⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠠⡀⢄⢀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢔⢈⠊⢌⠐⠄⠂⠅⠰⡀⠢⠐⠄⡡⠨⡈⠢⢂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡈⠢⠑⠠⢂⢁⢂⠌⡐⡁⠑⡐⢀⠑⡈⢂⠐⡁⣌⢐⡡⣈⢌⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢊⠐⢌⠐⢁⣿⡻⣳⣻⣝⣟⣽⡿⢀⠂⠠⠀⠄⠠⠰⣿⣾⣝⣽⣳⡻⣿⠀⡎⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡃⡑⡈⠢⠠⠁⠄⠛⡛⠛⠍⢋⠉⡈⠄⠠⠐⠀⠂⠐⢀⠀⡀⠄⡉⡉⡙⠛⢋⠌⡊⢔⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠠⡀⠀⣐⡕⠨⠠⡈⠂⠡⠈⠄⠡⡈⢄⠑⠄⢌⠠⢊⠐⢄⠁⡈⢀⠢⠈⠄⢌⠐⢄⠪⡈⢆⢌⠢⡈⡪⢈⢕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠄⢀⡨⡇⢑⢾⠊⡀⠑⢄⠐⡁⠨⠀⡕⡨⠢⡁⢊⢂⠂⡡⠠⠑⢄⢅⠄⠐⢄⠃⢌⠠⠑⣀⣑⣈⣲⣐⢅⠪⠀⢕⠠⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⠀⢈⣨⠚⢗⢡⣂⣮⣈⢄⣱⣄⣌⣢⣮⣾⣾⣿⣿⣿⣿⣿⣶⣷⣤⣢⣂⠑⡄⣥⣴⣶⣿⣿⢿⡿⣿⢿⣿⣿⣾⣶⣶⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡁⠐⠡⣪⡱⣘⠋⠛⢟⠚⠻⢿⣿⣿⣿⣿⣻⣵⡿⣺⢷⣯⢿⣽⣿⣿⣿⣿⣿⣿⣿⣟⣽⡾⣟⣽⣯⣟⡷⣿⣿⣿⣿⠛⡍⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡔⠀⠀⢌⢾⠕⢁⠢⡞⠣⡀⢮⢀⢽⣿⣿⡳⣟⣾⣻⡽⣟⡾⣯⢷⡯⣿⣿⣿⣿⣿⢷⣯⣻⣞⣿⡵⣷⣽⣻⡮⣿⣿⠇⡘⢔⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡰⠀⠄⠀⣪⠃⠔⠠⡀⠘⣔⢕⢣⠣⡚⣿⣿⣽⣻⢞⡷⣿⢽⣯⣻⣻⢞⣿⣿⠗⣿⣿⣷⡻⣮⢿⣮⢟⣷⡻⣮⢿⣿⠟⢠⢑⢑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡔⠠⠂⡰⡭⣈⡣⠦⠪⡚⢡⢑⠕⡱⡡⠹⣿⣿⣽⣯⣻⣗⡿⣮⣯⣯⣿⣿⠏⡰⡙⢿⣿⣯⣟⣷⣯⣻⣳⣿⣽⣿⢋⠡⡢⠡⡪⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠈⠉⠊⢻⠰⡣⡕⡱⡈⠢⠠⡡⢃⠜⡠⢣⡈⠹⠿⣿⣿⣾⣿⣿⣾⡿⠟⠠⢂⠘⠜⡔⡙⠿⡿⣿⢾⡿⡿⢟⠋⣤⡪⡢⢑⠜⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⠈⠀⡯⡸⢄⡑⠡⡊⡐⢷⠮⣦⡥⣌⣢⢃⡬⣈⢃⠙⢌⠑⠐⠌⠠⢁⠐⠄⡨⢈⢊⢔⣤⡵⣴⢵⣯⠟⠡⡉⠪⡐⠡⣺⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠳⡜⡔⡡⠊⢄⠌⡐⢀⠊⠺⠦⣮⡢⠡⡩⡉⢙⠌⢫⠋⢋⠛⡞⠙⠙⢙⠋⡉⢡⣹⡠⢞⠶⠁⡐⢌⠄⡑⢄⢑⡞⠀⠀⠀⠀⠀⠰⡀⠀⡐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢎⠮⡨⢊⠐⠄⢂⠡⠈⠄⢂⠈⠙⢅⠚⠊⠄⠂⠱⠂⠐⠁⠻⠐⠉⠘⡑⠈⢂⢅⠠⠃⡠⢊⢌⠢⡈⡢⢢⣱⠃⠀⠀⠀⠀⠀⡸⠀⠀⡌⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣎⢎⢢⠁⠕⠠⢂⠑⡈⠢⡈⢂⠄⠙⠢⢢⠐⡡⠂⡁⠜⡰⠀⡊⢨⢂⢈⠆⢑⠁⡜⡰⢃⠢⡑⢌⢢⡱⠎⠀⠀⠀⠀⠀⠀⢸⡀⣈⠀⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⣅⢑⠡⡑⠠⡁⠔⢁⢈⠢⡢⡑⠐⠄⡡⠈⢊⠐⡈⠊⠢⢈⠂⡡⠐⡄⢣⡪⢎⢅⠱⡈⣆⢣⡵⠉⠀⠀⠀⠀⠀⠀⠀⡢⢺⡅⠀⠀⠀⠀⢀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣎⢪⢂⠎⡰⢀⠊⠠⠂⠢⢈⠘⡕⣔⡀⠑⠄⡡⢈⠌⢂⠢⢡⢘⣔⢕⢣⢑⠢⡢⢣⢪⢲⠕⠁⠀⠀⠀⠀⠀⠀⠀⡜⡢⡹⣄⠤⣰⢄⣤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢮⢪⡰⢡⢊⢄⢈⠀⡂⠡⠐⢌⠪⡛⡲⢲⠱⡪⡲⡳⡓⡫⢢⠱⡡⣑⢕⢬⡳⡓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⣜⠎⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣒⢕⠤⡣⡨⡂⢕⢡⢑⢅⢕⢩⢊⢕⢩⢊⢔⠱⣘⢢⢣⢕⢎⠶⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⡝⠎⠢⠠⠤⢄⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠹⠜⣦⡹⡢⣣⢱⡢⡱⣡⢪⡢⡣⣕⢕⣝⡴⠳⠕⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠙⠘⠑⠃⠙⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠐⠂⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀