⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠈⠀⠁⠈⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠺⡉⢂⠢⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢍⠌⡂⢌⠐⠄⠍⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠅⠅⠅⡂⡂⡂⠅⠅⡡⢁⢊⠻⡮⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡓⠡⠡⠡⠡⡁⡂⡂⡂⠅⠅⡂⡁⡂⠅⠪⡘⢝⢾⣄⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠢⠨⠨⠨⡈⡂⡂⡂⡂⡂⠅⡡⠂⡂⡂⠅⠅⡊⠔⡡⡩⡛⡷⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡋⡋⡛⡻⣦⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠝⢐⠨⠨⠨⠨⢐⢐⢐⠠⠂⡂⠔⠡⠠⣡⣢⢦⢥⣁⢂⠅⡂⡢⡑⢕⢕⢝⢻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡯⢐⢐⢐⠀⡇⡝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⢁⠌⡐⠨⢐⠁⢅⢂⠢⢐⠨⠐⠄⠅⠅⡱⣗⡿⠀⠻⣽⢶⡐⡐⡐⠌⡢⢃⢇⢇⢇⢏⢻⢶⣄⠀⠀⠀⠀⠀⠀⠐⢿⣔⡐⡄⡕⡜⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⢴⣔⠔⠨⠨⢐⠨⢐⠠⠨⢐⠨⠨⠨⠨⢐⢹⠫⠁⠐⠀⡈⠛⢷⡐⢄⢑⢈⠢⡱⡑⡕⡕⡅⡇⡻⢷⣄⠀⠀⠀⠀⠀⠈⠳⢷⡳⡵⠿⠉
⠀⠀⠀⠀⠀⠀⠀⣰⠏⡼⡏⠪⣟⡇⠅⠅⠢⠨⢐⠨⠨⢐⠨⢐⠁⢥⠂⡚⣾⢦⣈⠀⠠⢐⣴⡎⡐⡐⡐⢅⠢⡃⡇⡇⡇⡇⡇⡍⢿⣦⠀⠀⠀⠀⠄⡂⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡼⠡⡰⠏⠀⢄⢭⢊⠨⠨⠨⣨⡾⡯⣎⣄⣊⣐⣨⢼⢃⢂⠙⣯⣟⣦⠀⣯⡷⡃⡢⠢⡨⡐⢌⠜⢌⢎⢎⢎⢎⢎⠆⣟⣧⠠⠈⠂⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡞⠈⠄⣷⠄⣡⡿⠃⢦⣨⡨⣮⢗⣯⢿⢽⡺⣳⡭⢉⢂⢂⠢⠨⢀⠍⢚⢃⢋⠢⢊⠔⡡⢂⡊⡢⠡⡃⡇⡇⡇⡇⡇⡇⢎⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡾⠈⠄⠅⢻⢕⢏⠃⠅⠅⡉⠅⣿⢽⢺⢹⢸⡸⡸⣽⡐⡐⡐⠨⠨⢐⠨⢐⠐⡐⠨⢐⢐⠨⢐⠐⠌⡌⡪⡪⡪⡪⡪⡪⡪⢪⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⠏⠨⡨⢘⠄⠕⡠⠡⠡⢁⢂⢑⡯⡣⡳⡱⡣⡣⡳⣽⢂⠐⠄⠅⠅⠢⠨⢐⠨⠠⢑⢐⢐⠨⠠⠡⡑⢌⠆⡇⡇⡇⣇⢇⢇⢇⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠨⢊⠔⠡⢊⠐⠄⠅⠅⡂⠢⢘⢽⣪⣺⡸⣪⣺⢞⢃⠂⠅⠅⠅⠅⠅⠅⠢⠨⠨⢐⢐⢐⠨⠨⢊⠌⡢⢣⢣⢣⡣⡣⣣⢣⠱⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢷⠨⢐⠨⠨⠠⠡⠡⠡⠡⠨⠨⢐⠨⠨⠉⠍⠍⡂⡂⡂⠅⠅⠅⡊⠌⡨⠨⠨⠨⠨⢐⠐⠄⢅⠕⡡⠪⡸⡸⡸⡱⡱⡹⡸⡨⣪⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⡌⡐⠨⡈⠌⠌⠌⠌⡨⠨⠨⢐⠨⢐⠁⠅⠅⡂⢂⠂⠅⠅⡡⢂⢁⠂⠅⠅⢅⠑⠄⠕⡡⢑⢔⢸⢸⢸⢪⢣⢫⡪⡺⡸⣘⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣷⢨⢂⠂⠅⠅⡊⡐⠄⠅⡊⠄⢌⢐⠨⠨⢐⠨⢐⠨⢈⢂⢂⢂⠂⠅⢅⠑⠄⢅⠣⡑⢌⢢⢪⢪⡪⣣⢳⡱⡣⡣⡣⣱⣯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣧⢢⢅⠅⠅⡂⡂⠅⠅⡂⠅⡂⠢⠨⠨⢐⠨⢐⠨⢐⢐⠐⠄⢅⢑⢐⠡⡑⡡⢪⢰⡱⡕⣇⢗⢝⡜⡼⡸⡪⣱⣽⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣧⡣⡣⡣⣂⡂⢅⠊⠄⠅⡂⠅⠅⠅⠢⠨⢐⠈⢄⠢⠨⠨⡐⡐⡔⡱⡸⣸⢱⡣⡳⣹⢸⢪⡣⡫⡪⣪⡾⡟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⣮⣎⢖⢕⢵⢱⢕⢕⡔⡥⢥⢥⢱⢡⡢⡱⣰⢸⡸⡜⣜⢜⢮⢪⡳⡱⣣⢳⡹⡜⡎⣇⣧⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢮⣗⣵⢹⡪⡺⡸⣕⢕⢧⢳⡱⡝⣜⢎⢮⢺⡸⣱⢣⡳⡕⣝⢜⣼⣼⣺⠾⠫⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠽⣾⣮⣧⢷⣵⢵⣝⣜⣮⢧⣷⢽⣮⣾⠾⠾⠛⠋⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀