⠀⠀⠀⠀⠀⠠⠠⠠⠠⠠⠀⠀⠀⠀⠀⡐⠄⢂⠄⠄⠀⠀⠀⠀⢂⢂⢂⢂⢢⢂⢂⢂⢂⠀⠀⠀⠀⠐⡐⠄⢆⢂⠄⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀
⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠄⢢⠠⢂⠂⠀⠀⠀⠀⠀⠀⠀⢆⠢⢂⢂⠐⠔⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⢂⢂⠀⠀⠀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡐⠔⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⢆⠆⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢂⢂⢂⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣂⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⡀⠀⠀⠀⠆⠢⢂⢂⠀⠀⠀
⠀⠀⠀⠀⠀⠄⡐⡐⠀⠀⠀⠠⠀⠀⠀⡐⠔⠰⠠⠠⠀⠀⡀⡄⠔⠜⠔⠑⠥⡂⢣⢣⢣⢣⢢⢢⠤⡄⡀⠀⠀⡀⢀⢂⠀⠀⡀⠀⠀⠢⢂⢂⠀
⠀⠀⠀⠠⡐⠄⠂⠀⠀⠀⡐⠀⠀⠀⠄⠢⠠⢢⠚⠀⠀⠀⠀⠀⠀⠀⢀⢣⢣⢣⢣⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⡄⠄⢂⠀⠀⢂⠀⠀⠀⢂⢂
⠀⠀⡐⠄⡐⠀⠀⠀⠰⠠⠀⠠⢂⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⡑⡵⢁⠜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢂⠀⠀⢂⠀⠀⠀⠀
⢀⠄⠄⡐⠀⠀⠀⠐⡅⠂⠐⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢫⣚⢔⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⠀⠠⠠⢂⠀⠀
⠀⢂⠀⠀⠀⠀⠀⠢⡃⠀⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠣⣩⢭⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢂⢂⠀⠀
⠀⠠⡐⠀⠀⠀⠠⢢⡁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢈⢏⠐⡜⡭⢚⡝⡥⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⡰⠀⠢⠢⠂⠀
⠀⠠⠂⠀⠀⠀⡌⠎⡂⠀⡂⠄⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⡹⣹⣹⡜⡝⣟⡽⡹⡥⡀⠀⠢⣀⢀⠀⠀⠀⠀⠀⠀⢁⠐⡘⠄⠀⢆⠅⠀
⠀⠀⠄⠀⠀⠀⡜⡜⠄⠰⡰⡰⡤⡀⠀⠀⠀⠀⢤⣚⠴⢃⠄⢠⣚⢽⡹⣻⡅⠄⠌⣿⣹⡝⣝⢆⢂⢣⡄⠀⠀⠀⠀⠤⡜⡜⡜⡜⡄⠀⢌⢆⠀
⠀⠀⠀⠀⠀⡌⢎⢎⠀⡜⡵⣘⡜⡕⡭⣫⡹⡹⡹⠡⢠⢏⢯⢫⠩⡂⣰⡿⠀⡐⡜⣝⢆⠣⡙⡽⣝⡽⢦⠘⡙⡝⡖⢩⢎⢎⢎⢎⠆⠀⠠⡱⡀
⠀⠀⠀⠀⠀⢣⢣⢣⠃⢘⡜⡭⡭⣚⢭⢫⢉⢦⢫⣫⢏⢯⡳⡙⢡⡞⣿⢀⢸⢯⡃⠠⣏⢖⢬⢢⢢⢉⢯⢫⣫⢎⢣⢣⠘⡄⠡⠣⡃⠀⠄⡱⠡
⠀⠠⠀⠀⢌⢎⢎⠆⡅⠠⡡⡠⠀⡜⣍⡝⡝⣝⣝⢟⢽⣹⡽⡽⡽⡽⣞⡽⢧⣋⢯⡳⡽⡽⡽⡽⡽⣹⡝⣝⡜⠽⡹⡹⡱⠈⡎⡆⠄⢀⢌⢎⢌
⢀⠀⠄⠠⢪⢎⢃⢧⠀⢀⢆⢃⠍⢊⠜⠡⣰⡝⡽⡽⡽⡽⡽⡽⡽⡽⡝⣝⡽⣯⡻⡽⡽⡹⡽⡽⣹⣝⠽⣹⡹⣘⢖⡉⡇⡅⠀⡀⢆⠠⡃⢣⢡
⡐⢀⠄⠎⡎⠂⡜⢧⠀⡝⠠⣍⢂⡖⠝⢌⢞⡽⣹⢽⢽⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡝⡝⡝⡭⣂⠀⠀⠀⠆⢣⠡⢨⣊⢌
⠀⠄⢢⠃⠄⣎⢧⡹⡄⠭⠐⡅⠀⠀⢰⡹⡹⡹⠉⠀⠀⠀⠀⠀⡀⢠⣧⠀⣠⡄⢀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡜⡜⢌
⢀⠄⡁⠀⡜⣎⠧⣋⢏⠀⠀⢘⠀⠀⠀⠀⠀⠀⢠⡀⢾⡇⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢀⡷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡱⡡⡡
⡐⡐⠠⢣⢣⢣⢣⢣⢣⡃⠀⠀⡃⠀⠀⠀⠠⠨⢸⣷⣿⠃⣿⢙⡟⣉⢿⣍⠿⢧⡹⣏⡘⣿⡟⢿⣿⣹⡟⣽⠡⡂⠀⠀⠀⠀⠀⠄⠀⡱⡐⠥⡌
⢂⠰⡱⡱⡱⡱⡹⡜⡭⡃⠀⠀⢥⡂⠀⢀⢠⢎⢖⢭⣚⡕⡝⡞⡝⡭⡺⡹⡜⡝⡭⣚⡝⡵⡱⣍⢎⢳⢩⣊⠦⢦⢣⠁⠀⠀⠀⠀⠀⡱⢨⢊⠜
⢐⠱⡱⡱⡱⣣⠇⡭⡭⡃⠀⠀⠈⠀⠀⡄⠘⡝⡝⡝⡝⡝⡝⡝⡜⡝⣝⡝⡭⣫⢫⢭⢫⢳⢭⣚⢭⣚⢭⣚⠵⣍⠀⠰⠀⠀⠀⠀⠀⠥⢨⢂⠜
⡱⡱⡱⡱⡱⡹⡸⡭⡭⠀⠀⠀⠀⠀⢢⢸⡆⢧⢫⢫⢫⢫⢫⢫⢸⡹⡹⡭⣚⡝⡭⣫⢫⢭⢭⢚⠵⡭⣚⢭⣚⠀⠀⡇⠂⠀⠀⠀⠄⠂⡱⡡⡡
⡱⡱⡱⡱⡱⡍⢧⡹⠠⡀⠀⠀⠀⠀⠀⠆⣏⣆⢏⢏⢏⢏⢏⢏⢎⢏⢏⢏⡌⣏⢏⢏⡝⡭⡣⣣⢣⢭⡚⡰⡱⡁⡜⠠⠀⠀⠀⢀⢂⠰⡡⡡⡌
⠥⢣⢣⢣⢣⢣⢭⢂⢂⠄⠀⠠⡀⠀⠀⠀⠌⡳⡣⡨⣫⢫⡹⡹⣣⢹⢭⡹⡭⣚⡝⡭⣫⡹⡜⡵⢭⢎⢧⢭⢢⡘⠀⡁⠀⠀⠀⠄⠄⢘⢌⢌⢆
⡱⡱⡱⡱⡱⡱⡱⡐⠄⠂⠀⠄⢧⠀⠀⠀⠀⠂⣏⢎⢂⡝⡭⣫⡹⡭⣫⡹⡭⣫⢫⢫⢫⡹⡭⣎⢧⢭⢎⢃⠇⠁⠀⠀⠀⠀⠠⢂⠄⠐⠥⢣⢡
⡱⡱⡱⡱⡡⣣⢃⠄⠆⠂⡀⠄⣏⠆⠀⠀⠀⠀⠀⣏⡝⡜⡭⣫⢫⢫⡹⡹⡹⡹⡹⡭⣫⢭⢣⢭⢭⢭⢎⢧⠂⠀⠀⠀⠀⠀⠄⣃⠄⠀⡌⢎⢌
⢣⢣⢣⢣⠱⡱⡁⡜⡐⠄⡸⠠⣫⢭⠀⠀⠀⠀⠀⠀⢹⡹⡹⡹⡹⡭⣫⢫⢫⢫⡹⡭⣫⢭⢭⢭⡹⡱⡡⠀⠀⠀⡰⡱⠀⠀⢀⢣⠂⠄⢣⠱⡡
⢣⢣⢣⢣⢣⢃⢌⢂⢂⠄⡳⢀⢏⡝⡜⠀⠀⠀⠀⠀⠀⠈⢏⡝⡝⡝⡝⡝⡝⡝⡝⡝⡝⡭⣫⡹⠁⠀⠀⠀⢠⡹⡱⡡⠀⠀⢐⡕⠥⠀⢈⢎⢎
⢣⢣⢣⢣⢣⢣⡃⠐⠄⢘⡜⡄⡹⡭⣎⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠫⢋⢋⠍⠉⠈⠀⠀⠀⠀⠀⠠⡘⡜⡝⡵⡱⡀⠀⡜⡜⡜⠄⠀⡣⣊
⢣⢣⢣⠱⡱⢭⠂⢂⠀⡌⣏⠇⡹⡹⡭⣫⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢥⢊⢞⡝⡜⡜⡅⠀⡭⡭⣎⢎⠀⢘⢜
⢣⢣⢭⢪⢎⢎⠠⠀⢀⢭⣚⢭⢸⢣⡳⡹⡱⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡹⣣⢫⢫⢫⢫⠆⠰⡭⣫⢭⢎⢆⠀⠀
⣣⢣⢣⡍⢎⠆⢢⠀⣘⢭⢭⡹⡀⢏⢧⢫⢭⢎⡝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡝⡞⡝⣝⡝⡝⠄⢭⢫⢫⢭⢭⢭⢂⠠
⠣⡸⡜⠄⠌⠰⠀⠄⡭⣚⢭⢫⢂⠸⣣⢫⢫⢫⢪⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⢏⢏⢏⢏⢏⢏⠠⡹⡭⣫⢭⢭⢭⢎⠀
⢣⠭⢂⠐⠄⠀⡐⡜⡭⡭⡭⣣⢂⠂⡏⡞⡭⡭⣣⢩⢫⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⢏⢏⢏⢏⢏⢏⢏⢸⢭⢣⢫⢭⢫⣚⢭⢣
⡃⠄⡐⠄⠀⠄⡰⡹⣜⢧⢫⢣⢣⠠⠨⡎⡭⡭⡭⡭⢪⢭⢣⢣⢆⢄⠀⠀⠀⢀⠀⣀⡄⠄⢢⢫⢫⢫⢫⡹⡭⣫⢣⢣⡹⢭⢭⢭⢭⢭⢭⢭⢣