⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢰⠸⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢞⣽⣫⡷⣻⣷⠛⠀⠀⠀⠀⡠⣐⣸⣽⣷⡶⣦⡄⠀⠀⠀⠀⠠⡼⣭⣾⣿⣖⢦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⡾⣱⡿⣤⡟⢻⡇⠀⠀⠀⠀⣾⣑⢿⣿⣿⣷⠹⣟⡄⠀⠀⠀⠀⣾⢹⣯⢿⣞⢷⡝⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣚⢍⣴⠟⣡⢿⠃⡾⣰⡌⣧⠀⠀⢠⢡⠆⡭⣺⣗⡶⣫⠸⣇⢳⠀⠀⠀⠘⡿⠈⢿⡎⣿⡜⣿⡜⠷⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣵⡾⣳⢟⣡⢆⡽⣫⠆⣧⣿⡇⣿⠀⠀⠪⠞⣧⡱⣯⣷⡮⠋⣼⣿⢜⡄⠀⠀⡰⡇⣿⡜⡇⢹⣿⡈⠻⣦⣺⣝⠦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣈⣑⣻⡿⡱⣱⣿⠿⡸⡱⣿⢐⣫⠿⣣⡻⡧⠀⠈⢷⣝⠻⢮⣿⡶⠿⢛⣷⡞⠅⠀⠀⢙⡇⢿⡇⡏⣷⡹⣦⣷⣮⢷⢻⣾⣮⡢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢐⣏⣾⡿⠛⠘⢾⣿⠻⣱⣱⣿⠿⢈⡀⣿⢖⡧⢻⡄⠀⢸⡄⠑⠠⡻⣿⠐⠂⣺⢸⣷⡀⠐⡿⣱⣽⡅⢉⢹⣷⡹⣨⢿⣷⡱⡻⣿⣿⡡⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣬⣿⡇⡌⣾⣿⡇⣐⡇⣿⣾⣿⡯⡆⡷⣵⢿⢨⣧⣈⡇⡋⣷⣰⣿⡐⢹⡛⣻⡜⣻⡦⣸⣧⢼⣟⡄⣤⢘⣿⣗⢳⠋⣿⣷⡁⡀⢻⢿⣹⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠷⣿⣿⢱⣼⣿⣿⡷⢲⠻⣟⣿⣿⡷⢃⠾⠋⠁⠘⢫⣿⣅⠇⡏⢸⡏⢸⡎⠿⣆⢯⢸⢿⡿⢇⣻⡏⠇⢀⣿⣿⣿⢾⣓⢹⡿⣵⢠⢰⣿⣇⡆⠀⠀⠀
⠀⠀⠀⠀⡘⣿⣾⠏⣿⣛⣿⡿⣸⣿⢸⣿⣯⣿⡾⢸⠀⠀⠀⠀⠈⣿⡌⠀⠇⡈⡇⢰⢃⡿⣌⢧⢢⣸⡿⠀⠈⡢⢁⢰⣟⡻⣿⡞⡟⣾⣽⣿⡈⡎⣷⢱⡡⠀⠀⠀
⠀⠀⠀⢰⣹⡿⣟⢷⣬⣭⣷⢾⣫⡏⣾⢻⣿⣿⢾⡏⡀⠀⠀⠀⠀⡁⡁⠞⢂⣸⠇⠠⢖⠱⣏⢸⢀⣧⠟⠀⠀⠈⢸⢈⣷⣪⣟⡇⣿⣿⣿⣽⣿⣸⣷⣿⣝⡄⠀⠀
⠀⠀⢠⢧⣛⣟⢺⢨⡿⢟⢿⣟⣱⣷⡇⣿⡿⣫⣩⡟⢣⠀⠀⠐⡩⡼⢁⡆⢠⠏⠠⢷⡜⢸⡗⢁⠈⠈⠀⠀⠀⠀⠌⠿⣛⠿⠋⣅⢿⡯⣿⣿⣿⡏⣸⢟⣽⡴⠀⠀
⠀⠠⠎⣿⡿⡟⣾⢸⣿⣿⣫⣝⣿⣽⣸⢱⢟⡯⠈⠓⢨⡄⠀⠀⠀⡇⢐⡔⠁⠀⠀⠈⢟⡄⢷⠼⠀⠀⠀⠀⠀⢀⢀⠠⠻⠀⣀⠣⣠⣾⣿⡿⣿⡗⣷⢻⣿⣧⢧⠀
⠀⡘⠀⠀⠁⠀⠙⠼⠸⠛⣭⣿⣿⣿⠄⠉⠙⠀⠀⠀⠡⡆⠀⠀⠀⢣⡁⢴⠀⡀⢄⠀⠈⣢⢨⡂⠂⠙⠀⠀⠀⠀⠈⠡⠱⣦⡀⢆⣭⣺⢧⣾⣯⡆⣿⡟⣿⣿⢿⡦
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠀⠀⠈⠉⠘⠀⠀⠀⠀⠀⠉⡇⠀⠀⡀⠧⠐⠞⢀⠀⠁⠠⠂⠨⠀⢀⠔⠀⠀⠀⠀⠴⠄⠈⢜⢒⢐⠄⠹⢻⡛⠿⠻⠇⠏⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢆⡄⠀⠠⠀⠀⢠⠇⠀⣬⠣⠀⠀⠀⠀⠏⠀⠀⠀⠀⣄⠥⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣿⠡⠀⠀⢠⢀⠂⢀⢀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠃⠆⠀⠀⠀⠢⠀⢀⠈⠀⠓⠗⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠⣀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀