⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢼⢻⠁⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢾⠈⠀⠐⡄⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⢸⠀⠆⠀⠰⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⡄⠀⡇⢧⡇⠀⠀⠀⠀⠀⠀⣀⣜⠏⠀⢀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⠀⠄⢠⠘⡇⠀⢀⠔⡉⣡⢋⡜⡞⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠠⡀⣸⠀⣿⣠⠂⡜⢠⠇⡞⠰⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣵⢀⢿⠇⡾⢀⠎⡼⠀⡇⠀⠘⣜⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢸⡮⠂⠁⣸⠃⢠⠃⠀⠀⠈⠁⠀⠀⠀⢙⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣄⢆⠀⠀⠀⠀⠀⠀⣀⣀⠀⡸⡸⠀⠀⠀⡏⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⡟⡌⠀⠀⠀⣆⠸⠁⠈⣇⠀⢻⠀⠀⢠⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠇⡇⠀⢰⢉⡀⠈⡶⡆⢸⠀⠈⣇⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢧⠀⡇⠀⢇⡼⠀⠘⡈⣂⠀⠘⣄⢸⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⡟⢿⡦⡈⣷⠀⠀⠘⢄⠑⢄⠘⣜⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠜⠉⠐⠒⠊⠡⠆⠀⠀⠈⠓⢄⠙⢮⣧⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⣠⡀⡠⠤⣤⡤⢄⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠆⣠⣤⡗⠶⠦⠵⣕⠄⠀⠀⠀⠑⡈⢿⢳⡀⠀⠀⠘⣆⠀⠀⠀⠎⠀⢗⠁⠀⠀⠀⠀⡇⠀⠀⢎⡔⠉⠀⠀⠠⠀⠀⢸⡱⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢦⠉⠓⢤⡀⠉⠠⢀⢀⠀⠈⢻⠀⠻⢦⡀⠀⠈⢦⠀⠘⠀⠀⠈⡄⠀⠀⠀⠀⢸⡄⠀⡎⠀⠀⠀⡐⠁⠀⠀⣸⠧⠀⠁⠄⡀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠁⠓⠰⠶⡞⠳⠿⣿⣦⡀⠐⢕⢄⠀⠀⠳⡄⠀⠀⠀⠡⠀⠀⠀⠀⠀⢳⣼⢁⠀⠀⠰⠁⢀⠴⠊⠀⠀⡀⠀⠀⠀⠉⠐⠢⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠻⡀⠀⠰⡈⠙⠲⢤⣑⣅⢄⠀⢱⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⢿⣿⠃⠀⠇⢠⠂⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣕⣠⣤⣤⣬⡽⣷⣷⣤⣧⡀⠀⢀⡀⠉⠈⢆⣿⡄⠈⡏⠀⢰⢀⠃⠔⢀⠠⠐⠀⢀⡀⠠⠤⠄⠀⠀⠀⠀⣸⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠘⣦⡀⡴⠂⠁⠀⠀⠀⠉⠢⢘⠟⠁⣿⠄⡫⣱⡀⡇⠀⢸⡜⢌⠔⠀⢀⣀⣀⣀⣀⡀⠠⠤⡄⠔⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠠⠐⠒⠒⠒⠂⠠⠄⢙⡲⢥⣈⢪⡪⡷⣰⡀⢸⣿⣧⠼⣚⡋⠉⠉⠉⠁⠉⠉⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡠⠙⢓⣻⡿⠿⣹⣧⢸⠏⠉⠁⠀⠉⠤⢤⣀⠀⠀⣀⠈⢶⣯⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢸⣀⡤⠒⠒⠒⠖⢲⠤⠤⠤⣤⠴⠚⠉⠀⠀⠈⡉⠕⠋⢉⣽⠙⠩⡐⠠⡀⠐⠠⠀⠈⣶⠋⢥⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡞⣦⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠑⢄⡞⠉⠀⠀⠀⢀⠔⠈⠀⠀⠀⠂⣷⠀⠇⠀⠄⠈⠀⣀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⢸⠁⠀⠀⠀⢰⢠⡀⢳⡀⠀⠀⠀⣀⣼⠀⠀⠀⢀⠀⠁⠀⠀⡠⠀⢀⣼⣷⠀⠠⠀⠀⢀⠀⠁⢀⠀⠀⠀⠸⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⡏⠀⠈⠂⠥⣀⣠⡼⢅⠀⠀⠔⠁⠀⠀⠈⣀⣤⢾⠛⢁⠟⣇⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢣⠈⠡⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠈⡙⢀⠂⠀⠀⣠⡤⠋⢍⠀⢸⡂⣸⠀⠘⠁⠶⠠⣄⡀⠀⠐⠠⢀⠐⠄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢀⠆⠀⢀⡴⠉⠁⢹⡄⠈⡄⠀⣧⡇⠀⠀⠀⠀⠀⠈⠘⠓⠲⠤⠠⢤⣠⣄⣈⣣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠳⠀⢠⠖⠀⠀⠀⠘⠦⠒⣋⠀⠀⠀⡄⢿⡀⢠⠀⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠞⡔⠁⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⢷⢸⠀⡇⡏⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢱⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢀⣧⡇⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⣒⣒⡲⠶⠤⠴⣖⢶⢤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢹⠀⠀⠀⠀⢀⠠⠂⠁⣠⠴⢚⡽⠋⠁⠀⠀⠀⠀⠀⠙⠧⡪⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⣏⠀⠀⡠⠊⢀⣠⠖⠉⣠⡮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣰⠏⢀⣶⠏⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸𝔈⠞⠁⢴⠟⠁⠀⣴⡫⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⣠⠞⠁⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣒⣉⣀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀