⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢐⠸⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡔⡔⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠱⠣⠀⠀⠀⠈⡄⢣⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠜⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⢇⢣⠀⠀⠀⠘⡄⢣⠀⠀⠀⠐⠀⠀⠀⠀⠇⢰⠀⠀⠀⡜⡸⠀⠀⠀⢀⠔⡨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠡⡙⠢⡀⠀⠀⠈⠆⢃⠀⠀⠀⢃⠈⡆⠀⢠⠀⡆⠀⠀⢰⠀⡎⠀⠀⡘⠰⠁⠀⠀⢀⠎⡈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡢⠀⠀⠀⠀⠈⠣⡌⠢⡀⠀⠸⡀⢃⠀⠀⡘⠀⡇⠀⢰⠀⡇⠀⢠⠃⠰⠀⠀⡐⢁⠆⠀⠀⢀⠌⠰⠁⠀⠀⠀⠀⢔⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡰⢄⠀⠀⠀⠘⡄⠑⡀⠀⢡⠨⢆⠀⠇⡀⠇⠀⢸⠀⡇⢀⢦⢢⠃⠀⡰⠁⡌⠀⠀⡠⠊⡠⠃⠀⠀⣀⠔⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢟⢄⠀⠀⠀⠀⠀⠘⢦⠑⢄⠀⠀⠘⡐⡱⠀⠀⢃⢎⢄⢸⢡⢢⠀⢸⡰⡇⠘⢠⠀⠀⡠⡱⡙⠀⡠⡪⢠⠔⠁⠀⡠⠊⡤⠋⠀⠀⠀⢀⠠⢀⣠⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢤⠛⠠⠄⣀⠀⠀⠀⠻⡀⠣⡀⠀⢣⢇⢣⡀⠘⡸⡘⡀⡇⡇⠇⢸⣿⠃⠀⢇⠘⢀⢃⢇⠃⡘⡠⡠⠃⠀⢀⠜⢀⠜⠀⠀⠀⠀⡠⢃⡜⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⡈⠢⢄⠀⠈⠪⡪⡣⢄⠣⡱⠜⢄⢱⢱⡱⢰⢸⡸⡄⣿⢡⡆⡧⣌⢎⡎⠎⡌⡜⡰⠀⡠⢔⢕⠕⠁⠀⠀⣀⠤⠊⡠⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠖⣢⠄⢀⡀⠀⠀⠀⠀⠈⠢⡀⡱⢀⠀⠈⠮⠢⡐⢌⢎⢣⡙⡆⠷⠛⠈⠁⠉⠉⠉⠈⠁⠛⠾⢰⢎⡜⡑⡡⢂⠕⡡⢃⠠⡔⠀⣍⠀⠔⠊⠀⠀⠀⢀⡀⠠⠲
⠀⠀⠀⠀⠀⠉⠒⠬⣑⠂⠠⢄⡀⠀⠈⠪⡒⢍⡂⠤⡑⢌⢳⣕⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣫⡴⡣⢊⠔⡡⢪⠔⠊⠀⠀⠀⡠⠄⠐⣊⠥⠒⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡉⢖⡠⠠⣑⠨⢝⠢⣭⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣪⠔⡣⠊⣀⠄⢄⡒⢉⡠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠹⢐⠤⠤⠤⠐⠒⠂⠤⠄⣀⠀⠈⠀⠊⠅⣒⠭⣄⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣚⣢⠭⣒⠨⠕⠈⣁⣀⡀⠀⢀⣀⠀⠤⠒⡀⠤⠢
⠀⠀⠈⠉⠀⠉⠁⠒⠐⠤⣀⠭⣒⡀⢀⡀⣀⠙⠴⠏⠀⠀⠀⠀⡴⠚⣋⣉⠙⠒⣦⠀⣴⠒⢋⣉⢛⠓⠤⡀⠀⠀⠀⠹⠦⢌⣀⣒⠭⠑⣀⣀⣀⣀⣀⡠⠄⠒⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠉⠩⣽⠀⠀⠀⠀⠀⠖⢕⣽⣿⢺⢦⠘⠀⡇⠶⡟⣿⡯⡪⡶⠀⠀⠀⠀⠀⣛⡭⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠰⠀⠀⠀⠀⠄⠀⠀⠀⢀⡉⢉⣉⣉⣉⣹⣻⠷⠷⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠈⠁⢨⠀⡅⠈⠁⠛⠁⠉⠀⠀⠀⠀⠀⠀⠷⠶⢿⣛⣏⣉⣉⣉⣉⠉⡀⠀⠀⠀⠄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⣒⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⡇⠀⢘⢂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣒⣀⢀⡀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉⣉⠉⠉⠠⢄⣒⠭⠁⣒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠌⠠⠭⢒⠉⠒⠤⠀⢀⡀⠀⢀⣀⠀
⠀⠢⠒⠂⠈⠤⠒⠉⠉⠀⠀⠀⠉⢁⡀⢔⡂⠭⣒⠊⣭⢄⠀⠀⠀⠀⠀⠀⠀⠘⠣⣒⠒⣒⠼⠂⠀⠀⠀⠀⠀⠀⠀⡰⡭⠍⣒⠭⣐⡢⢀⡀⠀⠈⠁⠒⠂⠤⠐⠒⠥⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠊⣁⠬⠑⠂⠉⡠⢊⠔⡫⡧⡀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠒⠄⠀⠀⠀⠀⠀⠀⢀⢼⣙⠲⣕⡂⢍⡐⠈⠥⣘⠑⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠤⢒⡩⠄⠒⠉⠀⠀⠀⡀⠔⡡⢊⠕⡉⢊⡼⣫⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢟⠳⡑⢌⠒⠨⢑⠬⡢⣀⠀⠈⠁⠒⠠⢍⡒⠄⣀⠀⠀⠀
⠀⠀⠀⠦⠝⠂⠈⠁⠀⠀⠀⡠⠔⠈⣑⠨⠜⠂⢁⢎⠔⡡⢊⢄⡞⡱⠏⡶⣤⢀⣀⡀⣀⢀⣀⡠⣤⢶⠹⢎⢣⡱⠕⢬⡢⡱⢄⠀⠑⠮⡈⠢⡀⠀⠀⠀⠀⠈⠁⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠒⠉⠀⠀⢀⢔⢕⠕⠉⠀⡌⡜⡈⡰⡸⡱⠘⢼⠘⢡⣿⡘⠎⡇⠇⢎⢇⢆⠑⢜⢎⠢⠉⠪⡪⡣⡀⠀⠑⠢⡈⠑⠠⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡜⢠⠊⠀⠀⠀⠀⡔⠁⡔⠁⠀⢠⠊⡎⡌⢰⢱⢡⠁⠀⡎⢠⢸⢻⡅⢰⢸⢸⠈⡌⡎⡆⠈⢣⠑⢣⠀⠈⢢⠈⢢⠀⠀⠀⠉⠑⠂⣤⠑⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠋⠁⠂⠁⠀⠀⠀⢠⠊⡤⠊⠀⢀⠄⠃⡪⠊⠀⡄⢎⠊⠀⠇⡌⡆⢸⠊⡇⠀⢃⢣⠇⠑⡱⣠⠀⠀⢎⠆⡄⠀⠀⠑⢦⠑⣄⠀⠀⠀⠀⠀⠑⣵⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠡⠋⠀⠀⢠⠊⡠⠊⠀⠀⡘⢐⠎⠀⢀⢣⠳⠁⢸⠀⡇⠀⢸⠀⢸⠀⠱⡀⢃⠀⠈⢆⠘⡄⠀⠀⠀⠉⠢⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠕⠁⠀⠀⠀⢀⠆⡐⠁⠀⠀⠰⢁⠌⠀⠀⠆⢡⠂⠀⠸⠀⡇⠀⢸⠀⠌⠀⠀⠱⡈⠆⠀⠈⠢⡈⠢⡀⠀⠀⠀⠈⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡌⡰⠁⠀⠀⢀⠆⡌⠀⠀⠸⠀⡃⠀⠀⠘⠀⠁⠀⠸⡀⢸⠀⠀⠀⢱⠘⡀⠀⠀⠈⠲⢌⢢⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠪⠔⠁⠀⠀⠀⠎⡜⠀⠀⠀⢣⢰⠀⠀⠀⠀⢀⠀⠀⠀⢣⡈⡄⠀⠀⠀⢣⠱⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡔⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢣⠘⠀⠀⠀⠀⢣⢆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠜⠜⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀