⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄⠀⠀⠀⠀⠀⣲⢠⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠱⡂⠀⠀⣠⠚⢄⢑⠐⠄⢍⢙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢠⡂⣳⠀⡲⠡⡑⡐⢄⢅⢑⣐⡐⠄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⣼⠈⠒⣃⣉⠓⠗⢗⡓⠧⠱⡣⠉⠛⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠚⠮⣍⡑⡑⡑⡒⠦⢄⢄⠀⠀⠹⣷⡂⢠⣉⣨⡈⠁⠀⠀⠚⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡹⢆⠢⠨⡈⠢⠨⠩⡒⢴⣞⠎⢹⡛⣾⢻⢧⠀⠀⠺⣟⣇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡔⢎⠑⢌⠢⠡⡑⠌⠌⢌⠢⡈⡮⣪⢣⡚⠣⠻⠜⠙⠀⠀⠀⠰⣿⣝⣇⠀⠀⠀⠀⠀⠐⠱⡠⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣔⠣⡈⠢⡑⠄⢅⠑⠌⠌⢌⠢⡑⢌⠳⣕⣇⢯⠁⠀⠀⠘⢄⣀⣀⣀⣀⣄⢜⠀⠀⠀⠀⠀⠀⢄⠃⠡⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⢝⠤⠵⢬⠢⠨⡈⠢⠡⠡⡑⢄⢑⢌⠢⡑⢜⡌⠑⠙⢦⢄⢀⠠⡰⠐⠒⠁⠁⠁⠀⠀⠀⠀⠀⠀⠐⢄⣑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢐⠏⢌⠢⠨⠨⠨⡨⡨⠢⡢⡑⢕⢮⠦⢽⠀⡠⠪⡦⡢⣁⡸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢬⠁⢠⢭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠞⢌⠢⠡⠡⡑⠕⢔⢌⠪⡨⠪⡢⣑⠧⠒⠉⢹⠀⠈⠒⢜⠬⠺⡈⠣⡀⠀⠀⠀⠀⢰⠈⠀⢳⠀⢪⢋⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡰⣫⣨⠢⠡⠡⡑⢌⢊⠢⡑⢕⢌⠪⣪⠂⠀⠀⠀⠣⠢⠢⡄⠀⠙⢄⡇⠠⢼⠄⠀⠀⠰⡌⠀⢐⠜⠤⠤⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⢠⠎⠌⢌⠢⡈⡂⠢⡑⢌⠢⡑⢕⢼⠀⠀⠀⢠⠀⢀⠎⠀⠀⠀⠀⠣⠀⠈⡗⡄⢀⡇⢱⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡮⠨⡈⠢⡑⡐⢌⢂⢊⠢⡑⢌⢢⠇⠀⠀⢀⢸⢱⠀⠙⢢⡀⠀⠀⠱⡀⠀⡅⢣⡜⡆⠈⢮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠡⡑⢌⢂⠢⡈⡂⢆⠢⡑⢌⠢⡝⠀⠀⢀⢂⠇⠀⢧⡀⠀⠘⢢⠀⠀⡃⢠⠃⢢⠁⢱⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠘⠊⣇⠢⡑⡐⢌⠢⡑⢌⠢⡱⡁⠀⢀⢂⠎⠀⠀⠈⣎⢐⠀⠀⠱⡄⡪⢸⠀⠱⡀⢀⠗⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣐⠐⢌⠞⢱⢌⠢⡑⢜⢦⠀⠀⠁⠙⢄⡀⠀⡸⠀⠀⠀⠀⠱⢹⣅⢣⢀⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠱⢕⠃⠀⣸⠢⡑⢌⠢⣱⠹⣄⠀⠀⠀⠳⡰⣅⠀⠀⠀⠀⠁⢌⣿⡀⠱⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢌⠪⡢⣱⠃⠀⠈⢣⢄⢀⠴⠁⠀⡇⠀⠀⠀⠠⡐⣿⣷⡥⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡣⣑⡵⠜⠁⡀⣄⣴⣴⡱⠩⠠⠠⠀⢕⠀⠀⠀⠀⠐⣿⡷⣿⢦⢲⠀⠀⠀⢀⢀⠦⠊⠉⠁⠁⠁⢉⢭⢋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠊⢁⣠⡴⣯⢿⣻⣗⣯⠏⠀⠀⠀⠀⢱⠀⠀⠀⢄⠨⣿⣻⢮⣢⡕⠃⢀⡔⠎⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠒⢤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣞⣯⡿⣽⣟⣷⣻⣇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢱⣿⣻⣟⣿⣽⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⣿⣞⡷⣟⣿⣺⣗⢏⠆⢧⢂⢢⠥⠃⠁⠀⠀⠠⡈⣺⡽⣽⢹⠣⡻⡲⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣄⡦⢂⢀⠀⠀⠀⠀⠈⢧⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣞⣿⣻⣞⣷⠋⡼⠀⠢⠉⠀⠀⠀⠀⠀⠀⠠⡸⠩⠑⠁⠀⠀⢨⡣⠀⠀⠀⢠⣖⡯⢀⡠⣦⢿⣽⣻⣽⠟⠉⠉⠓⠒⠴⣄⡀⢱⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⣿⣺⢷⣻⢾⢐⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⢅⠅⠀⠀⠀⠀⡎⢗⠄⢠⢼⣻⣞⣷⣳⣟⣯⡿⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢾⣽⣻⢷⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡌⣸⠠⠀⠀⠀⡜⠌⢌⢣⡿⣯⢿⣺⢷⡯⣷⠟⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣟⣯⡷⣟⣿⣳⡇⠀⠀⠀⠀⠀⠀⠀⡀⡐⡜⡐⡅⠁⠀⠠⡪⠨⠨⢸⢘⡿⣽⣻⣽⢯⣿⣻⣞⣾⢾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣟⣿⣺⣽⡇⠀⠀⠀⡀⡀⢠⢐⡐⡜⡐⠄⣇⣤⣴⡤⣇⢅⢑⢸⠀⢻⣯⢿⣺⣟⣷⣻⢾⡽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣟⢽⣾⢅⠠⣐⡴⣴⣞⣯⣗⢐⠐⢌⣄⢽⣾⣳⣟⣿⠔⢔⢼⠲⠾⡽⣻⣽⠾⠷⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⠀⢸⡢⣓⡱⣟⣿⣺⣽⣾⠀⠁⠁⠀⢸⣷⣻⢾⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⣿⣺⣽⢾⣽⡂⠀⠀⠀⠈⣾⡯⣿⢾⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⡷⣟⣯⣷⣇⠀⠀⠀⠀⢺⡯⣿⡽⣾⣳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣯⣟⣯⡷⠿⢾⣄⡀⠀⠀⠈⣿⢷⣻⢫⢩⢭⢫⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⡯⡣⡱⣹⣆⣵⡽⣄⡀⠀⠹⢿⣱⣑⡷⣿⠾⠷⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠓⠊⠓⠻⠽⠛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀