⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⡄⠀⡀⠀⠀⡀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠴⠔⠐⠈⠀⠀⠀⠀⢀⠀⡐⠀⠁⠁⠄⠐⠀⠈⠀⠂⠄⠆
⠀⠀⠀⠀⠐⠀⠀⠀⣇⠀⠀⠀⢠⠂⢂⠁⠀⠀⣄⡀⠀⠀⠀⠀⠈⡐⠀⢀⠀⠂⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⢰⢰⠌⠀⠈⠀⠠⠤⢱⠹⠬⠆⠀⠭⣧⠱⢴⢥⠀⣤⠈⠀⠀⠠⠅
⠀⠀⠀⠘⢰⡐⠅⠀⠀⠀⠈⣘⠒⠁⡀⠀⢠⢠⠀⣀⡂⡄⡀⣦⡰⠰⢚⠚⣉⣀⡃⡀⢀
⠀⠀⠤⠐⢠⠐⣤⢥⠀⠀⡤⡜⠀⢀⠁⠃⠈⢠⠐⢨⢥⡥⡇⠇⡤⣴⢸⠸⢁⡥⡇⡏⡭⡜⢴⢰⣤⡀⠀⠀⠀⢀
⠁⠀⠐⠒⠍⠆⡄⠠⢒⠘⢰⡀⠄⠀⠀⢈⠡⢀⠰⠘⡗⡇⡇⢴⢺⡚⢀⡺⠋⡁⣅⣁⢉⢘⠚⠚⡔⡇⣇⣱⢠⠐⠐⠘⡒⠀⠀⠂
⠀⠀⠀⠀⠂⡂⡁⢴⣤⢈⠠⣥⡄⠀⠈⠀⠨⢰⠌⠠⡄⡧⣥⡌⢸⢬⢭⠁⡆⡧⣭⢍⢨⢸⠭⡥⡄⡅⠋⢭⠘⠨⣭⡥⡌⣀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠋⢲⠘⠨⡂⠄⠂⢇⢆⠀⢰⡸⡺⡄⣇⣇⢚⢿⣀⠙⠼⡄⣇⠇⠉⠉⠈⠘⠲⢇⡑⣇⣷⢲⢨⠘⠚⠅⡇⣗⣏⠑⢀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠠⠈⠙⠠⠄⡀⠀⠠⢱⢤⠀⠁⠣⢳⠌⠹⡤⡌⠋⡯⣤⢉⠑⠀⠀⠀⠀⠀⠀⠀⢱⢩⢉⠚⠎⡎⠻⣤⢑⠹⣽⡕⡌⠒⡄⠉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠐⠀⢀⠀⠁⠃⣆⡀⠢⢸⢰⣄⡒⡇⡆⣎⢸⢺⠲⡖⠂⡄⡄⣀⣀⢄⢗⣗⡿⡄⠘⢶⢶⢇⢇⠐⡶⡲⡰⡀⢀⠄⠁⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠠⢀⠀⠀⠀⠄⠀⠙⠱⢰⣌⠋⡏⡧⣦⣥⢉⢙⠘⠋⠏⠇⢋⣡⢼⢸⣼⠉⡇⡇⣣⠘⢹⠸⢼⠇⠏⣧⣮⣿⠠⢀⠄⠀⠀⠃⢣
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠄⠀⠀⠀⠀⡀⠃⠢⡦⢈⢸⠐⠲⡇⡇⡗⢷⠲⢘⣈⡀⡄⡆⣷⢆⢸⠐⣶⠂⡆⡇⢒⢶⠲⣸⠢⠘⠀⠂⠀⠀⠐⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠠⠀⠀⡈⠘⠺⣯⡷⢢⢨⣉⡙⡚⡚⠫⠣⠳⠻⠛⡘⡉⡔⡟⢁⢣⢻⢚⣽⡜⡏⠀⢂⠠⠁⠀⠀⠀⢢⠣⢃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⠂⠀⡄⠴⠶⠰⠰⠶⡆⡂⡆⣃⠒⢘⢠⢲⡆⠆⡢⠶⠆⠐⠀⠂⠀⠂⠀⠀⠀⠐⡆⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠐⠠⠨⠈⠁⠂⠄⡌⠐⠐⢠⠀⠀⢅⠁⠉⡙⠘⠙⠈⠀⠃⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠦⠄⠤⠠⢀⣀⠀⠤⠆⠇⠐⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⢀⡆⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠃⠄⠲⠀⢀⢠⡀⠀⠀⡀⠀⠀⠠⠈⢀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠘⠁⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠂⠀⠁⠰⠲⠦⠦⠦⠶⠒⠀⠁⠀⠀⠀⠀⠐⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠁⠄⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈