⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣀⡀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⣀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣟⡟⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣸⣿⣿⣭⣿⣯⡻⢟⣽⣽⢿⣽⣧⣀⣿⣿⠓⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⢀⡀⠀⠀⠀⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠀⠀⢀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣑⢮⣑⢄⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣟⡲⣽⣄⣴⣵⠮⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠋⡟⣚⣽⣯⣿⣿⣿⣿⡿⢟⠭⣲⢏⣣⡯⠽⡼⣙⣺⣕⢪⢛⣿⣿⣿⣿⣿⣿⠟⠋⢧⢡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⡜⡰⢁⢒⣿⢿⣵⣿⣏⣾⠚⠉⡏⢂⡇⢳⠀⡇⢸⡟⠣⡍⠓⢻⢜⣿⣿⣿⣧⠢⡈⢆⢿⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢃⠇⣼⢿⡿⣿⡻⢠⡟⠀⡸⠀⠄⡇⡿⡇⡇⠀⡇⠀⢻⡜⠸⣄⢣⣿⣿⢻⣇⠸⡘⡜⣿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠃⡬⣿⠆⡟⣸⡏⡿⣯⣿⠁⡰⠥⠤⡇⣷⢠⠹⣴⠀⠀⠄⠀⠻⡄⢿⠿⢶⣏⣇⢫⠄⠹⠜⢼⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⡘⣴⠟⣼⢡⣿⣦⠁⣠⢻⣘⣀⣀⡀⣱⠈⣜⡀⢸⠢⢸⢠⣤⣤⣾⣾⠀⣞⣯⣾⡌⠶⡀⢈⠈⢿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡔⠽⢁⣾⢃⢾⢿⠹⠐⠀⡿⠉⡋⢹⠙⡾⠒⠘⠒⠘⠃⠟⢛⠰⠂⡁⣙⡃⡇⡇⡸⠟⡌⠵⡀⡄⠈⢫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⢌⡴⡟⣅⢎⠆⠘⡄⢶⠁⡷⠁⠰⠤⠔⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠂⡸⠆⣿⣰⠃⠘⡘⠌⢆⠘⢦⡂⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⣪⣾⠋⣼⡞⠎⠀⠀⠈⣿⡄⡧⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢑⠁⣿⡇⠀⠀⠐⣫⣯⢢⡹⣳⡜⢝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣴⣿⠟⢁⢼⠟⠌⠀⠀⠀⠀⢉⡇⢸⡡⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣽⢸⢻⠀⠀⠀⠀⠐⠞⢷⣝⢵⢝⡦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⢟⠕⣡⠔⢉⢊⠎⠀⠀⠀⠀⠀⢸⣿⡘⣇⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡙⡆⡞⢨⠀⠀⠀⠀⠀⠈⠪⠊⡑⢧⡌⠋⢦⡑⢕⡠⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⡠⠕⡡⢖⠥⠊⢁⢔⠔⠁⠀⠀⠀⠀⠀⠀⢸⠇⠳⡹⡦⠀⠀⢣⣇⣐⣠⢤⣂⣉⡴⢁⢔⡿⡜⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⡈⠣⢆⡘⠢⢝⠔⡥⢂⠀⡀
⠀⠀⢠⣐⠬⢊⣉⡤⠟⣊⣡⡴⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⡚⢀⡨⠟⠛⠧⠤⠛⠛⢿⣃⣝⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢄⠄⡉⠒⠄⡃⠌⢂⠌⡀
⣐⠌⣊⣡⡴⠮⡗⠬⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠀⠐⠒⠂⣝⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⣝⡆⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠥⢂⠄⣉⠒⢤⡆
⢰⣫⠾⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠀⠀⠀⠀⠀⠀⠀⣼⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡀⠀⠀⠈⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠡⠌
⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⡀⠀⠀⠀⠀⠀⠀⠀⣸⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣇⠀⠀⠀⠀⠀⠀⠈⣿⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣵⢿⣱⢣⠀⠀⠀⡄⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡀⠀⠀⠀⠀⠀⠀⡸⣽?