⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢰⡄⠐⣀⠛⠛⠛⠐⠒⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠉⠀⠀⠘⢁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠁⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⡴⠂⠀⠤⠀⠀⠀⠐⠂⢰⠀⢠⠀⠀⠀⡄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣨⡋⠰⠀⢰⡆⠀⠀⠀⣷⢀⣤⠀⠀⠱⣆⠀⢡⠀⠀⠀⣠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠀⠇⠀⣤⠀⠀⠀⢠⡄⠘⠃⢂⠀⠀⠹⠆⠘⠀⠀⠀⠿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⠀⠸⠀⠀⠿⠀⠀⠀⠸⣧⣤⠀⠀⢦⠀⠀⠈⡄⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⡀⠀⢰⡆⣇⠀⢀⣿⣿⢠⡴⠾⢷⡀⠀⠘⡅⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⡇⠀⠀⣠⣏⡄⠀⢉⣿⠀⠀⠀⠀⠹⣆⠀⢸⠀⠀⠀⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠠⢤⠀⣶⠀⢃⠐⠘⠿⣻⣬⣷⠶⢶⣶⡤⠥⣸⠀⠀⠀⡇⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⢥⣤⠈⡠⠛⠀⠀⠀⢐⣿⠟⠁⣏⣾⠋⠡⠖⠀⢸⠀⠀⠀⠃⠀⢠⡤⠖⠢⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢻⣴⢿⠿⣷⡀⠀⠀⠀⠈⠁⢀⡤⠏⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠛⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣧⡈⠭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢰⡆⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢉⡾⠙⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊⢁⡄⠀⠀⠀⢠⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⢀⡤⠤⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡈⠀⣤⢸⡇⠀⠀⠀⠘⠃⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⠀⣿⢸⡇⠀⠀⠀⠀⢰⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢸⠀⠀⠀⢀⡇⠀⠋⣸⡇⠀⠀⠀⠀⠸⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⡀⠴⠋⠁⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣤⠀⠒⡀⠀⡀⠤⠒⠈⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣄⡇⠀⠀⣶⠀⠀⠀⠀⠀⠀⢠⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡿⠀⠀⠑⠓⠒⠚⠉⠉⢇⠀⢀⣤⠖⠒⢹⠀⠀⠀⡇⢠⠀⠀⢩⡄⠀⠀⠀⠀⠀⠘⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⢰⡄⣿⠀⠀⠀⠀⠀⠀⣾⡴⠋⠀⠀⠀⠸⠀⠀⣴⠀⠈⠧⡀⠀⢱⠀⠀⠀⠀⠀⠀⢱⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟⠘⣃⠛⡀⠀⠀⠀⠀⠀⡟⡁⠀⠀⠀⠀⡀⠀⢀⡛⠀⢀⠴⢫⣿⠿⠓⡲⣶⡦⠤⡦⠔⠓⠛⠒⠒⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⠀⢛⡀⠇⠀⠀⢀⣠⣄⠃⢱⡀⠀⠀⠀⡇⠀⠸⠇⠀⠣⣀⣀⣠⠔⡆⠉⠉⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠈⣥⣸⡤⠊⡽⠿⢿⠇⡴⢁⠤⠐⠈⡇⠀⠿⠀⠀⣠⣿⣿⣿⣾⣶⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣏⣤⡴⠊⠉⣉⠤⠾⠷⢰⠏⠀⡇⠀⠀⠀⢀⠇⢰⡄⠀⣴⣿⣿⣿⣿⣿⡟⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠀⠀⣠⠁⠀⣠⣶⡎⠀⠀⠀⠰⠏⠀⠀⠸⠀⠀⠀⢸⠀⣌⢡⡾⣄⠙⠿⣿⣏⣻⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢸⠀⠀⣿⣴⣿⣿⣿⠀⠀⠀⢠⠟⣀⠀⠀⠀⢿⣀⣠⡆⢀⠛⠻⣦⡈⠋⢹⣯⣽⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠸⠀⢸⣿⣿⣿⣿⠿⠶⠶⠶⣧⣠⠿⣠⡴⠖⠁⠀⣸⠁⡜⢀⣬⣿⠟⠋⣝⠟⢸⣿⢦⡀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡆⠀⣶⣛⣛⠿⠋⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣠⣼⢿⢀⢃⣾⣿⠃⠀⠀⢿⡇⠈⢻⠈⠙⢶⡆⠀⠀⣤⠤⣤⣔⣒⡚⣳⢤⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠃⢰⡟⣨⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢸⢮⣛⠂⠀⠀⢸⡌⠁⠀⠈⡆⢀⡿⠀⠀⠀⠈⠉⠉⠉⠑⠦⡤⠖⠚⢻
⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⢸⣠⠛⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡇⢸⠳⠀⠀⠀⠀⡌⡇⠀⠀⠀⢙⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⡜⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⣷⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣧⠈⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠈⣅⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠃
⠒⠒⠒⠂⠀⠀⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠁⠀⠀⠀⠀⠃⠂⠀⠀⠀⠃⠀⠛⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠛

⠿⠿⠶⠿⢿⣿⣿⣿⣿⣦⣤⣄⢀⡅⢠⣾⣛⡉⠄⠄⠄⠸⢀
⣴⣶⣶⡀⠄⠄⠙⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢃⣤⣄⣀⣥⣿
⣿⣿⣿⣧⣀⢀⣠⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿
⣤⣤⣤⣬⣙⣛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡍⠄⠄⢀⣤⣄⠉
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠶⠶⢿⣿⣿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣥⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣿⣧⠙⠛⠛⡭⠅⠒⠦⠭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⡆⠄⠄⠄⠄⠄⠄⠄⠄⠹⠈⢋⣽⣿⣿⣿⣿⣵⣾
⣿⣿⣿⣿⣿⠄⣴⣿⣶⣄⠄⣴⣶⠄⢀⣾⣿⣿⣿⣿⣿⣿⠃
⠛⢿⣿⣿⣿⣦⠁⢿⣿⣿⡄⢿⣿⡇⣸⣿⣿⠿⠛⠁⠄⠄⠄
⠄⠄⠉⠻⣿⣿⣿⣦⡙⠻⣷⣾⣿⠃⠿⠋⠁⠄⠄⠄⠄⠄⠄
⣮⣥⠄⠄⠄⠛⢿⣿⣿⡆⣿⡿⠃⠄⠄⠄⠄⠄⠄⠄⣠⣴⣿