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣷⠀
⡼⠃⠀⠀⠀⠆⡇⢀⠟⡆⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⢻⠀
⠁⠀⠀⠀⠀⠀⠁⡾⠀⢹⡘⠃⠀⠀⠀⠀⠀⠈⢣⢤⡀⠀⠀⠀⢠⠇⠀⢸⢸⡆
⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠆⠀⢠⠏⠀⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠏⠀⠀⠀⡇⠀⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣻⠁⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠳⢶⣦⠤⣀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡇⡴⠋⣀⠴⣊⣩⣤⠶⠞⢹⣄⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⢠⠈⠙⠢⣙⠲⢤⠤⠤⠀⠒⠳⡄⣿⢀⠾⠓⢋⠅⠛⠉⠉⠝⠀⠼⠀⠀⠀
⠀⠀⠀⠀⢸⠀⢰⡀⠁⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠈⠺⢿⣂⠀⠉⠐⠲⡤⣄⢉⠝⢸⠀⠀⠀
⠀⠀⠀⠀⢸⠀⢀⡹⠆⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠙⣷⡄⢸⠀⠀⠀
⠀⠀⠀⠀⢸⡀⠙⠂⢠⠀⠀⡠⠊⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠄⠀⠀⠑⢦⣔⠀⢡⡸⠀⠀⠀
⠀⠀⠀⠀⢀⣧⠀⢀⡧⣴⠯⡀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢸⡠⠔⠈⠁⠙⡗⡤⣷⡀⠀⠀
⠀⠀⠀⠀⡜⠈⠚⠁⣬⠓⠒⢼⠅⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡀⢹⠀⠸⡄⠀⠀
⠀⠀⠀⡸⠀⠀⠀⠘⢸⢀⠐⢃⠀⠀⠀⡰⠋⡇⠀⠀⠀⢠⠀⠀⡿⣆⠀⠀⣧⡈⡇⠆⢻⠀⠀
⠀⠀⢰⠃⠀⠀⢀⡇⠼⠉⠀⢸⡤⠤⣶⡖⠒⠺⢄⡀⢀⠎⡆⣸⣥⠬⠧⢴⣿⠉⠁⠸⡀⣇⠀
⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⣰⠋⠀⢸⣿⣿⠀⠀⠀⠙⢧⡴⢹⣿⣿⠀⠀⠀⠈⣆⠀⠀⢧⢹⡄
⠀⣸⠀⢠⠀⠀⢸⡀⠀⠀⢻⡀⠀⢸⣿⣿⠀⠀⠀⠀⡼⣇⢸⣿⣿⠀⠀⠀⢀⠏⠀⠀⢸⠀⠇
⠀⠓⠈⢃⠀⠀⠀⡇⠀⠀⠀⣗⠦⣀⣿⡇⠀⣀⠤⠊⠀⠈⠺⢿⣃⣀⠤⠔⢸⠀⠀⠀⣼⠑⢼
⠀⠀⠀⢸⡀⣀⣾⣷⡀⠀⢸⣯⣦⡀⠀⠀⠀⢇⣀⣀⠐⠦⣀⠘⠀⠀⢀⣰⣿⣄⠀⠀⡟⠀⠀
⠀⠀⠀⠀⠛⠁⣿⣿⣧⠀⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⠈?