⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠉⠒⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠮⠊⡄⠀⠀⢰⠒⠒⠒⠤⠬⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣀⠭⠴⠒⠒⠒⠒⠒⠒⠒⠤⣄⣄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠖⠉⣀⠤⠤⠒⠒⠒⠒⠒⠒⠲⠤⢤⡀⣀⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠁⠘⠢⠤⣀⣀⠀⡍⠉⠉⠉⠲⣀⣀⡴⡄⠀⠀⠀⡔⠒⠛⠒⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣄⠸⠤⠤⣀⠀⠀⠀⠀⣀⠑⠒⠒⣁⠀⠀⠀⢫⠀⡇⡼⠀⠀⠀⢰⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠙⡀⠀⠀⡇⠀⠀⠀⡇⠑⠉⠉⠀⠐⠀⢀⢚⠚⠒⠒⠦⠤⠤⣋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡍⡦⡒⠤⣀⠀⠀⡇⠀⠀⠀⢸⠀⢀⠚⠀⠀⠀⣀⠔⠋⠀⠀⡦⡤⣀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⢀⠀⠀⠉⠢⣑⡀⡇⠀⠀⠀⣞⠖⠑⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⡄⠙⢌⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠄⠀⢠⢋⡤⠤⠂⢸⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⠚⠁⠀⠀⣁⠀⠀⠀⣠⢚⢑⠞⢸⡇⠀⠀⠑⡀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠤⢤⠃⢀⣀⢡⡡⡇⠀⠀⠀⠀⠀⠀⠀⠤⠋⠀⠀⢀⢄⠞⠀⠈⠑⠊⡠⡰⠁⡞⣇⠸⠀⠀⠀⠈⣄⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠐⠉⢉⠁⣠⠴⠥⣂⡱⠜⠀⢄⣀⣀⣀⠤⠔⠾⠁⠓⠪⠭⠭⠔⠀⠀⠀⠂⠀⢠⢠⠀⠀⠀⠈⢆⠰⠀⠀⠑⠀⢣⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠋⠀⠀⠀⡴⡁⠰⠤⠖⠊⠁⡜⣎⢈⠙⠒⠒⡠⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠤⠥⣃⠀⠀⠀⢠⠁⢦⠙⡀⠀⡜⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠀⠀⠀⡜⡔⢰⡀⠀⠀⠀⡜⠖⢳⠁⢠⠶⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢕⠀⠏⠀⠀⢳⠈⢄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡜⡀⡇⠀⠀⠜⠀⢊⠰⣓⣀⢀⣀⣑⡪⣀⠄⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⢸⠊⠓⢕⠀⡏⠙⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠊⡜⡄⢀⢋⠴⢸⡬⡝⠞⢰⠀⠀⠀⠀⠀⠀⠉⠛⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠖⠉⠉⠑⠲⠮⣀⣀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡏⣌⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠏⠜⠇⢠⠋⠀⠔⠸⠔⠈⣀⠀⠉⠒⠢⢤⣀⠀⠀⠀⠀⢀⠃⠒⠒⠤⢤⡀⠀⠀⢀⡊⠀⠀⠀⠀⠀⡴⣡⠀⠀⠀⠉⠙⠚⠤⣉⣢⣙⢄⠀⡇⠀⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢋⠗⠀⠃⠀⠋⠀⡜⠀⠀⠀⠒⠭⣑⠒⠤⢄⡈⠉⠒⠤⠥⣀⠀⠀⠀⠀⠀⠈⠓⢼⠲⠤⣉⠉⢄⠞⣰⠀⠀⠀⠀⠀⠀⢞⠋⠀⠀⠀⠀⠈⠉⠒⢢⠵⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠃⠀⠀⠸⠀⠃⠀⠀⠈⠤⣀⡀⠀⠀⠀⠀⠈⠁⢂⠎⢬⣉⠒⠤⡄⢀⠭⠶⣒⠤⢤⣓⠀⣑⠢⠤⣉⣓⠣⢌⣉⠒⠢⠄⠘⠃⠀⠀⠀⠀⠀⠀⢀⢡⠁⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠃⡰⠀⡤⠖⠒⠒⠤⢤⡀⠞⡔⠭⠉⠙⢖⠤⣀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠢⣤⡰⣺⡄⠀⠀⠉⠒⠬⣑⡒⠤⠤⡨⠀⠉⠉⢒⣒⠭⢍⣒⠦⠤⠰⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠃⡡⢚⠜⠁⢀⣒⡒⠤⡀⡇⠁⠀⣁⢃⠄⠀⢧⠀⠈⢢⠉⠒⠠⠤⣀⡎⢀⡕⠤⢄⣀⠀⠀⠉⠉⠒⠤⣀⠀⠈⠉⠒⠲⠤⣄⡑⠲⠤⣈⠉⠒⠤⣍⣉⠈⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠊⠔⠏⣀⠀⠬⡶⠥⢞⢊⠋⢠⠑⡔⢁⢤⣀⠀⠙⠀⡜⠀⠏⠉⡒⠤⣄⢧⠀⠀⠀⠀⠀⠉⠂⡆⠀⠀⠀⠀⠉⠓⠢⠤⣄⢀⠀⠀⢉⣓⠦⢍⣉⠓⠒⠤⣈⠃⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡞⠀⠀⠈⠂⢆⠀⠀⠀⠀⣅⣀⠧⠼⠀⣏⡠⡜⠀⠀⢀⠉⠢⡤⣀⣀⠀⣀⢣⠀⠀⠆⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠥⢒⠋⠀⡼⢠⠁⠈⢐⣉⠒⠢⠤⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⠀⠀⠓⡣⠀⠀⠒⠒⠊⠉⡅⠀⡇⢣⣇⢴⠔⠢⢀⠔⡎⠀⠀⠀⠀⠁⢀⠀⠬⣀⠀⠈⠈⠉⠒⡄⠀⡄⠀⠀⠠⠭⢍⠒⡴⢢⡴⠀⠀⠎⠀⡃⠀⠀⠈⠒⠒⡄⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢁⠀⠀⠀⠀⠀⠀⠀
⢀⢁⣀⠀⠀⠘⣈⠦⢤⡲⠤⠵⠘⠀⠈⠀⣠⠞⠉⠀⢀⠊⠑⠒⠤⠥⣄⡠⠃⢀⡪⠃⡼⠑⠒⠤⣀⠘⠀⠁⠀⠀⠇⠀⡎⡔⠀⡰⠀⢣⡜⠉⡎⠀⠑⠤⠤⣀⠚⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⢜⣀⠀⠈⠉⠑⠒⠤⣀⠀
⡜⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠓⢦⠤⣄⣀⠜⠀⠠⣀⣀⣀⡠⡅⠫⠓⠀⠞⠀⠀⠀⠀⠔⠈⠒⠢⢄⠀⠀⡀⣷⠀⢰⠀⠀⡰⠀⠀⠧⠔⠒⡑⠢⠤⣀⠁⣄⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⢀⣀⣤⣀⣀⣀⠋⠉⠒⠤⢄⡀⠱⠇
⠙⣌⠉⠉⠁⠀⠈⠲⠀⣀⣀⠤⠒⠁⠀⠀⠀⠈⠲⣀⣀⣀⣀⣀⣀⠀⠀⡜⢉⣉⠁⠀⠀⠀⠎⢳⢭⠭⡆⠈⢅⠴⠋⢣⠃⠀⠏⠒⠊⢣⣀⡜⡇⠀⠀⠇⠀⠚⠭⡐⠀⠄⠉⠑⠒⠴⣉⡀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⡇⠀⠉⠪⢄⣀⡸⠎⠀⠈⠁⢆⣀⠥⠴⠒⢺⠀⡸⠠⡠⡸⠀⠀⢀⠣⠤⠴⠀⡼⠀⠀⢧⢰⠀⠀⠀⠀⠀⡠⠤⡈⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡔⠉⠉⠉⢱⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⢑⡀⠀⠀⠃⠈⠛⢸⠀⠸⠈⠀⡇⠀⢰⡆⡇⠀⠀⠀⠀⠀⢰⡀⠀⠀⡰⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⢢⠤⠤⡎⠀⠔⠀⠢⡀⠀⠀⠀⣀⣀⠤⠴⠒⠁⠦⢄⡀⡀⢰⠙⠒⠤⣀⠀⠸⠀⠀⡇⠑⠣⠀⢣⠱⠹⠤⡠⠔⠊⠉⠈⠓⠤⣀⠁⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠸⠤⠀⠀⠀⠀⠀⡇⢸⢺⠑⠒⠤⣀⠀⢯⡵⣒⠁⠀⣿⠏⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⢆⠤⣀⡀⢣⠈⠭⣒⠬⠑⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀