⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡜⡴⢇⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠁⠲⡇⢠⠣⠌⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣟⠀⢘⡤⠀⡿⢴⣠⠏⠷⣼⡯⠟⢿⠄⢾⡇⠏⡰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣗⣀⣇⢬⣶⣷⠛⢏⣟⣯⣸⣆⣀⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡧⡤⣃⣢⣽⠋⢸⡇⠀⢠⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⣳⠻⠻⠏⢼⣞⣟⡗⢒⡞⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣩⠿⡩⠭⠯⣅⡬⣤⡾⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡵⢋⡏⠈⠦⣀⣀⠤⠊⡵⠋⡄⠑⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡳⠉⠁⠀⡖⠀⠀⠀⠀⠈⠑⢐⠁⢀⣾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣺⣁⡀⠀⡴⣠⠒⠒⠒⡆⠀⠀⠅⢀⠄⢠⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⣄⡢⠔⠚⡍⠀⠁⠁⠁⡁⡀⠁⠚⢕⣏⠯⠜⢢⠏⠠⡘⢀⠊⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡢⢻⡋⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠉⠀⠉⢟⡈⢉⠅⡘⠐⠂⣠⡦⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠊⠁⠈⠀⡈⠒⢄⣀⣀⣀⡇⠀⠠⠂⠊⠀⠁⠉⠂⠀⠈⢎⣤⡎⢀⠣⡎⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡀⠁⠀⠂⠀⠀⠀⠀⠀⡀⠔⠐⠐⠀⠀⡀⠀⠀⠀⢀⡖⠙⠙⣆⢀⡉⣭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡁⠀⠀⠀⢾⡼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢐⠱⡂⠁⠀⢀⠁⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠑⠍⢖⣒⠉⣽⣗⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆⠂⠀⠀⠄⠀⠀⠌⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⠀⠡⢸⠒⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢁⠀⠀⠁⠀⢈⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡁⠀⠀⠀⢀⠁⢄⣀⣟⠈⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠄⠀⠀⠀⡁⠀⠀⠀⡠⠁⠀⢀⠒⠃⠤⢀⣸⢚⡄⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠡⠀⠀⠀⡀⠘⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠠⠁⡈⢥⣀⢑⠏⢅⡯⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡣⡀⠈⠁⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠂⡀⡀⡡⠜⢘⢏⠇⠉⡁⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠃⠄⠈⠐⠄⠁⠀⠀⠀⠀⢀⣀⠠⠀⠁⡀⠄⡬⠆⣡⠾⡋⣡⢀⠀⢔⠀⠇⠀⠀⠀⣀⡠⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠑⠢⣁⡲⡀⠀⠈⠀⠂⠀⠄⠠⠀⢄⠀⣡⣨⠥⡎⠐⢃⢣⣈⡇⡨⠡⠠⢗⠁⢹⡀⢱⠾⠛⠛⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⡠⠂⠀⠀⠀⠀⡐⠉⠑⠊⠦⠤⢤⡠⣠⡤⠖⡲⠛⠍⠀⠀⢣⢠⢂⢀⡿⠎⠰⢠⠨⢦⠁⠁⠱⠀⠀⢀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠁⠀⠀⠀⠀⠣⣄⡀⢙⣓⣓⣋⣁⠤⠶⠤⠚⡖⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡖⠚⠤⠶⠤⣁⣋⣓⣓⢙⡀⣄⠣⠀⠀⠀⠀⠁⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⡀⠹⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⢀⠀⠀⠱⠁⠁⢦⠨⢠⠰⠎⡿⢀⢂⢠⢣⠀⠀⠍⠛⡲⠖⡤⣠⡠⢤⠤⠦⠊⠑⠉⡐⠀⠀⠀⠀⠂⡠⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠛⠛⠾⢱⡀⢹⠁⢗⠠⠡⡨⡇⣈⢣⢃⠐⡎⠥⣨⣡⠀⢄⠀⠠⠄⠀⠂⠀⠈⠀⡀⡲⣁⠢⠑⠀⠀⠁⠖⡠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠤⡠⣀⠀⠀⠀⠇⠀⢔⠀⢀⣡⡋⠾⣡⠆⡬⠄⡀⠁⠀⠠⣀⢀⠀⠀⠀⠀⠁⠄⠐⠈⠄⠃⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⡁⠉⠇⢏⢘⠜⡡⡀⡀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣧⠻⠁⠈⡀⡣⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡯⢅⠏⢑⣀⢥⡈⠁⠠⠀⠀⠀⠀⠂⠈⠀⠀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠡⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠂⡄⢚⣸⢀⠤⠃⠒⢀⠀⠁⡠⠀⠀⠀⡁⠀⠀⠀⠄⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⣟⣀⢄⠁⢀⠀⠀⠀⡁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⢈⠀⠁⠀⠀⢁⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⢸⠡⠀⢀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⠀⠀⠄⠀⠀⠂⠆⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢡⣗⣽⠉⣒⢖⠍⠑⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠂⡤⠀⠀⠀⠀⠁⢀⠀⠁⡂⠱⢐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡼⢾⠀⠀⠀⡁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⣏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣭⡉⢀⣆⠙⠙⡖⢀⠀⠀⠀⡀⠀⠀⠐⠐⠔⡀⠀⠀⠀⠀⠀⠂⠀⠁⡀⠀⠎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⡎⠣⢀⡎⣤⢎⠈⠀⠂⠉⠁⠀⠊⠂⠠⠀⡇⣀⣀⣀⢄⠒⡈⠀⠈⠁⠊⡪⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⡦⣠⠂⠐⡘⠅⢉⡈⢟⠉⠀⠉⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⡋⢻⡢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠊⢀⡘⠠⠏⢢⠜⠯⣏⢕⠚⠁⡀⡁⠁⠁⠁⠀⡍⠚⠔⡢⣄⠅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡃⢠⠄⢀⠅⠀⠀⡆⠒⠒⠒⣠⡴⠀⡀⣁⣺⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡆⣾⢀⠁⢐⠑⠈⠀⠀⠀⠀⡖⠀⠁⠉⡳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠑⡄⠋⡵⠊⠤⣀⣀⠦⠈⡏⢋⡵⠜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⡾⣤⡬⣅⠯⠭⡩⠿⣩⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠊⡞⢒⡗⣟⣞⢼⠏⠻⠻⣳⣿⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⢠⠀⡇⢸⠋⣽⣢⣃⡤⡧⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡟⣀⣆⣸⣯⣟⢏⠛⣷⣶⢬⣇⣀⣗⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡰⠏⡇⢾⠄⢿⠟⡯⣼⠷⠏⣠⢴⡿⠀⡤⢘⠀⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠌⠣⢠⡇⠲⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⢇⡴⡜⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀