⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠏⡋⠅⠅⠕⡙⢻⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⠫⢂⢐⢐⢐⠨⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⠌⠢⠨⠨⠨⠨⢐⢁⢺⡇⠀
⠀⠀⠀⠀⠀⠀⢸⡗⢈⢐⢐⠐⠄⠅⠕⡐⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢑⠐⠅⢌⠨⢨⠨⡈⡂⠢⡑⡗⠀
⠀⠀⠀⠀⠀⠀⢸⡪⢐⢐⢐⠡⡑⡡⢁⢂⠢⣳⠀⠀⠀⠀⠀⠀⠀⣸⡃⢂⠃⢅⣢⣥⣦⡄⡂⠌⡂⣪⡇⠀
⠀⠀⠀⠀⠀⠀⢸⡎⠄⡑⣴⠛⠛⠳⣇⠄⢅⢚⡆⠀⠀⠀⠀⠀⠀⡗⠔⡐⣘⡞⠉⠀⠈⢻⡐⠅⡐⣸⠇⠀
⠀⠀⠀⠀⠀⠀⠀⣧⠁⡊⣺⠀⠀⠀⠈⡧⡁⠢⡇⠀⠀⠀⠀⠀⢨⡇⡃⡂⡟⠀⠀⠀⠀⣾⢈⠂⡪⡾⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡐⠄⡹⡆⠀⠀⠀⢱⠌⢌⡧⠀⠀⠀⠀⠀⢸⠱⢀⢪⠃⠀⠀⠀⢠⢇⠢⠑⣼⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠅⡂⢧⠀⠀⠀⠸⡊⠄⣗⠀⠀⠀⠀⠀⢸⠌⡂⡯⠀⠀⠀⠀⡞⠆⠌⣂⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠢⠹⡄⠀⢀⡤⠷⠷⠷⢤⡀⠀⠀⠀⢽⢐⢔⠇⠀⠀⠀⢸⠣⡡⢡⡾⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡨⠨⢣⠀⢺⠀⠀⠀⠀⠀⠉⢦⠠⢄⡿⡀⣽⠀⠀⠀⢀⡏⢔⠠⡵⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⡡⢙⣇⡬⠗⠀⠀⠀⠀⠀⠀⠀⠀⣏⠆⡏⠀⠀⠀⡾⠁⢆⣺⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢢⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⡇⠀⠀⣸⠃⠅⡾⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠹⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢵⡃⠀⣰⠣⠑⡽⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠞⠛⢿⡀⠀⣀⣄⡀⠀⣀⡾⠶⡏⠌⠍⠳⡃⠌⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⢖⠋⢅⠂⠆⠅⢅⠛⡛⠍⠄⠝⡙⢍⠣⡁⡊⡌⠌⠢⢘⡼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡼⡑⣰⣯⡁⠙⡆⠡⡁⡂⡂⠅⠅⠅⡂⠅⡂⡬⠶⠦⣅⢑⠐⠄⡑⠝⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡞⡡⢰⣿⡿⠇⠀⡅⠅⡂⡢⠊⠌⡌⠌⢄⠃⣼⣶⣶⡄⠈⣇⠨⠨⡐⡁⡊⢿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡼⣑⡐⢸⣿⣿⡆⢀⠇⡘⠔⢐⠡⡑⠄⡃⢕⠀⣿⣿⣏⠁⠀⡔⠅⢅⠢⡁⡂⡑⣻⡄⠀⠀⠀⠀
⠀⠀⠀⠀⡗⠀⠀⠆⠻⠭⠴⠋⡰⠐⢼⡑⣒⠖⡇⢐⢐⠁⡻⡿⠟⢁⡴⢁⠊⠄⠅⣂⢊⡐⢘⣷⠀⠀⠀⠀
⠀⠀⠀⠀⡏⢆⢀⠁⡂⠑⠨⠨⠠⠑⠌⠳⡔⠋⠡⠂⡂⠕⡠⡉⡩⠉⠄⠅⡊⠌⡎⠀⠀⠀⠡⣿⠄⠀⠀⠀
⠀⠀⠀⠀⢿⢐⠔⣿⣿⣿⣿⣿⣿⣿⠙⢛⡟⠛⠛⢛⣿⣶⣶⣶⣬⣬⣬⣂⣈⡂⠣⡀⠀⢀⠜⣾⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣧⢂⠹⣿⣿⣿⣿⣿⣿⡆⠀⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⢩⠀⣪⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢧⡢⡘⣿⣿⣿⣿⣿⣿⣦⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠠⡡⠑⣰⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠪⢂⣢⡵⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡍⢄⣡⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡩⣟⢹⠛⠛⠿⠿⠿⠿⠯⠯⡷⠾⢞⠞⠛⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢐⠐⢼⡗⡍⠀⠀⠀⠀⠀⠀⠀⠀⢳⠹⣦⠂⠅⢂⠚⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⢐⠡⢂⢕⣽⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢈⢻⡌⢄⠂⠢⠹⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡾⡁⢂⠕⠰⣹⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠰⢀⣿⡔⠨⠨⠈⡜⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢗⡌⢔⡾⠧⠋⢸⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⡊⢄⣿⡣⢐⠨⠐⠨⣹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⣗⢇⠀⠀⠀⠀⠀⠀⠀⢀⡼⡁⡪⢸⡏⠚⠻⣎⠌⣐⡼⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢯⡓⡤⣀⣀⣀⡠⡴⠪⡂⠅⡂⢽⠇⠀⠀⠨⡟⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⡗⠕⠙⢮⣤⣑⣄⣑⣔⡬⢰⠒⢄⢻⣁⡤⣀⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡘⡉⠠⡊⠰⣽⠈⠈⠉⢉⡧