⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀WAY TO FRAKING GOATED⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⡀⠄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀TIMMY⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠁⢀⡕⠓⠒⠂⠂⠒⠓⠐⠀⠂⠀⠈⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠋⠁⡀⠂⣀⠠⠎⠁⡀⣆⠁⠇⡀⠄⡂⠁⣂⠀⠀⠢⠀⢀⠂⠁⠀⠀⠀⠀⠀⠁⢅⠰⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠄⡍⡄⡑⠀⠀⠀⠀⠀⠂⢢⡊⠭⠀⠌⠱⠎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠄⠀⠀⠀⠀⠀⠁⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢂⠁⠆⣀⡄⠀⠂⡀⣈⠀⠀⡀⠀⠂⠁⡀⠈⢀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠊⠀⠀⠀⠄⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡞⠁⣏⠁⡏⠀⢠⠀⡄⠀⣤⡀⠆⢡⠗⠉⠑⠙⠃⠀⢡⠁⢀⠉⠧⠁⠈⠀⠀⠁⠀⠙⠆⣀⡀⠀⠄⠀⠀⠀⡀⠀⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠇⡐⢬⡐⠈⠀⢀⡠⠃⠑⠀⠀⠀⠀⠀⠁⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡖⠩⠛⡀⠀⠀⠀⠀⠀⠢⠇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣑⣀⠀⠀⠀⡊⡰⠚⠀⡘⠉⠠⠇⠀⠁⣀⠒⠉⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡯⡆⠠⠀⠀⢆⠀⠁⠀⠀⠀⠀⠀⠀
⢑⡀⠀⠃⠐⡆⡋⠀⠀⠀⠂⠁⠈⠖⢀⠭⠕⣀⣉⡀⡄⠺⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠦⠥⢑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀
⠀⡇⡝⡇⡠⠁⠁⠀⠄⠀⠀⡈⡆⡫⠏⠀⠀⠀⠀⠀⠀⠀⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⡧⠂⠀⠀⠀⠀⠀⠀⠁⠅⠀⠀⠀⠀⠀⠌⠠⡀⠀⠀⠘⠀⠀⠀⠀⠀
⠸⡇⡀⢁⡎⡅⠀⠀⠀⠀⠸⢀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠆⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢲⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠻⡅⡃⡄⠄⠀⠀⠀⠀⠀⠌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⣤⡟⡅⠄⡀⠀⠂⠀⠀⠀⣓⣀⠀⠀⠀⠋⡁⠀⠀⠀⠇⠀⠀⠀⠀
⠀⠀⠑⡡⡄⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⣤⣥⠃⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⡷⡇⠊⠔⡐⠂⠀⡀⠀⠈⡀⠀⠀⠀⠀⢡⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⡛⠏⣟⡗⢈⠘⠀⠀⠀⠀⠀⠀⠀⠀⡫⣛⣟⣉⡃⠂⠠⠀⠀⠂⠀⠀⢁⠀⡀⢀⠂⠀⠈⣒⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠑⡃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠤⢧⡿⢇⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⡅⣯⡇⡐⡀⡄⠀⠈⠈⠀⢘⠠⠴⢠⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡂⡶⣏⣁⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣯⢹⠀⡌⠆⡀⠀⠀⠀⣸⠃⠀⠀⠀⠌⠈⠀⡋⢬⠀⠀⠀⠀
⠀⠀⠀⠀⠁⢳⡀⠀⠀⠀⠘⣇⡠⠀⠀⠀⢠⠏⡋⡥⣿⠃⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⣤⣀⠀⠀⢀⡇⠀⠀⢀⠅⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢓⡅⠁⡆⠀⠀⠀⠈⠓⣯⣍⣭⡯⠟⡁⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⢀⡧⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠵⠒⢮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠃⠀⠀⠀⠀⠀⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡹⢴⠄⣖⡂⠖⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠑⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⣥⠄⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢃⠀⠀⠤⣄⡀⡀⠀⠀⠀⠀⠁⢀⡀⡀⢀⡀⠖⢻⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⡷⠉⠀⠀⠩⣎⡧⠄⡀⠀⣀⡀⡀⠐⠀⠊⠀⣇⡑⣀⡀⣀⣀⣀⡤⠌⠓⠉⠉⠀⠀⠀⠀⠀⠉⡁⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⠂⠆⠓⠍⠅⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠃⠽⣖⡒⠂⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡶⠖⠒⠊⠙⠛⠓⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⡄⠀⠀⠀⢀⡮⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⡁⠀⠄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠔⠒⠐⠋⠉⠉⠁⠁⠀⠚⠀⠁⠀⠈⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⡂⠂⢀⡠⣅⣀⣀⢀⣀⠀⠀⠕⡄⠀⡀⡀⠀⠢⠀⢤⡀⠀⡀⡀⡀⠀⠀⣀⡀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠨⡟⡏⠀⠉⣿⡍⠀⣸⠟⠃⠀⢉⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡃⡇⡧⠇⠀⠀⡧⡧⢿⠀⠀⠀⠀⡅⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠿⣟⣗⡟⠏⢸⠏⠧⠶⡏⣀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⡀⠀⠀⠀
⠀⠀⡞⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣚⠀⢀⡧⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀
⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣷⣶⡝⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀